WO2019106878A1 - Information processing system, information processing method, and computer program - Google Patents

Abstract

A system of the present disclosure calculates an eigenvector of a special Hermitian adjacency matrix in each of one or more virtual file networks which correspond to one or more file networks. The special Hermitian adjacency matrix is a modification of a Hermitian adjacency matrix of N rows by N columns based on a connection relationship between D[m](1≤m≤N) files that form a corresponding virtual file network. The calculated eigenvector corresponds to an eigenvalue of the maximum absolute value. The eigenvector has components which respectively correspond to the D[m](1≤m≤N) files. The system calculates, on the basis of a component that corresponds to a starting point file, respective scores of the D[m](1≤m≤N) files on the basis of a positional relationship between the D[m](1≤m≤N) files on a complex plane, when each component of the eigenvector is arranged on the complex plane.

Description

INFORMATION PROCESSING SYSTEM, INFORMATION PROCESSING METHOD, AND COMPUTER PROGRAM Cross-reference to related applications

This international application claims the priority based on Japanese Patent Application No. 2017-227936 filed with the Japanese Patent Office on November 28, 2017, and the Japanese Patent Application No. 2017-227936 The entire contents are incorporated into this international application by reference.

The present disclosure relates to an information processing system, an information processing method, and a computer program.

Techniques for scoring / ranking web pages are already known (see Patent Document 1). In a simple example of this technique, page rank is determined as high as web pages linked from many web pages. The page rank calculation includes an adjacency matrix in which the connection relationship between web pages is binary-represented by the values 0 and 1, and values 0, 1 and other real numbers obtained by changing each component of the adjacency matrix. A matrix is used.

JP, 2017-102712, A

In the conventional method of determining page rank based on the above-described adjacency matrix, it is necessary to estimate virtual connection relationships from all web pages to all web pages in addition to actual connection relationships between web pages. Because of this, it is difficult to make a good ranking of web pages.

Thus, according to one aspect of the present disclosure, it is desirable to be able to provide a technique capable of scoring / ranking multiple documents more appropriately than in the past based on a novel adjacency matrix.

According to one aspect of the present disclosure, an information processing system for scoring a plurality of documents is provided. The information processing system includes an identification unit, a determination unit, a setting unit, a definition unit, an eigenvector calculation unit, and a score calculation unit.

The specifying unit specifies one or more document networks including at least a weakly connected document group based on data representing a connection relationship between a plurality of documents. The determination unit determines, for each of the one or more document networks, start point documents that are documents located at the start point of the corresponding document network.

The setting unit connects dummy documents for each of one or more document networks by connecting virtual dummy documents of in-degree 1 and out-degree 0 to documents of out degree 0 in the corresponding document network. Set up a virtual document network to include.

The definition unit defines a special Hermite adjacency matrix for each of the one or more virtual document networks corresponding to the one or more document networks. The special Hermite adjacency matrix is a modification of the N-by-N Hermitian adjacency matrix based on the connection between documents D [m] (1 ≦ m ≦ N) constituting the corresponding virtual document network. Here, m is an integer.

The Hermitian adjacency matrix is a Hermitian matrix with zero diagonal components. In the Hermitian adjacency matrix, the component h (p, q) at the p-th row and the q-th column has a link from the document D [p] to the document D [q] and the document D [q] to the document D [p] Indicates a value of 1 when there is a link to and when there is neither a link from document D [p] to document D [q] nor a link from document D [q] to document D [p] A value + i (i is an imaginary unit) when 0 indicates that there is a link from document D [p] to document D [q] but no link from document D [q] to document D [p] When the link from the document D [p] to the document D [q] does not exist but the link from the document D [q] to the document D [p] exists, the value −i is indicated.

The eigenvector calculation unit calculates an eigenvector corresponding to the largest absolute value eigenvalue of the special Hermite adjacency matrix. The eigenvectors have components corresponding to each of the documents D [m] (1 ≦ m ≦ N). According to an aspect of the present disclosure, the eigenvector calculation unit can calculate an eigenvector corresponding to a positive eigenvalue, when a positive eigenvalue and a negative eigenvalue are present as the maximum absolute value eigenvalues.

For each of the one or more virtual document networks, the score calculation unit determines the document D [m] (1 ≦ m ≦) when each component of the eigenvectors is arranged on the complex plane based on the component corresponding to the start document. N) Based on the positional relationship on the complex plane between them, the score of each of the documents D [m] (1 ≦ m ≦ N) is calculated.

According to this information processing system, a plurality of documents are scored using a special Hermite adjacency matrix corresponding to a Hermitian adjacency matrix capable of expressing the connection relation between documents with four values of 1, 0, + i and -i. For this reason, it is not necessary to presume virtual connection relationships from all documents to all documents, and scoring / ranking of each document based on the connection relationship between documents can be realized more appropriately than in the past.

In one aspect of the present disclosure, the definition unit is configured such that when each component of the eigenvector is placed on the complex plane, all components fall within an angular range of π / 2 radians (that is, 90 degrees) in the complex plane. The Hermitian adjacency matrix may be modified to be configured to define a special Hermitian adjacency matrix.

In this information processing system, the hermite is arranged so that the components of the eigenvector corresponding to each document do not go through more than one rotation on the complex plane, in particular, the components fit within the area corresponding to one quadrant on the complex plane. Since the adjacency matrix is deformed to calculate the score, distance information on the rotational direction on the complex plane can be used to appropriately score each document.

In one aspect of the present disclosure, the special Hermitian adjacency matrix substitutes the component indicating the value + i in the Hermitian adjacency matrix with the value C1 (C2 + i) based on the first correction amount C1 and the second correction amount C2, The component indicating i is replaced by the value C1 (C2-i), and the value C1 (C2 + i) of the component of each row in the Hermite adjacency matrix after the replacement is represented by the value C1 (C2 + i) and the value 1 in the same row. Change to a value {C1 (C2 + i) / W} divided by a number W, and further change the value {C1 (C2 + i) / W} to a value that is symmetrical about the diagonal component with the component It may correspond to a Hermitian matrix defined by changing the value C1 (C2-i) to the complex conjugate {C1 (C2-i) / W} of the value {C1 (C2 + i) / W}. The first correction amount C1 and the second correction amount C2 can be determined as follows using the parameter n.

The parameter n is an angle of π / 2 radians in the complex plane based on the number of documents max {N} in the virtual document network where the number of documents N is the largest among the one or more virtual document networks It may be determined to fall within the range.

The first correction amount C1 and the second correction amount C2 are special Hermite adjacency matrices such that all components fall within an angular range of π / 2 radian in the complex plane while maintaining the relationship of each component of the eigenvector Help to define

In one aspect of the present disclosure, the special Hermitian adjacency matrix replaces the component indicating the value + i with the value C1 (C2 + i) in the Hermitian adjacency matrix and replaces the component indicating the value -i with the value C1 (C2-i). The value C1 (C2 + i) of the component of each row in the Hermite adjacency matrix after the replacement is changed to the value {C1 (C2 + i) / W} divided by the number C of the components showing the value C1 (C2 + i) and the value 1 in the same row Further, the value C1 (C2-i) of the component which is in a symmetrical positional relationship across the diagonal component with the component changed to the value {C1 (C2 + i) / W} is set to the value {C1 (C2 + i) / Change the complex conjugate of W} to {C1 (C2-i) / W} and change the component value {C1 (C2-i) / W} of each row in the modified Hermite adjacency matrix H in the same row before the change C1 (C2-i) and the component showing the value 1 Change to the value {C1 (C2-i) Z / W} multiplied by the number Z, and further symmetrical about the diagonal component with the component changed to the value {C1 (C2-i) Z / W} Hermitian defined by changing the component value {C1 (C2 + i) / W} in positional relationship to the complex conjugate {C1 (C2 + i) Z / W} of value {C1 (C2-i) Z / W} It may correspond to a matrix.

In one aspect of the present disclosure, the special Hermitian adjacency matrix substitutes the component indicating the value + i in the Hermitian adjacency matrix with the value C + i based on the correction amount C, and indicates the value C + i of each row in the Hermitian adjacency matrix after the substitution. Is changed to the value {(C + i) / R} divided by the number R of components indicating the value C + i in the same row, and the value of the component indicating the value −i is further symmetrical with respect to the diagonal components. It may correspond to a Hermitian matrix defined by changing to complex conjugates {(Ci) / R} of components in a certain positional relationship. The correction amount C may be determined as follows using the parameter n.

The correction amount C serves to define a special Hermitian adjacency matrix such that all components of the eigenvectors fall within an angular range of π / 2 radians in the complex plane.

In one aspect of the present disclosure, the score calculation unit determines, for each of one or more virtual document networks, the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector and the component corresponding to the start document is complex. Rotation conversion may be performed so as to be disposed at a specific position in the plane. The score calculation unit may calculate each score of the document D [m] (1 ≦ m ≦ N) based on the value Vc [m] after rotational conversion of the corresponding document D [m].

By calculating the score in this way, it is possible to place the source documents of each of the plurality of document networks at the same position on the complex plane, and the documents belonging to each of the plurality of document networks are appropriately determined by the same evaluation criteria. It can be scored.

In one aspect of the present disclosure, the score calculation unit is configured to arrange the component corresponding to the start document as a specific position at a predetermined angle that is not zero from a specific axis located at a boundary of one quadrant in the complex plane. Then, the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector may be subjected to rotational conversion.

In one aspect of the present disclosure, the score calculation unit determines, as each score of the document D [m] (1 ≦ m ≦ N), based on the value Vc [m] after rotational conversion of the corresponding document D [m]. A value corresponding to the product (θ [m] · L [m]) of the angle θ [m] of the value Vc [m] from the specific axis in the complex plane and the absolute value L [m] of the value Vc [m] It may be calculated.

In one aspect of the present disclosure, the score calculation unit determines, for each of the one or more virtual document networks, the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector and the value of the component corresponding to the start document By dividing by a specific value E based on V [s], the component corresponding to the start document may be arranged on a specific axis of the complex plane. The score calculation unit then rotates the value V [m] / E (1 ≦ m ≦ N) of each component of the eigenvector so that the component corresponding to the start document is rotated from the specific axis to the position of a predetermined angle that is not zero. Rotation conversion may be performed.

In one aspect of the present disclosure, the score calculation unit divides the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector by the specific value E, and in the complex plane, the rotation conversion is based on rotation conversion rather than the specific axis. When there is a component located upstream in the rotational direction, the value V [m] / of each component of the eigenvector is set to rotate the component located most upstream from the specific axis to a position at a predetermined angle other than zero. E (1 ≦ m ≦ N) may be subjected to rotational conversion.

In one aspect of the present disclosure, each score of the document D [m] (1 ≦ m ≦ N) is set such that the minimum value of all the scores of the document D [m] (1 ≦ m ≦ N) is zero. It may be calculated as a value obtained by subtracting the product (θ [m] · L [m]).

In one aspect of the present disclosure, the score calculation unit determines, for each of the one or more virtual document networks, the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector and the value of the component corresponding to the start document By dividing by the specific value E based on V [s], the component corresponding to the start document is placed on the specific axis of the complex plane, and the score of each of the document D [m] (1 ≦ m ≦ N) is obtained. The product of the angle θ [m] of the value V [m] / E of the component of the corresponding document D [m] from the specific axis and the absolute value L [m] of the value V [m] / E (θ [m ] · A value corresponding to L [m]) may be calculated.

In one aspect of the present disclosure, the particular axis may be a real axis in the complex plane. The score calculation unit divides, as the specific value E, the value V [m] of each component of the eigenvector by the value V [s] of the component corresponding to the start document to obtain the component corresponding to the start document an actual complex plane. It can be arranged on the axis.

In one aspect of the present disclosure, the determination unit may determine a document located at the start point of the longest path in the corresponding document network as a start document.
In one aspect of the present disclosure, when the plurality of paths correspond to the longest path in the corresponding document network, the determination unit determines the document with the highest out-degree among the documents located at the start points of the plurality of paths. The document with the lowest degree may be determined as the start document.

In one aspect of the present disclosure, in the case where the plurality of routes correspond to the longest route in the corresponding document network, the determination unit is a virtual in-degree zero connected to the document located at the start point of the plurality of routes. The dummy document may be placed, and the placed virtual dummy document may be determined as the start point document. In one aspect of the present disclosure, the determination unit determines that the plurality of paths correspond to the longest path in the corresponding document network, and further, the document or output document with the highest outdegree in the plurality of documents located at the start points of the plurality of paths. When there are a plurality of documents with the lowest degree, a virtual dummy document with an in-degree of zero connected to a plurality of documents with the highest out degree or the lowest out degree located at the start points of the plurality of paths The arranged and arranged virtual dummy documents may be determined as the start document.

In one aspect of the present disclosure, the arrangement determination unit may be configured to determine the arrangement of documents in the list of documents corresponding to the search query based on the scores of the plurality of documents calculated by the score calculation unit. In one aspect of the present disclosure, the sequencing unit may generate a list of documents corresponding to a search query such that documents with higher scores are placed higher in the list.

According to this information processing system, it is possible to generate a list in which a plurality of documents corresponding to the search query are arranged in the order according to the importance, and it is possible to output an appropriate search result.
In an aspect of the present disclosure, an information processing method may be provided that includes a procedure performed by the above-described information processing system. That is, according to one aspect of the present disclosure, an information processing method for scoring a plurality of documents may be provided.

An information processing method according to an aspect of the present disclosure includes identifying one or more document networks including at least a weakly linked document group based on data representing a connection relationship between a plurality of documents. For each of one or more document networks, determining a start document which is a document located at the start of the corresponding document network, and in the corresponding document network, an in-degree 1 and an out-degree in a document with an out degree of zero Setting up a virtual document network including dummy documents for each of one or more document networks by connecting 0 virtual dummy documents, and one or more virtual documents corresponding to one or more document networks Defining a special Hermitian adjacency matrix for each of the document networks, and Calculating an eigenvector having a component corresponding to each of the documents D [m] (1 ≦ m ≦ N), which is an eigenvector corresponding to a pairwise maximum eigenvalue, and for each of one or more virtual document networks , Document D based on the positional relationship on the complex plane between documents D [m] (1 ≦ m ≦ N) when the components of the eigenvector are arranged on the complex plane based on the component corresponding to the start document Calculating each score of [m] (1 ≦ m ≦ N).

The special Hermite adjacency matrix is defined by transforming the Hermitian adjacency matrix so that when each component of the eigenvector is placed on the complex plane, all the components fall within the angular range of π / 2 radian in the complex plane. May be

According to an aspect of the present disclosure, a computer program for causing a computer to execute the above-described information processing method may be provided. According to an aspect of the present disclosure, a non-transitional tangible storage medium storing the computer program may be provided. According to one aspect of the present disclosure, an information processing system may be provided that includes a processor and a memory that stores a computer program for causing the processor to perform processing for scoring a plurality of documents.

It is a block diagram showing composition of an information processing system. It is a functional block diagram regarding an information processing system. It is a functional block diagram showing the detail of a query response part. It is a flowchart showing the process which a 2nd scoring part performs. FIG. 5A is a diagram showing an example of a linked document network, and FIG. 5B is a diagram showing a corresponding virtual document network. FIG. 6A is a diagram showing an example of a linked document network, and FIG. 6B is a diagram showing a corresponding virtual document network. FIG. 7A shows an example of a linked document network, and FIG. 7B shows a corresponding virtual document network. FIG. 8A shows an example of a linked document network, and FIG. 8B shows a corresponding virtual document network. FIG. 9A shows an example of a linked document network, and FIG. 9B shows a corresponding virtual document network. FIG. 10A is a diagram showing an example of a linked document network, and FIG. 10B is a diagram showing a corresponding virtual document network. FIG. 1 illustrates an example of a consolidated document network. It is a flowchart showing the process which a 2nd scoring part performs in order to set a starting point page. It is a figure explaining the generation method of a special Hermite adjacency matrix. It is a flowchart showing the process which a 2nd scoring part performs for rotation conversion. FIG. 15A is an explanatory diagram of the arrangement of a plurality of components on a complex plane, and FIG. 15B is a diagram illustrating a method of calculating a score. It is a figure which shows the modification of a special Hermite adjacency matrix. In another modification, it is a flow chart showing processing which a 2nd scoring part performs. It is a figure which shows another modification of a special Hermite adjacency matrix. It is a figure explaining the calculation method of the score in another modification.

DESCRIPTION OF SYMBOLS 1 ... Information processing system, 5 ... User terminal, 10 ... Arithmetic unit, 11 ... Processor, 15 ... Memory, 20 ... Storage part, 30 ... Communication part, 110 ... Crawler, 120 ... Indexer, 130 ... Query processing part, 140 ... Query response unit, 141: first scoring unit, 143: second scoring unit, 145: ranking unit, 147: output unit, 210: page repository, 220: index storage unit, SP: start point page, EP: end point Page, DP ... dummy page.

Exemplary embodiments of the present disclosure are described below with reference to the drawings.
The information processing system 1 of the present embodiment shown in FIG. 1 is configured to provide the user terminal 5 with a list of documents corresponding to the search query in response to the search query input from the user terminal 5. The document is a web document, specifically a web page. That is, the information processing system 1 functions as a search engine available to the user terminal 5 through the communication network. The communication network is, for example, the Internet.

The information processing system 1 includes an arithmetic unit 10, a storage unit 20, and a communication unit 30. The arithmetic unit 10 includes a processor 11 and a memory 15. The storage unit 20 stores computer programs and data executed by the processor. The storage unit 20 can include one of a hard disk drive and a solid state drive.

The communication unit 30 is configured to be able to communicate with the user terminal 5. Arithmetic unit 10 implements a search function, that is, a function as a search engine by executing processing in accordance with the computer program stored in storage unit 20. Specifically, the processing for realizing the search function is executed by the processor 11. Specifically, the information processing system 1 schematically shown in FIG. 1 can be configured by one or more group of cooperating server devices.

In the search function, the operation unit 10 functions as the crawler 110, the indexer 120, the query processing unit 130, and the query response unit 140 shown in FIG. 2, and the storage unit 20 functions as the page repository 210 and the index storage unit 220. It is realized by doing.

The crawler 110 is configured to collect web pages that reside in a communication network, similar to known crawlers. The web pages collected by the crawler 110 are stored in the page repository 210.

The indexer 120 is configured to analyze and index web pages stored in the page repository 210. Through indexing, information valuable for search is extracted from the web page, and index data corresponding to the web page is generated.

Index data includes information valuable to searches extracted from web pages. Specifically, index data includes content index, structure index, and special purpose index. The content index includes information on web page keywords, titles, and key sentences. The structure index includes information representing the hyperlink structure of the web page. Special purpose indexes hold information useful for special query processing such as image indexes and pdf indexes. The index data for each web page generated by the indexer 120 is stored in the index storage unit 220. A group of index data represents a connection between web pages.

The query processing unit 130 receives a search query from the user, and extracts a related page group which is a set of web pages corresponding to the search query from among all the web pages. All web pages here are found in the communication network by the crawler 110, and correspond to web pages in which index data is registered in the index storage unit 220.

Specifically, based on the content index of each web page stored in the index storage unit 220, the query processing unit 130 sets a set of web pages including a vocabulary corresponding to the search query as a related page group from among all the web pages. Extract. Then, the information on the related page group is provided to the query response unit 140.

The query response unit 140 transmits a search result list in which related page groups are arranged in page rank order, to the user terminal 5 as response data to the search query, based on the information on the related page group provided from the query processing unit 130. Each of the related pages is ranked higher on the web page with higher relevance and importance to the search query, and is placed at the top of the search result list. The search result list is configured as a web page with links to the listed related pages, as well as response data from conventional search engines. The links referred to here are so-called hyperlinks.

More specifically, as shown in FIG. 3, the query response unit 140 includes a first scoring unit 141, a second scoring unit 143, a ranking unit 145, and an output unit 147.
The first scoring unit 141 scores each of the related pages for the related page group corresponding to the search query based on the degree of association of the page content with the search query, and sets each of the related pages as a first score. Configured to give content points.

The second scoring unit 143 operates independently of the search query, and is configured to give each of the web pages collected by the crawler 110 an important score based on the connection relationship between web pages as a second score. Be done.

The second score is calculated so as to indicate a larger value as the web page estimated to be more important from the connection relationship between web pages, and is assigned to each web page. Specifically, a web page with many links, a web page linked from a web page with a high importance score, and a web page with a link from a web page with few links to other web pages have a larger value. It is calculated to indicate and given to each web page.

The ranking unit 145 is based on the first score calculated for each of the related pages by the first scoring unit 141 and the second score calculated for each of the related pages by the second scoring unit 143, It is configured to calculate each page rank of the related page.

According to a simple example, each page rank of the relevant page corresponds to a weighted sum of the first score and the second score. For example, using the first score X1, the second score X2, and the weighting coefficient α taking a value between 0 and 1, the page rank Y of each related page is expressed by the equation Y = α · X1 + (1−α) It can be calculated according to X2. The page rank of each related page may be understood as an overall score including the content score based on the search query and the important score based on the connection relationship between web pages.

The output unit 147 arranges the page list in which related pages corresponding to the search query are arranged in order from the related page having the highest page rank based on the page rank of each related page calculated by the ranking unit 145. , And transmits it as a search result list to the user terminal 5 of the search query transmission source.

Subsequently, the details of the process of calculating the second score, which is characteristic of the present embodiment, as well as the details of the process performed by the second scoring unit 143 will be described below.
Conventionally, scoring of web pages based on the connection relationship between web pages is performed using an adjacency matrix in which each component is represented by a binary value (1, 0) (real number). On the other hand, in the present embodiment, web page scoring is performed using a Hermite adjacency matrix H represented by four values (complex numbers) of values 1, 0, + i, -i. Here, i represents an imaginary unit.

A Hermite adjacency matrix H is generated for each web page group in a weakly connected relationship. As well known, when a network consisting of nodes in a weak connection relationship ignores the connection direction of the link between the nodes, it links from any one node of the nodes belonging to the network to the remaining nodes. Correspond to reachable networks. Similarly, a document network consisting of web pages in a weak link relationship may at least be indirectly linked to the remaining web pages when any one of the web pages belonging to the document network ignores the link connection direction. It consists of a group of web pages that have various connection relationships.

The second scoring unit 143 periodically executes the flow chart shown in FIG. 4 so that, based on the latest index data stored in the index storage unit 220, the corresponding web page group for each web page group in a weakly connected relationship. Calculate a second score for each web page that belongs to the page group.

When the process shown in FIG. 4 is started, the second scoring unit 143 extracts one or more connected document networks from all the web pages (S110). Specifically, by referring to the index data stored in the index storage unit 220, each web page group having a weakly connected relationship is extracted as one connected document network among all web pages (S110). . One linked document network is composed of web pages having weak link relationships.

5A, 6A, 7A, 8A, 9A, 10A, and 11 show examples of linked document networks. One circle in FIGS. 5A, 6A, 7A, 8A, 9A, 10A, and 11 corresponds to one node, in other words, one web page.

The arrow in the figure indicates that a link (hyperlink) to the web page corresponding to the end point of the arrow is formed on the web page corresponding to the start point of the arrow. That is, it means that the web page corresponding to the start point of the arrow can be moved via the link to the web page corresponding to the end point of the arrow. A double-headed arrow means that links to each other are formed in two web pages connected to the arrow and can be moved in both directions.

Each web page in the document network shown in the figure is at least indirectly connected to another web page when the direction of the arrow is ignored, as apparent from the figure. Hereinafter, these web pages will be expressed as the k-th web page using the number k shown in a circle in the figure.

In S120 following S110, the second scoring unit 143 sets the start page SP for each of the linked document networks. Specifically, the second scoring unit 143 sets the start point page SP by executing the process shown in FIG. 12 for each of the linked document networks.

When the process shown in FIG. 12 is started, the second scoring unit 143 searches for one or more paths corresponding to the longest path in the corresponding linked document network (S121). The second scoring unit 143 observes the rule that, for each of the nodes (web pages) in the corresponding linked document network, it can not move to the same node multiple times from the corresponding node to the adjacent node according to the arrow. Thus, it is possible to calculate the number of nodes constituting the route when moving until there is no destination, and search for the route with the largest number of nodes as the longest route.

Thereafter, the second scoring unit 143 determines whether a plurality of routes are found as the longest route (S122). When only one route is found as the longest route (No in S122), the second scoring unit 143 sets a web page corresponding to the start point of the route found as the longest route as the start page SP (S123).

For example, for the linked document network shown in FIGS. 5A, 6A, 7A, 8A, 9A, the first web page with zero indegree located at the start of the longest path is set as the start page SP .

When a plurality of routes are found as the longest route (Yes in S122), the second scoring unit 143 selects the specific route having the smallest or largest out-degree from the starting point among the plurality of routes corresponding to the longest route. Search one or more routes corresponding to (S124). The designer of the system can arbitrarily determine whether the specific route is defined as “a route with the smallest out-degree from the start point” or “a route with the largest out-order from the start point”. A plurality of routes corresponding to the longest route exist in the linked document network illustrated in FIGS. 10A and 11.

Here, the terms "out-degree" and "in-degree" will be described. In one linked document network, when there is a link from one web page to U1 web pages, the out-degree of one web page is U1. On the other hand, when there is a link from U2 web pages in one web page, the in-degree of one web page is U2.

After completing the search in S124, the second scoring unit 143 determines whether or not a plurality of routes corresponding to the specific route are found (S125). If it is determined that a plurality of paths are found (Yes in S125), the second scoring unit 143 determines that one in-order zero dummy connected to the start points of the plurality of paths upstream of the plurality of paths corresponding to the specific path. A page is arranged, and this dummy page is set as the start page SP (S126).

The dummy page said here means a virtual web page. According to FIG. 10B, one dummy page having links to the first web page and the third web page is provided as a start page SP upstream of the first web page and the third web page.

On the other hand, if the second scoring unit 143 determines that only one route is found as the specific route (No in S125), it sets the web page located at the start point of this route as the start page SP (S127). The linked document network shown in FIG. 11 includes a plurality of paths starting from the first, second, third, fourth, fifth, sixth, seventh and tenth web pages as the longest paths. The path whose starting point degree is the smallest is a path starting from the tenth web page. Therefore, when the specific route is defined as the route with the smallest outgoing order from the start point, the tenth web page is set as the start point page SP.

Thus, the second scoring unit 143 sets the start point page SP according to the network structure for each of the connected document networks (S120). Thereafter, the second scoring unit 143 sets a virtual document network corresponding to each of the connected document networks (S130). One virtual document network corresponds to one linked document network.

In S130, the second scoring unit 143 searches, for each of the linked document networks, a web page with an output degree of zero existing in the corresponding linked document network as the end page EP, and enters the found end page EP. A virtual document network is set by adding dummy pages DP of degree 1 and degree 0.

The dummy page DP connected to the end point page EP is a virtual such that there is a link from the end point page EP to the dummy page DP and no link from the dummy page DP to another web page in the corresponding virtual document network. It is a web page.

If a plurality of end point pages EP are found in the corresponding linked document network, the second scoring unit 143 adds a dummy page DP to each of the end point pages EP to set a virtual document network.

FIGS. 5B, 6B, 7B, 8B, 9B, 10B, and 11 are connected documents shown in FIGS. 5A, 6A, 7A, 8A, 9A, 10A, and 11 Shown is a virtual document network corresponding to each of the networks. The virtual document network corresponding to the linked document network shown in FIG. 11 is the same as the linked document network because there is no zero-degree web page in the linked document network.

The reason why the virtual document network is set by adding the dummy page DP to the end point page EP here is as follows.
If the scoring is performed using the hermitian adjacency matrix H based on the connected document network without the dummy page DP, the score of the end page EP with zero out degree is the adjacent page having a link to the end page EP It shows a tendency to lower against the score of. However, the end point page EP corresponding to the end of the connection direction between web pages can be said to be a web page of high importance and is a web page for which a high score is to be calculated.

For this reason, in the present embodiment, a dummy page DP is introduced to devise that a high score (second score) is calculated on the end point page EP.
After setting the virtual document network in S130, the second scoring unit 143 specifies the maximum value max {N} of the element number N of the virtual document network (S140). The number N of elements of one virtual document network corresponds to the total number of web pages and dummy pages belonging to the virtual document network. For example, the element number N of the virtual document network shown in FIG. 6B is 14 (N = 14). For example, the element number N of the virtual document network shown in FIG. 8B is 7 (N = 7). The maximum value max {N} corresponds to the number N of elements of the virtual document network with the largest number N of elements among all the virtual document networks.

In the following S150, the second scoring unit 143 selects one of the virtual document networks as a processing target. The virtual document network selected here is hereinafter referred to as a selected document network.

Thereafter, the second scoring unit 143 calculates, based on the Hermite adjacency matrix H of the selected document network, a second score for each of the web pages constituting the selected document network (S160 to S220). Below, one of the web pages which comprise a selection document network is expressed as web page D [m]. The variable m takes an integer value of 1 to N (1 ≦ m ≦ N), and the web page D [m] corresponds to the mth web page in the selected document network. N is the number N of elements of the selected document network.

In S160, the second scoring unit 143 generates a Hermitian adjacency matrix H representing the connection relationship of web pages in the selected document network with the values 1, 0, + i, -i. The Hermitian adjacency matrix H is a matrix of N rows and N columns (NxN) corresponding to the number N of elements of the selected document network, and each matrix is a matrix which takes any one of the values 1, 0, + i and -i. is there. The expression “component h (p, q)” in the following indicates the component of the p th row and the q column in the Hermite adjacency matrix H.

The second scoring unit 143 responds when there is a link from the web page D [p] to the web page D [q] and a link from the web page D [q] to the web page D [p]. Component h (p, q) is set to the value 1.

When there is no link from web page D [p] to web page D [q] and no link from web page D [q] to web page D [p], the corresponding component h (p, q) Is set to the value 0. Therefore, the second scoring unit 143 sets the diagonal component h (p, p) of the Hermitian adjacency matrix H to the value zero.

Furthermore, when there is a link from the web page D [p] to the web page D [q] but there is no link from the web page D [q] to the web page D [p], the second scoring unit 143 The corresponding component h (p, q) is set to the value + i. When there is no link from web page D [p] to web page D [q] but a link from web page D [q] to web page D [p], the corresponding component h (p, q) , Set the value -i.

Thus, the second scoring unit 143 sets the value of each component h (p, q) and generates a Hermite adjacency matrix H.

When the value of each component h (p, q) is set according to the above-mentioned rule, the q-th row having a symmetrical positional relationship with respect to the component h (p, q) in the p th row and q column The component h (q, p) in the p-th column is set to the complex conjugate of the component h (p, q). Thus, the Hermitian adjacency matrix H is a Hermitian matrix.

Thereafter, the second scoring unit 143 generates a special Hermite adjacency matrix H1 obtained by transforming the Hermitian adjacency matrix H (S170). The transformation is performed such that when each component of the eigenvector V of the special Hermite adjacency matrix H1 is arranged as a complex vector in the complex plane, all of the components fall within an angle range of π / 2 radians.

At the time of deformation, the second scoring unit 143 calculates a first correction amount C1 and a second correction amount C2 according to the following equation based on the maximum value max {N} calculated in S140.

Here, the parameter n is a natural number equal to or greater than the maximum value max {N} specified in S140.

It is sufficient to set n = max {N} in order to fit all of the above components into an angle range of π / 2 radians. As the value of the parameter n is made larger than the maximum value max {N}, all of the components fall within an angle range smaller than the angle range of π / 2 radians. The purpose of having all of the components in an angular range of π / 2 radians is to ensure that all of the components are in one quadrant on the complex plane. The parameter n can be set to any value as long as this object can be achieved. However, for good calculation of the second score, the parameter n is preferably set to a value as small as possible within the range in which the object can be achieved.

The second correction amount C2 contributes to adjustment of the angular range, and the first correction amount C1 helps to prevent the absolute value of the matrix component from changing due to the second correction amount C2.
After the calculation of the first correction amount C1 and the second correction amount C2, the second scoring unit 143 replaces the component of the value + i in the hermitian adjacency matrix H with the value C1 (C2 + i), and the component indicating the value -i Replace with the value C1 (C2-i). The second scoring unit 143 further calculates the value C1 (C2 + i) of the component of each row in the Hermite adjacency matrix H after the replacement, the number of the component indicating the value C1 (C2 + i) in the same row, and the number of the component indicating the value 1 Change to the value {C1 (C2 + i) / W} divided by the sum W of. The second scoring unit 143 further sets the value C1 (C2-i) of the component that is in a symmetrical positional relationship with respect to the component changed to the value {C1 (C2 + i) / W} and the diagonal component to the value {{ Change to the complex conjugate of C1 (C2 + i) / W} {C1 (C2-i) / W}. A Hermitian matrix defined by such permutations and changes is generated as a special Hermitian adjacency matrix H1.

A specific example of the transformation procedure from the Hermite adjacency matrix H to the special Hermite adjacency matrix H1 is shown in FIG. For example, among the total N components h (p1,1), h (p1,2),..., H (p1, N) in the p1-th row, the component taking the value + i and the component taking the value 1 are the total W1 If the number is i, then each component indicating the value + i in the p1th row in the Hermite adjacency matrix H is changed to the value {C1 (C2 + i) / W1}. Among the total N components h (p2,1), h (p2,2),..., H (p2, N) in the row p2, the component taking the value + i and the component taking the value 1 is the total W2 In some cases, each component indicating the value + i in the p2th row in the Hermite adjacency matrix H is changed to a value {C1 (C2 + i) / W2}.

Furthermore, the value of the component indicating the value -i is changed to the complex conjugate of the component in a symmetrical positional relationship with respect to the diagonal component. For example, the value of the component h (q1, p1) which has a symmetrical positional relationship with respect to the component h (p1, q1) representing the value {C1 (C2 + i) / W1} with respect to the diagonal component is {C1 (C2-) i) Change to / W1}. Similarly, the value of the component h (q2, p2) that is in a symmetrical positional relationship with respect to the component h (p2, q2) indicating the value {C1 (C2 + i) / W2} with respect to the diagonal component is {C1 (C2) Change to -i) / W2}.

In S180, the second scoring unit 143 calculates the eigenvalues and the eigenvectors of the special Hermite adjacency matrix H1 generated in S170. Since the special Hermite adjacency matrix H1 is an NxN matrix, the eigenvectors are N-dimensional vectors including N components. In the following, each component of the eigenvector V corresponding to the absolute value maximum eigenvalue is represented using V [m]. The variable m takes an integer value from value 1 to value N. That is, the eigenvectors are V = {V [1], V [2],..., V [N]}. Each component V [m] (1 ≦ m ≦ N) of the eigenvector V corresponds to each web page D [m] (1 ≦ m ≦ N) constituting the selected document network.

In the next S190, the second scoring unit 143 displays each component V [m] (1 ≦ m ≦ N) of the eigenvector V corresponding to the absolute value maximum eigenvalue of the special Hermite adjacency matrix H1 as the start page of the selected document network. Divide by component E corresponding to SP. Here, the start point page SP corresponds to the start point page SP set in S120 for the selected document network. When the start page SP is the s-th web page D [s], the component E corresponds to the s-th component V [s] of the eigenvector V (E = V [s]).

When each component V [m] (1 ≦ m ≦ N) of the eigenvector V is divided by the component E, the component of the eigenvector V corresponding to the start page SP is converted to the value “1”. In the following, the eigenvector V after division is expressed as an eigenvector V1. The eigenvector V1 is V1 = {V [1] / E, V [2] / E, ..., V [s] / E = 1, ..., V [N] / E}. By division, the components of the eigenvector V1 corresponding to the start page SP are arranged on the real axis in the complex plane.

When the process in S190 is finished, the second scoring unit 143 rotationally converts each component V [m] / E (1 ≦ m ≦ N) of the eigenvector V1 after division (S200). In S200, the second scoring unit 143 can execute the process shown in FIG.

When the process shown in FIG. 14 is started, when the second scoring unit 143 arranges each component of the eigenvector V1 in the complex plane, whether or not there is a component located on the first quadrant side of the real axis in the complex plane. It is determined (S201). The component located on the first quadrant side from the real axis does not include the component located on the real axis.

In many cases, there is no component located on the first quadrant side of the component of the start page SP located on the real axis. However, when a cyclic structure exists in the corresponding virtual document network, there may be a component located on the first quadrant side of the start page SP. The process of S201 is performed to determine the presence of such a component that occurs with low probability.

If it is determined that there is no component positioned on the first quadrant side from the real axis (No in S201), the second scoring unit 143 rotates each component of the eigenvector V1 by a predetermined angle θ1 to the fourth quadrant side. Rotation conversion (S203). In this manner, the second scoring unit 143 rotates each component of the eigenvector V1 so as to arrange the component corresponding to the start page SP at a specific position away from the real axis by the angle θ1 on the complex plane. Convert.

FIG. 15A illustrates the arrangement on the complex plane of each component before rotational transformation. In FIG. 15A, each of the black circle and the white circle corresponds to one of the components of the eigenvector V1, and the black circle particularly corresponds to the component of the start page SP. FIG. 15B illustrates the arrangement on the complex plane of each component after rotational transformation.

The angle θ1 is, for example, π / 180 radians. The angle θ1 is sufficient if the components corresponding to the start page SP are apart from the real axis within the range in which all components of the eigenvector V1 are all contained in the fourth quadrant, and is not limited to π / 180 radians . The reason for separating the component corresponding to the start point page SP from the real axis will be described later.

If it is determined that there is a component located on the first quadrant side from the real axis (Yes in S201), the second scoring unit 143 proceeds to S205. In S205, the second scoring unit 143 identifies the angle θ2 from the real axis of the component farthest from the real axis in the first quadrant. Thereafter, the second scoring unit 143 rotationally converts each component of the eigenvector V1 so as to rotate it by the angle θ1 + θ2 toward the fourth quadrant (S207).

The angle θ1 is as described above for the process of S203. By rotational conversion of the angle θ1 + θ2, the second scoring unit 143 puts all the components of the eigenvector V1 in the fourth quadrant of the complex plane, including the components located on the first quadrant side from the start page SP. Hereinafter, the eigenvector V1 after rotation conversion is expressed as eigenvector Vc = {Vc [1], Vc [2],..., Vc [s],..., Vc [N]}.

In S200, when the rotation conversion is performed as described above, the second scoring unit 143 arranges each component Vc [m] (1 ≦ m ≦ N) of the eigenvector Vc as a complex vector in the complex plane. A value Z [m] = L [m] · θ [m] (1 ≦ m ≦ N) corresponding to the distance from the real axis of Vc [m] (1 ≦ m ≦ N) is calculated (S210). FIG. 15B conceptually shows the value Z [m].

Here, the value L [m] corresponds to the absolute value | Vc [m] | of the component Vc [m]. The value θ [m] corresponds to the angle between the component Vc [m] and the real axis, in other words, the angle of the component Vc [m] clockwise from the real axis.

Thereafter, the second scoring unit 143 calculates the second score of each web page D [m] (1 ≦ m ≦ N) based on the value Z [m], and stores the calculated second score in the storage unit 20. (S220).

The second score X2 corresponding to the web page D [m] is calculated according to X2 = Z [m] -min {Z [m]}. min {Z [m]} means the smallest value in the group of Z [m] (1 ≦ m ≦ N). That is, as the second score X2 of each web page D [m] (1 ≦ m ≦ N), the second score X2 of the web page D [m] indicating the smallest Z [m] has a value of zero. A value obtained by subtracting the minimum value min {Z [m]} from [m] is calculated. However, it is not necessary to calculate the second score X2 for the component corresponding to the dummy page DP. This is because the dummy page DP which does not actually exist does not make sense even if the second score X2 is calculated.

Thus, the second scoring unit 143 calculates, as the second score, a higher score for a web page in which the component of the eigenvector V is farther from the real axis and for a web page in which the absolute value of the component is larger. .

In many cases, the component corresponding to the start point page SP is at the specific position closest to the real axis, and the second score corresponding to the start point page SP is zero. Therefore, according to the present embodiment, a higher second score is calculated as the web page is farther from the start point page SP. Specifically, in the complex plane, a web page in which the component of the eigenvector V is largely rotated from the component of the eigenvector corresponding to the start page SP and a web page having a larger absolute value of the component have a higher second score It is calculated. Even in the case where an affirmative determination is made in the process of S201 described above and the process proceeds to the process of S205, the angle θ2 is not large, so the second score of many web pages is calculated as a higher value as it is farther from the start page SP. Ru.

Based on the special Hermite adjacency matrix H1, thanks to the second correction amount C2, each component of the eigenvector Vc must be within the angular range of π / 2 radians of the complex plane without making one rotation on the complex plane. In the fourth quadrant. Moreover, the component corresponding to starting point page SP is arrange | positioned by rotation conversion at the specific position (position which has angle (theta) 1) on a complex plane. Then, a second score is calculated according to a value Z [m] = L [m] · θ [m] (1 ≦ m ≦ N) based on the real axis having a certain correspondence relationship with the specific position. Thus, the value Z [m] and the second score of each web page D [m] are calculated according to the positional relationship with the component corresponding to the start point page SP.

Therefore, according to the present embodiment, it is possible to easily and appropriately calculate the important score (second score) according to the connection relationship between web pages based on the start point page SP.
In the present embodiment, the rotational conversion is performed so that the component corresponding to the start point page SP is disposed offset from the real axis. Z [m] is the equation Z [m] = L [m] · θ [m It is because it calculates according to. According to this equation, components arranged on the real axis are all θ [m] = 0 since θ [m] = 0, and the value L [m] is not reflected in the second score. The rotational conversion of each component Vc [m] away from the real axis corresponds to the rotational conversion of each component of the eigenvector V1 such that θ [m] becomes nonzero. By this rotation conversion, the second score, in particular, the second score of the web page having an interactive link can be favorably calculated based on L [m].

According to the present embodiment, it is also significant that the second score of each web page can be calculated so that the second score corresponding to the end point page EP becomes high thanks to the dummy page DP. Therefore, according to the present embodiment, it is possible to calculate, as the second score, an appropriate score according to the connection relationship of web pages in the selected document network.

After calculating the second score of each web page D [m] in the selected document network in S220, the second scoring unit 143 proceeds to S230 and executes the processing of S160 to S220 for all virtual document networks, It is determined whether the second score for the web page has been calculated. Then, if there is an unprocessed virtual document network (No in S230), the process returns to S150, and one of the unprocessed virtual document networks is selected as a new virtual document network to be processed. That is, the selected document network is changed. Thereafter, the processing of S160 to S220 is executed for the new selected document network, and the second score of each web page in the selected document network is calculated and stored.

Then, when the processing of S160 to S220 is executed for all the virtual document networks, the second scoring unit 143 ends the processing shown in FIG. The second scoring unit 143 can read out the second score of each web page stored in the storage unit 20 by this processing from the storage unit 20 as needed. For example, when the search query occurs, the second scoring unit 143 can read out the second score of each of the related pages corresponding to the search query from the storage unit 20 and provide the second score to the ranking unit 145.

According to the present embodiment, the processing shown in FIG. 4 arranges the components corresponding to each web page in the fourth quadrant, and further arranges the components corresponding to the start point page SP at a specific position, with the value Z m The second score can be calculated on a common scale for web pages of different consolidated document networks.

Therefore, the ranking unit 145 appropriately calculates the overall score of each related page, that is, the page rank, based on the second score, even when web pages of different connected document networks are included in the related page group. can do.

That is, based on the second score of each web page, the ranking unit 145 sets the arrangement of the web page in the search result list in such a form that the page rank Y is based on the first score and the second score. , It can be determined that the corresponding web page is placed at the top.

The output unit 147 can provide the user terminal 5 with an appropriate search result list based on such a connection relationship between web pages. Specifically, it is possible to provide the user terminal 5 with a search result list that is positioned higher as the web page where links away from the start point page where a high second score is calculated gathers. Therefore, according to the present embodiment, scoring / ranking of a plurality of web pages according to the connection relationship more appropriately than in the past can be performed, and appropriate search results can be provided to the user terminal 5.

Here, regarding each of the linked document networks shown in FIG. 5A, FIG. 7A, FIG. 8A, FIG. 9A, and FIG. 11, ranking of web pages based on the second score calculated by applying the technique of this embodiment. Explain. Web pages of the linked document network shown in FIG. 5A are ranked in the order of “5” “4” “3” “2” “1” according to the conventional method. The numbers shown here correspond to the numbers described in the circles in the corresponding figures. That is, “5” indicates the web page corresponding to the node described as “5” in FIG. 5A. The arrangement of numbers here means that the second score of the '5' web page is the highest, so the rank is the highest, the second score of the '1' web page is the lowest, and so the rank is the lowest. Do.

According to the present embodiment, the web pages in the linked document network of FIG. 5A are ranked in the order of “5” “4” “3” “2” “1” as in the conventional method.
Web pages in the linked document network of FIG. 7A are ranked in the order of “4” “3” “7” “8” “6” “2” “5” “1” according to the conventional method, According to the present embodiment, the ranking is performed in the order of “4” “3” “2” “5” “6” “7” “8” “1”.

According to the conventional method, web pages in the linked document network of FIG. 8A are ranked in the order of “5” “4” “2” “3” “1”, and according to this embodiment “5” "4" "3" "2" "1" is ranked in the order.

Web pages in the linked document network of FIG. 9A are ranked in the order of “4” “3” “2” “1” according to the conventional method, and according to the present embodiment, similar to the conventional method. , "4" "3" "2" "1" is ranked.

According to the conventional method, the web pages in the linked document network of FIG. 11 are “4” “6” “7” “1” “2” “8” “9” “3” “5” “10” It is ranked in order, and according to the present embodiment, it is ranked in the order of “4” “6” “7” “2” “1” “3” “5” “8” “9” “10” .

As can be understood from this, according to the special Hermite adjacency matrix H1, the second score is calculated so as to indicate a larger value as the web page in which the links away from the start page SP gather. The second score is calculated to indicate a larger value as a web page with more links gathers. The second score is calculated such that web pages linked from web pages having high importance scores show larger values. The second score is calculated such that web pages having links from web pages with few links to other web pages show larger values.

The second score is further calculated to indicate a larger value as the web page with more links to other web pages. The second score is further calculated such that web pages having links to web pages having high importance scores show larger values. This point is particularly the feature of the special Hermite adjacency matrix H1. Therefore, according to the present embodiment, it is possible to realize good scoring of web pages.

Then, the modification of information processing system 1 mentioned above is explained. The modification described below is different from the above-described information processing system 1 only in part of the processing performed by the second scoring unit 143. The other configuration of the modification is the same as that of the information processing system 1 described above. Therefore, in the following, the contents of the process of the second scoring unit 143 characteristic of the modification will be selectively described.

First Modification
In S210 (see FIG. 4), the second scoring unit 143 uses the angle from the component corresponding to the start point page SP, not the angle from the real axis, as the angle θ [m], to obtain the value Z [m]. = L [m] · θ [m] is calculated. According to the first modification, the calculation of the angle θ [m] is more complicated than the above-described embodiment, but in many cases, the second score can be calculated appropriately.

Second Modification
The second scoring unit 143 executes the process of S210 after generating the eigenvector V1 in S190 without executing the process of S200. In S210, the second scoring unit 143 calculates the value Z [m] using the eigenvector V1 instead of the eigenvector Vc described above. That is, based on the values L [m] and θ [m] corresponding to the component V [m] / E of the eigenvector V1, the value Z [m] is expressed by the equation Z [m] = L [m] · θ [m Calculate according to]. This example can be applied to a linked document network in which there is no bi-directional link, and in which no web page placed in the first quadrant side of the start page SP appears.

Alternatively, in S210 of the second modification, the value Z [m] may be calculated according to the equation Z [m] = L [m] · (θ [m] + β). β may be set to a small value such as π / 180 radians so that θ [m] + β does not exceed π / 2 radians. According to this example, even when there is a bi-directional link in the linked document network, non-zero value Z [m] including information of value L [m] can be calculated, and an appropriate second score can be calculated. It can be calculated.

Third Modification
In S170, the second scoring unit 143 generates another special Hermite adjacency matrix H2 instead of the above-mentioned special Hermite adjacency matrix H1. In S180, the eigenvalues and eigenvectors of the special Hermite adjacency matrix H2 are calculated (S180). The processes after S190 are executed using the eigenvector V corresponding to the eigenvalue with the maximum absolute value calculated here. That is, the second scoring unit 143 of the third modification executes the same process as the above-described embodiment, using another special Hermite adjacency matrix H2 instead of the special Hermite adjacency matrix H1.

The special Hermite adjacency matrix H2 shown in FIG. 16 is an example of the special Hermitian adjacency matrix H2 corresponding to the Hermite adjacency matrix H shown in the upper part of FIG. In S170, second scoring unit 143 replaces the component of value + i in Hermitian adjacency matrix H with value C1 (C2 + i), and replaces the component indicating value -i with value C1 (C2-i). The second scoring unit 143 further performs the following processing A and processing B.

(Process A)
The second scoring unit 143 is a value obtained by dividing the value C1 (C2 + i) in the component of each row in the Hermite adjacency matrix H after replacement by the number W of the components indicating the value C1 (C2 + i) and the value 1 in the same row { Change to C1 (C2 + i) / W}, and further change the value {C1 (C2 + i) / W} to the value C1 (C2-i) in the component which is in a symmetrical positional relationship with respect to the diagonal component. Change) to the complex conjugate {C1 (C2-i) / W} of value {C1 (C2 + i) / W}.

(Process B)
The second scoring unit 143 multiplies the values C1 (C2-i) in the components of each row in the Hermite adjacency matrix H after replacement by C1 (C2-i) and the number Z of the components indicating the value 1 in the same row. Change the value to {C1 (C2-i) Z}, and further change the value to a value {C1 (C2-i) Z} and the value in the component in a symmetrical positional relationship with respect to the diagonal component. Change C1 (C2 + i) to the complex conjugate {C1 (C2 + i) Z} of value {C1 (C2-i) Z}.

By such substitution and modification, a special Hermite adjacency matrix H2 is generated. The second scoring unit 143 may execute the process B after the execution of the process A, or may execute the process A after the execution of the process B. It may be executed. The same special Hermite adjacency matrix H2 is generated by performing process A and process B in any manner.

Here, the processing procedure in the case of executing the process B after the execution of the process A will be described again for correct understanding. The second scoring unit 143 is a value obtained by dividing the value C1 (C2 + i) of the component of each row in the Hermite adjacency matrix H after replacement by the number W of the components indicating the value C1 (C2 + i) and the value 1 in the same row {C1 Change to (C 2 + i) / W}, and further, change the value {C 1 (C 2 + i) / W} to the component and the value C 1 (C 2 -i) of the component in symmetrical positional relationship across the diagonal component. , To the complex conjugate {C1 (C2-i) / W} of value {C1 (C2 + i) / W}. The second scoring unit 143 sets the values {C1 (C2-i) / W} of the components of each row in the Hermitian adjacency matrix H after the change to C1 (C2-i) and the value 1 in the same row before the change. Is changed to the value {C1 (C2-i) Z / W} multiplied by the number Z of the components that have been indicated, and further, the component and the diagonal component changed to the value {C1 (C2-i) Z / W} Change the value of the component {C1 (C2 + i) / W} in a symmetrical positional relationship with respect to n to the complex conjugate {C1 (C2 + i) Z / W} of value {C1 (C2-i) Z / W} . The special Hermite adjacency matrix H1 is first generated by the above-described processing A after substitution, and the special Hermite adjacency matrix H2 of this modification is generated by the subsequent processing B.

The value Z1 in the special Hermite adjacency matrix H2 shown in FIG. 16 takes the value -i among the components h (p3, 1), h (p3, 2), ..., h (p3, N) in the p3 row. It corresponds to the number of components and components that take the value one. The value Z2 is a component taking the value -i and a component taking the value 1 out of a total of N components h (p4,1), h (p4,2), ..., h (p4, N) in the p4th row Correspond to the number of Line p3 may be understood as the line whose value {C1 (C2-i) Z1 / W1} is shown in FIG. Line p4 may be understood as the line whose value {C1 (C2-i) Z2 / W2} is shown in FIG.

The second scoring unit 143 uses the special Hermite adjacency matrix H2 thus calculated in place of the special Hermitian adjacency matrix H1 to execute the processing of S180 to S220.
For each of the linked document networks shown in FIGS. 5A, 7A, 8A, 9A, and 11, the ranking of web pages based on the second score calculated by applying the third modification is described above. A description method similar to the description method in the embodiment will be described.

According to a third variant, the web pages in the consolidated document network of FIG. 5A are ranked in the order of “5” “4” “3” “2” “1”. Web pages in the consolidated document network of FIG. 7A are ranked in the order of “3” “4” “2” “5” “6” “7” “8” “1”.

Web pages in the consolidated document network of FIG. 8A are ranked in the order of “5” “4” “3” “2” “1”. Web pages in the consolidated document network of FIG. 9A are ranked in the order of books “4” “3” “1” “2”. Web pages in the linked document network of FIG. 11 are ranked in the order of “4” “6” “7” “2” “1” “3” “5” “8” “9” “10” .

The special Hermitian adjacency matrix H2 is different from the special Hermitian adjacency matrix H1 in that the second score is calculated to indicate a larger value as the web page having links to web pages with more links from other web pages. Is different. This point is particularly the feature of the special Hermite adjacency matrix H2.

The special Hermitian adjacency matrix H2 exhibits features similar to the special Hermitian adjacency matrix H1 in other respects, but the second score shows larger values for web pages having links to web pages with higher importance scores. The calculated features are specific to the special Hermitian adjacency matrix H1. According to the third modification, it is possible to realize good scoring of web pages.

Fourth Modified Example
In the fourth variation, it is assumed that the connected document network includes in-degree zero web pages and out-degree zero web pages. Furthermore, it does not deal with a linked document network having a cyclic structure in which a plurality of paths exist from one start page SP to one end page EP, and a linked document network in which mutual links exist. On the premise of these, the second scoring unit 143 is configured to execute the process shown in FIG. 17 instead of the process shown in FIG. The process shown in FIG. 17 has many parts that are the same as the process shown in FIG. Therefore, in the following, the description of the same parts will be simplified.

When the process shown in FIG. 17 is started, the second scoring unit 143 extracts one or more connected document networks from all the web pages, as in S110 (S310). Thereafter, the second scoring unit 143 sets the start point page SP for each of the connected document networks (S320). When there is only one web page with an in-degree of zero included in the linked document network, the start page SP of the corresponding linked document network is set to the web page with an in-degree of zero. If the corresponding connected document network includes a plurality of web pages with zero indegree, the start page SP is set based on the path length.

Specifically, the second scoring unit 143 searches for a path having the largest path length among the paths according to the direction of the link from the web page with zero in-degree to the web page with zero in-degree. The second scoring unit 143 sets a web page with an in-degree of zero as the start point page SP in the path with the largest path length. When there are a plurality of paths having the largest path length, the second scoring unit 143 arranges dummy pages of in-degree zero connected to the start points of the plurality of paths as shown in FIGS. 10A and 10B. A dummy page can be set as the start page SP. Specifically, the second scoring unit 143 performs the second scoring when there are a plurality of paths with the largest path length and there are a plurality of start points with the smallest (or largest) outdegree at the start points of the plurality of paths. As shown in FIGS. 10A and 10B, the unit 143 can arrange a dummy page of in-degree zero connected to the start points of a plurality of paths, and set the dummy page as the start page SP. When there are a plurality of paths with the largest path length but there is only one starting point with the smallest (or largest) outgoing degree at the starting points of the plurality of paths, the second scoring unit 143 is the smallest (or the largest) The start point of the out-degree of) can be set in the start page SP.

After the process of S320, the second scoring unit 143 sets a virtual document network for each of the connected document networks, as in the process of S130 (S330). That is, a web page with a zero outgoing degree existing in the corresponding linked document network is searched as the end point page EP, a dummy page DP is added to the end page EP, and a virtual document network is set.

Thereafter, the second scoring unit 143 specifies the maximum value max {N} of the number N of elements of the virtual document network, as in S140 (S340). In the subsequent S350, the second scoring unit 143 selects one of the virtual document networks as a processing target.

In S360, the second scoring unit 143 generates a Hermitian adjacency matrix H corresponding to the selected document network, as in S160. Furthermore, the second scoring unit 143 generates a special Hermite adjacency matrix H3 by the deformation of the Hermite adjacency matrix H (S370). At the time of deformation, the second scoring unit 143 calculates the correction amount C according to the following equation based on the maximum value max {N} calculated in S340.

The parameter n in the above equation is predetermined so that all of the components fall within an angle range of π / 2 radian when each component of the eigenvectors of the special Hermite adjacency matrix H3 is arranged as a complex vector in the complex plane. The parameter n may be defined as a natural number equal to or greater than the maximum value max {N} specified in S340. The parameter n may be, for example, n = max {N} or n = 2 (max {N} -1). In the case of the fourth modification, since the component corresponding to the start page SP is arranged on the real axis in the complex plane, theoretically all components are complex even if n = max {N} -1 is set. It can fit in the fourth quadrant of space.

After calculating the correction amount C, the second scoring unit 143 replaces the component of value + i in the Hermite adjacency matrix H with a value (C + i), and further, the value of each row in the Hermite adjacency matrix H after the replacement (C + i The component which shows) is changed into the value {(C + i) / R} which divided the number R of the components which show value (C + i) in the same line, and further, the value of the component which shows value -i, the diagonal component Change to the complex conjugate {(C−i) / R} of the components in symmetrical positional relationship with each other.

The second scoring unit 143 generates a Hermitian matrix defined by such permutations and changes as a special Hermite adjacency matrix H3. The special Hermite adjacency matrix H3 shown in FIG. 18 is an example of the special Hermitian adjacency matrix H3 corresponding to the Hermite adjacency matrix H shown in the upper part of FIG.

In the Hermitian adjacency matrix H, of the total N components h (p1,1), h (p1,2),..., H (p1, N) in the p1-th row, the component taking the value + i is R1 In the case, each component indicating the value + i in the p1 row is changed to the value {(C + i) / R1}. Among the total N components h (p2,1), h (p2,2),..., H (p2, N) in the row p2, if there are R2 components taking the value + i, Hermitian adjacent Each component indicating the value + i of the p2 th row in the matrix H is changed to the value {(C + i) / R2}.

Furthermore, the value of component h (q1, p1) that is in a symmetrical positional relationship with respect to component h (p1, q1) indicating the value {(C + i) / R1} with respect to the diagonal component is {(Ci) / It is changed to R1}. Similarly, the value of the component h (q2, p2) that is in a symmetrical positional relationship with respect to the component h (p2, q2) indicating the value {(C + i) / R2} with respect to the diagonal component is {(Ci) Change to /). Thus, the special Hermitian adjacency matrix H3 is generated.

According to a fourth variant, it does not handle linked document networks in which bi-directional links exist. Therefore, the Hermitian adjacency matrix H does not include the component of value 1. As can be understood from this, the number R corresponds to the number W of the above embodiment.

In the following S380, the second scoring unit 143 calculates the eigenvalues and eigenvectors of the special Hermite adjacency matrix H3 generated in S370, as in the process of S180. In the following S390, the second scoring unit 143 processes each component V [m] (1 ≦ m ≦ N) of the eigenvector V corresponding to the eigenvalue with the maximum absolute value of the special Hermite adjacency matrix H3, as in the process of S190. , Divide by the component E corresponding to the start page SP of the selected document network. Corresponds to each component V [m] (1 ≦ m ≦ N) of the eigenvector V corresponding to a positive eigenvalue when the maximum absolute value eigenvalue includes a positive eigenvalue and a negative eigenvalue to the start page page SP of the selected document network Can be divided by the component E. By this division, the components of the eigenvector V corresponding to the start page SP are arranged on the real axis in the complex plane.

In S400, the second scoring unit 143 arranges each component V [m] / E (1 ≦ m ≦ N) of the eigenvector V1 after division on the complex plane as a complex vector. ] / E (1 ≦ m ≦ N) A value Z [m] = L [m] · θ [m] (1 ≦ m) corresponding to the distance in the rotational direction from the component (real axis) corresponding to the start point page SP ≦ N is calculated as the second score X2 = Z [m] (1 ≦ m ≦ N) of the corresponding web page D [m] (1 ≦ m ≦ N). It is not necessary to calculate the second score X2 for the component corresponding to the dummy page DP. Then, the calculated second score X2 is stored in the storage unit 20.

The value θ [m] in the fourth modified example corresponds to the angle in the clockwise direction from the real axis of the component V [m] / E, as shown in FIG. The start page SP is arranged on the real axis. Therefore, the value θ [m] can also be referred to as an angle in the clockwise direction with respect to the component corresponding to the start point page SP. That is, the value θ [m] corresponds to the angle formed by the component V [m] / E and the component V [s] / E corresponding to the start page SP. The value L [m] corresponds to the absolute value | V [m] / E | of the component V [m] / E. The meanings of the white and black circles shown in FIG. 19 are as described in connection with FIG. 15A.

In this way, the second scoring unit 143 calculates, as the second score, a score that is higher for web pages in which the component of the eigenvector V is farther from the start page SP, based on the special Hermite adjacency matrix H3.

Based on the special Hermite adjacency matrix H3, thanks to the correction amount C, each component V [m] / E (1 ≦ m N N) of the eigenvector V1 must be in the complex plane without making one rotation on the complex plane. Arranged in one quadrant. In particular, the start page SP is fixed on the real axis corresponding to the value 1 in the complex plane, and each component V [m] / E of the eigenvector V1 is arranged in the fourth quadrant. Therefore, according to the fourth modification, it is possible to easily and appropriately calculate the important score (second score) in accordance with the connection relationship between web pages based on the start page.

After calculating the second score of each web page in the selected document network in S400, the second scoring unit 143 proceeds to S410, executes the processing of S360 to S400 for all virtual document networks, and executes the second scoring for the web page. 2 Determine whether the score has been calculated.

If the second scoring unit 143 determines that there is an unprocessed virtual document network (No in S410), the process returns to S350, and one of the unprocessed virtual document networks is used as a new virtual object to be processed. Select to document network. Thereafter, the processing of S360 to S400 is executed for the new selected document network, and the second score of each web page in the selected document network is calculated and stored. Then, when the processing of S360 to S400 is executed for all the virtual document networks, the processing shown in FIG. 17 ends. According to the fourth modification, there is a technical advantage that the amount of calculation required to calculate the second score can be suppressed.

Although the exemplary embodiments of the present disclosure including the modifications have been described above, the technology of the present disclosure is characterized by using a special Hermitian adjacency matrix as described above. It is mathematically proved that the eigenvalues are always real in a Hermitian matrix including a Hermitian adjacency matrix and a special Hermitian adjacency matrix.

Furthermore, the Hermitian adjacency matrix and the special Hermitian adjacency matrix generally have only positive eigenvalues whose absolute values are only positive eigenvalues for the eigenvalues with the maximum absolute value, provided that the connection between documents (web pages) is at least weakly connected. The degree of duplication is 1 or the eigenvalue with the largest absolute value is only the negative one and the degree of duplication is 1 or the eigenvalue with the largest absolute value is the positive and negative eigenvalues and the degree of each duplication is 1 It has been demonstrated in several cases.

Therefore, by designating a simple rule that if the eigenvalue with the largest absolute value is a positive and negative one, adopt the positive eigenvalue to ensure that the eigenvector corresponding to the eigenvalue with the largest absolute value is unique. be able to. When the maximum absolute eigenvalue includes positive and negative eigenvalues, in general, the complex numbers of each component of the negative eigenvalue eigenvector hold or change each of the real part plus and minus signs and the imaginary part plus and minus Match each corresponding component of the positive eigenvector.

A change in the sign of the real part of the complex corresponds to moving the complex to a position symmetrical about the imaginary axis in the complex plane, and a change in the sign of the imaginary part of the complex means that the complex in the complex plane is symmetrical with the real axis It corresponds to moving to the following position. That is, when the eigenvalue with the largest absolute value includes positive and negative eigenvalues, the positional relationship of each component of the eigenvector of the negative eigenvalue on the complex plane and the position of each component of the eigenvector of the positive eigenvalue on the complex plane The relation has a correspondence relation through the symmetrical relation about the real axis and the symmetrical relation about the imaginary axis. Therefore, if the eigenvalue with the largest absolute value is a positive or negative eigenvalue, specify a simple rule of adopting a negative eigenvalue and perform an operation that produces the same result as adopting a positive eigenvalue. It is possible.

According to the present disclosure, the special Hermite adjacency matrix corresponding to each of the document networks forming weak linkage is defined using the common term of the number of documents of the document network having the largest number of documents among all the document networks. . Therefore, the score given to each document in each document network can be meaningfully compared / ranked not only within the same document network but also among different document networks.

In the conventional adjacency matrix which expresses the connection relation between documents as 0, 1 in a mathematical manner, it is mathematically guaranteed that the multiplicity of eigenvalues that are real among the largest eigenvalues is 1 and corresponding In order to ensure that the eigenvectors are unique, one way is to add virtual connections from every document to all documents in addition to the actual connections from each document to every other document. It must be assumed that the former is used with a certain probability and the latter is used with a certain remaining probability. Therefore, in the comparison / rank among documents, changing the probability of the former changes the rank of each document and makes it inconsistent, and what should the probability of the former be for the appropriate comparison / rank to be obtained? There was a drawback in that there was nothing other than to explore mainly empirically, that the setting of the probability of the former had room to be used for arbitrary ranking, etc. The former probability is called a damping factor, and a typical numerical value is 0.85. However, the assumption that the actual connection relationship is used only with a probability of 0.85 is far from reality. Furthermore, regarding the latter probability, in the virtual connection relation from all documents to all documents, the assumption that the probability that the virtual connection relation from a certain document to each document is used is also largely divergent from the reality .

The special Hermite adjacency matrix of the present disclosure does not have to determine virtual connection relations from all documents to all documents. Then, the special Hermite adjacency matrix of the present disclosure has the same tendency with regard to scoring / ranking of each document based on the connection relation between documents as in the case where the damping factor is 0.85 in the conventional adjacency matrix method. Give the result.

Furthermore, according to the present disclosure, if it is desirable to realize different results, the degree of appearance of the document needs to change the score instead of changing the damping factor and searching for necessary values empirically. By adding only the required number of dummy or in-order dummy, appropriate scoring / ranking can be realized in that it is more systematic, systematic and theoretical.

Furthermore, for documents whose score needs to be changed, a plurality of dummy documents constituting a path of a length corresponding to the change in the required score (ie, the number of continuous arrows protected in the direction) are placed between the dummy documents. Scoring that is more systematic, systematic, and theoretical by adding multiple connection relations to start from documents that need to change scores, or by adding them to arrive / It is possible to realize the ranking.

In addition, the special Hermitian adjacency matrix of the present disclosure responds to the necessary change while maintaining the property of the Hermitian matrix at two locations representing the connection between a document whose score needs to be changed and one other document. It is also possible to realize scoring / ranking more appropriately in that it is more systematic, systematic, and theoretical by changing it.

The special Hermite adjacency matrix H2 is a systematic, systematic and theoretical development of the special Hermitian adjacency matrix H1. The advantages of the special Hermitian adjacency matrix H1 described above hold also for the special Hermitian adjacency matrix H2. In this sense, the present disclosure provides significant technical improvements over the prior art.

It goes without saying that the present disclosure can adopt various aspects without being limited to the above embodiment and modifications. For example, the second scoring unit 143 divides each component V [m] of the eigenvector V by the component V [s] of the start page SP in S190 and S390 to form the start page SP on the complex plane, It arranges to the point of value 1 on real axis.

However, in S190 and S390, each component V [m] of the eigenvector V may be divided by -V [s] or may be divided by + V [s] · i, or -V [s] It may be divided by i or divided by a predetermined multiple (real number multiple) thereof. For example, when each component V [m] of the eigenvector V is divided by -V [s], the start page SP is placed at a point of -1 on the real axis in the complex plane, and each of the divided eigenvectors V1 is The components are arranged in the second quadrant in the complex plane. Also in this case, it is possible to appropriately calculate the second score.

In addition, in S124 shown in FIG. 12, the second scoring unit 143 selects one or more paths corresponding to the specific path having the largest output degree from the start point among the plurality of paths corresponding to the longest path. You may search. The present disclosure may be applied to the scoring of documents having link / quoting relationships not limited to web documents.

The functions of one component in the above embodiment may be distributed to a plurality of components. The functions of multiple components may be integrated into one component. A part of the configuration of the above embodiment may be omitted. All the aspects contained in the technical thought specified from the wording as described in a claim are an embodiment of this indication.

Finally, the correspondence between terms will be described. The processes of S110 and S310 executed by the second scoring unit 143 correspond to an example of the process implemented by the identifying unit. The processes of S120 and S320 correspond to an example of the process implemented by the determination unit. The processes of S130 and S330 correspond to an example of the process realized by the setting unit. The processes of S160, S170, S360, and S370 correspond to an example of the process realized by the definition unit. The processes of S180 and S380 correspond to an example of the process realized by the eigenvector calculation unit. The processes of S190 to S220 and S390 to S400 correspond to an example of the process realized by the score calculation unit. The process performed by the ranking unit 145 and the output unit 147 corresponds to an example of the process implemented by the arrangement determination unit.

Claims (18)

1. An information processing system for scoring a plurality of documents, wherein
   A specification unit that specifies one or more document networks including at least a weakly connected document group based on data representing the connection relationship among the plurality of documents;
   A determination unit that determines, for each of the one or more document networks, a start point document that is a document located at a start point of the corresponding document network;
   A virtual document including the dummy documents for each of the one or more document networks by connecting a virtual dummy document of in-degree 1 and an out-degree 0 to a document with an output degree of zero in the corresponding document network A setting unit for setting a document network;
   A definition unit defining a special Hermite adjacency matrix for each of the one or more virtual document networks corresponding to the one or more document networks, wherein the special Hermitian adjacency matrix is a document constituting the corresponding virtual document network It is a modification of the Hermitian adjacency matrix of N rows and N columns based on the connection relation between D [m] (1 ≦ m (integer) ≦ N), and the Hermitian adjacency matrix is a component h of p th row q th column , Q) indicate a value of 1 when there is a link from document D [p] to document D [q] and a link from document D [q] to document D [p], and When there is neither a link from p] to document D [q] nor a link from document D [q] to document D [p], a value of 0 is indicated, and from document D [p] to document D [q] Link exists but from document D [q] When there is no link to [p], it indicates the value + i (i is an imaginary unit), and there is no link from document D [p] to document D [q] but document D [q] to document D [p A definition part which is a Hermitian matrix with zero diagonal components indicating a value -i when there is a link to
   An eigenvector calculation unit that calculates an eigenvector corresponding to an eigenvector corresponding to the absolute value maximum of the special Hermite adjacency matrix, and having a component corresponding to each of the documents D [m] (1 ≦ m ≦ N);
   For each of the one or more virtual document networks, the document D [m] (1 ≦ m ≦ N) when each component of the eigenvector is arranged on a complex plane based on the component corresponding to the start document A score calculation unit that calculates the score of each of the documents D [m] (1 ≦ m ≦ N) based on the positional relationship on the complex plane between them);
   And the definition unit arranges the Hermitian adjacency matrix such that when the components of the eigenvector are arranged on the complex plane, all the components fall within an angular range of .pi. / 2 radians in the complex plane. An information processing system which deforms and defines the special Hermite adjacency matrix.
2. The information processing system according to claim 1, wherein
   The special Hermite adjacency matrix substitutes the component indicating the value + i in the hermitian adjacency matrix with the value C1 (C2 + i) based on the first correction amount C1 and the second correction amount C2, and the component indicating the value -i The value C1 (C2-i) is substituted, and the value C1 (C2 + i) of the component of each row in the Hermite adjacency matrix after the substitution is divided by the number W of components showing the value C1 (C2 + i) and the value 1 in the same row Change the value to {C1 (C2 + i) / W}, and further change the value of the component changed to {C1 (C2 + i) / W} to the value of the component C1 (C2−) in a symmetrical positional relationship with respect to the diagonal component. correspond to a Hermitian matrix defined by changing i) to the complex conjugate {C1 (C2-i) / W} of the value {C1 (C2 + i) / W},
   The first correction amount C1 and the second correction amount C2 are determined as follows using a parameter n:
   

   

   The parameter n is π / 2 radians in the complex plane based on the number of documents max {N} in the virtual document network where the number of documents N is largest among the one or more virtual document networks An information processing system determined to fall within the angle range of.
3. The information processing system according to claim 1, wherein
   The special Hermite adjacency matrix substitutes the component indicating the value + i in the hermitian adjacency matrix with the value C1 (C2 + i) based on the first correction amount C1 and the second correction amount C2, and the component indicating the value -i The value C1 (C2-i) is substituted, and the value C1 (C2 + i) of the component of each row in the Hermite adjacency matrix after the substitution is divided by the number W of components showing the value C1 (C2 + i) and the value 1 in the same row Change the value to {C1 (C2 + i) / W}, and further, change the value {C1 (C2 + i) / W} to the value of the component C1 (C2) having a symmetrical positional relationship with respect to the diagonal component. -I) is changed to the complex conjugate {C1 (C2-i) / W} of the value {C1 (C2 + i) / W}, and the value {C1 (C2-C2) of each row component in the modified Hermite adjacency matrix H i) / W} before the change Change to the value {C1 (C2-i) Z / W} multiplied by the number Z of the components that indicated C1 (C2-i) and the value 1 in a row, and further, the value {C1 (C2-i) Z The value of the component {C1 (C2 + i) / W} in a symmetrical positional relationship with respect to the component changed to / W} and the diagonal component is a complex of the value {C1 (C2-i) Z / W}. Corresponds to the Hermitian matrix defined by changing to the conjugate {C1 (C2 + i) Z / W},
   The first correction amount C1 and the second correction amount C2 are determined as follows using a parameter n:
   

   

   The parameter n is π / 2 radians in the complex plane based on the number of documents max {N} in the virtual document network where the number of documents N is largest among the one or more virtual document networks An information processing system determined to fall within the angle range of.
4. The information processing system according to claim 1, wherein
   The special Hermite adjacency matrix substitutes the component indicating the value + i in the Hermite adjacency matrix with the value C + i based on the correction amount C, and the value of the component indicating the value C + i in each row in the Hermitian adjacency matrix after the replacement is the same. Change to the value {(C + i) / R} divided by the number R of components showing the value C + i in the row, and further, the values of the components showing the value −i have a symmetrical positional relationship across diagonal components. Corresponds to the Hermitian matrix defined by changing to the complex conjugate of the component {(Ci) / R},
   The correction amount C is determined as follows using a parameter n:
   

   

   The parameter n is π / 2 radians in the complex plane based on the number of documents max {N} in the virtual document network where the number of documents N is largest among the one or more virtual document networks An information processing system determined to fall within the angle range of.
5. The information processing system according to any one of claims 1 to 4, wherein
   The score calculation unit determines, for each of the one or more virtual document networks, the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector and the component corresponding to the start document in the complex plane Rotation conversion is performed so as to be disposed at a specific position, and the score of each of the documents D [m] (1 ≦ m ≦ N) is converted to the value Vc [m] after the rotation conversion of the corresponding document D [m]. Information processing system to calculate based on.
6. The information processing system according to claim 5, wherein
   The score calculation unit is configured such that the component corresponding to the start document is disposed at a predetermined angle that is not zero from a specific axis located at the boundary of the one quadrant in the complex plane as the specific position. An information processing system that rotationally converts values V [m] (1 ≦ m ≦ N) of respective components of the eigenvectors.
7. The information processing system according to claim 5 or 6, wherein
   The score calculation unit determines the score of the document D [m] (1 ≦ m ≦ N) on the complex plane based on the value Vc [m] after the rotation conversion of the corresponding document D [m]. Calculate the value corresponding to the product (θ [m] · L [m]) of the angle θ [m] of the value Vc [m] from the specific axis and the absolute value L [m] of the value Vc [m] Information processing system.
8. The information processing system according to any one of claims 1 to 4, wherein
   The score calculation unit determines, for each of the one or more virtual document networks, the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector and the value V [s of the component corresponding to the start document. By dividing the component corresponding to the starting document on a specific axis of the complex plane by dividing by a specific value E based on the following equation, and thereafter, the component corresponding to the starting document is a predetermined angle which is not zero from the specific axis Values of each component of the eigenvector are rotated and the score of each of the documents D [m] (1 ≦ m ≦ N) The angle θ [m] of the value Vc [m] from the specific axis in the complex plane and the value Vc [m] based on the value Vc [m] after the rotation conversion of the corresponding document D [m] as Product with the absolute value L [m] (θ [m] · L [m ] The information processing system which calculates the value corresponding to].
9. The information processing system according to claim 8, wherein
   The score calculation unit, when dividing the value V [m] (1 m m N N) of each component of the eigenvector by the specific value E, in the complex plane, the rotation due to the rotation conversion by the rotation conversion than the specific axis. When there is a component located upstream of the direction, the value V [m] of each component of the eigenvector is set to rotate the component located most upstream from the specific axis to a position at a predetermined angle that is not zero. An information processing system that rotationally converts / E (1 ≦ m ≦ N).
10. The information processing system according to any one of claims 7 to 9, wherein
    Each score of the document D [m] (1 ≦ m ≦ N) is multiplied by the product (θ such that the minimum value of all the scores of the document D [m] (1 ≦ m ≦ N) is zero. An information processing system that calculates a value obtained by subtracting [m] · L [m]).
11. The information processing system according to any one of claims 1 to 4, wherein
    The score calculation unit determines, for each of the one or more virtual document networks, the value V [m] (1 ≦ m ≦ N) of each component of the eigenvector and the value V [s of the component corresponding to the start document. The component corresponding to the start point document is arranged on the specific axis of the complex plane by dividing by the specific value E based on [], and the score of each of the documents D [m] (1 ≦ m ≦ N) is obtained. The product of the angle θ [m] of the value V [m] / E of the component of the corresponding document D [m] from the specific axis and the absolute value L [m] of the value V [m] / E (θ [ m] · L [m]) An information processing system which calculates a value corresponding to.
12. The information processing system according to any one of claims 8, 9, and 11.
    The score calculation unit divides, as the specific value E, the value V [m] of each component of the eigenvector by the value V [s] of the component corresponding to the start document, and thereby the component corresponding to the start document An information processing system that arranges on the real axis of the complex plane.
13. The information processing system according to any one of claims 1 to 12,
    The information processing system, wherein the determination unit determines a document located at a starting point of the longest path in the corresponding document network as the starting document.
14. The information processing system according to claim 13, wherein
    When the plurality of routes correspond to the longest route in the corresponding document network, the determination unit determines that the document with the highest out-degree and the out-degree are the most among the documents located at the start points of the plurality of routes. An information processing system for determining one of a small number of documents as the start document.
15. The information processing system according to claim 13, wherein
    The discrimination unit is a virtual dummy document having zero in-degree connected to a document located at a start point of the plurality of paths when a plurality of paths correspond to the longest path in the corresponding document network An information processing system that arranges the virtual dummy documents arranged as the start point document.
16. The information processing system according to any one of claims 1 to 15,
    An information processing system comprising: an arrangement determination unit configured to determine an arrangement of documents in a list of documents corresponding to a search query based on the scores of the plurality of documents calculated by the score calculation unit.
17. An information processing method for scoring a plurality of documents, wherein a computer is
    Specifying one or more document networks composed of at least a weakly connected document group based on data representing a connection relationship between the plurality of documents;
    Determining, for each of the one or more specified document networks, a start document which is a document located at a corresponding document network start;
    A virtual document including the dummy documents for each of the one or more document networks by connecting a virtual dummy document of in-degree 1 and an out-degree 0 to a document with an output degree of zero in the corresponding document network Setting up a document network,
    Defining a special Hermitian adjacency matrix for each of the one or more virtual document networks corresponding to the one or more document networks, the special Hermitian adjacency matrix comprising a document D constituting a corresponding virtual document network [M] is a modification of a Hermitian adjacency matrix of N rows and N columns based on a connection relation between [m] (1 ≦ m (integer) ≦ N), and the Hermitian adjacency matrix is a component h (p, q) of the p th row and q th column q) indicates a value of 1 when there is a link from document D [p] to document D [q] and a link from document D [q] to document D [p], document D [p] ] Indicates that the link from document D [q] to the link from document D [q] to document D [p] does not have a value of 0, and from document D [p] to document D [q] A link exists but document D [q] to document D When there is no link to p], the value + i (i is an imaginary unit) is indicated, and there is no link from document D [p] to document D [q], but document D [q] to document D [p] Defining that the diagonal component is a Hermitian matrix of zeros indicating a value -i when there is a link to
    Calculating an eigenvector having a component corresponding to each of the documents D [m] (1 ≦ m ≦ N), which is an eigenvector corresponding to an absolute value maximum eigenvalue of the special Hermitian adjacency matrix;
    For each of the one or more virtual document networks, the document D [m] (1 ≦ m ≦ N) when each component of the eigenvector is arranged on a complex plane based on the component corresponding to the start document Calculating the score of each of the documents D [m] (1 ≦ m ≦ N) based on the positional relationship on the complex plane between them).
    When the components of the eigenvector are arranged on the complex plane, the special hermitian is modified by deforming the hermitian adjacency matrix so that all components fall within an angle range of π / 2 radian in the complex plane. An information processing method that defines an adjacency matrix.
18. A computer program for causing a computer to execute the information processing method according to claim 17.

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