JP5569728B2 - Image ranking method, program, storage medium, and image display system - Google Patents

Description

  The present invention relates to an image ranking creation method, a program, a storage medium, and an image display system using the method.

  In recent years, there is a huge amount of information on the Internet, and how to efficiently search only useful information from the information has become a big issue. For example, it is well known that there is Non-Patent Document 1 as a technique for searching for text information, thereby providing a system for displaying useful information from a large amount of text information.

  On the other hand, not only text information on the Internet, but with the spread of album services on the web and cameras with GPS functions, there is a huge amount of information on images with latitude and longitude information of shooting locations added as metadata. However, research is not as advanced as text search.

  Non-patent documents 2, 3, and 4 are prior arts for obtaining a ranking of images useful for the user from such a large amount of image information.

  In Non-Patent Document 2, as an image database analysis method, there is a technique in which the relationship between images is first graphed, a transition probability between images by a Markov model is obtained, and a representative image is determined using an eigenvector of a transition probability matrix. It is disclosed.

  In Non-Patent Document 3, a technique for ranking images by applying the algorithm of Non-Patent Document 1 to images and using a matrix representing similarity between images instead of a matrix representing a link structure between Web pages. (VisualRank) is disclosed. In this technique, VisualRank is used to correct a text-based image search result, but the number of corresponding points of SIFT (Scale Invariant Feature Transform) features is used for the similarity between images. The similarity based on the number of corresponding points of the SIFT feature is effective when the same object such as a product image or a landmark image is captured and the corresponding point is likely to appear. There is a problem of lack of diversity.

  Non-Patent Document 4 is an improvement of the problem of Non-Patent Document 3 described above. First, image clustering is performed, VisualRank is applied to each cluster, and the results for each cluster are presented in parallel. A technique for ensuring the diversity of the above is disclosed.

S. Brin and L. Page, “The anatomy of a large-scale hyper-textual Web search engine,” Computer networks and ISDN systems, vol.30, no.1-7, pp.107-117, 1998. X.He, W.Y.Ma, and H.Zhang, “ImageRank: spectral techniques for structural analysis of image database,” IEEE ICME, 2003. Y. Jing and S. Baluja, “VisualRank: Applying pagerank to large-scale image search,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, no.11, 1870-1890, 2008 Mitsuru Abe and Junichi Yoshida, “Extension of Visualrank to Multiple Classes: Automatic Classification and Ranking Method for Similar Images Using Image Features” PRMU2008-178, pp.183-188

  As a result of earnest research on a technique for displaying an image considered to be of interest to the user from a large amount of image information among a large amount of image information, the inventors of the present application have found position information not considered at all in the prior art documents. Taking into account the above, we obtained the knowledge that applying VisualRank technology to images with position information and creating a ranking based on both image feature values and position information is useful in image information search technology. It was.

  Therefore, the present invention has been made based on the above knowledge, and the object of the present invention is to provide a ranking method that considers both position information and image feature amounts, and images using this ranking method. It is to provide a display system.

In order to solve the above-described problem, according to an aspect of the present invention, a method for searching for an image having metadata and creating a ranking, wherein an input including location information is received, and based on the input, Searching the image; extracting a feature vector of the searched image; creating a similarity matrix; position information in the metadata of the searched image; and a position indicated by the input; Creating a bias vector based on the distance of the step, and creating a ranking by repeatedly calculating the following equation (1) using the similarity matrix and the bias vector. Providing a method of creating a ranking, wherein the smaller the distance, the larger the bias is given. It is. Where R is a ranking value, S is a normalized similarity matrix, P is a normalized bias vector, and α is a parameter for adjusting the bias strength (0 <= α <= 1).
R = α (S × R) + (1−α) P (1)
According to this configuration, it is possible to provide a ranking method for displaying an image considered to be of interest to the user from a large amount of image information.

Further, the feature quantity vector may be extracted based on the following equation (2). However, Sv is a visual feature vector, St is a metadata feature vector, β is a parameter (0 <= β <= 1) for adjusting the weight of the visual feature vector and the metadata feature vector.
S = β × Sv + (1−β) × St (2)
According to this configuration, it is possible to provide a ranking method based on the visual feature amount and metadata feature amount of an image.

The visual feature vector may be obtained from a plurality of images.
According to this configuration, it is possible to provide a ranking method based on visual feature amounts of a plurality of images.

In the step of creating the bias vector, a bias vector may be created based on the plurality of pieces of location information.
According to this configuration, it is possible to provide a ranking method based on a plurality of position information.

In the step of creating the bias vector, a larger bias may be applied as the distance increases.
According to this configuration, it is possible to provide a method of ranking an image having position information at a position far from a position in which the user is interested in higher rank.

The step of receiving the input may further receive an input of the value of α.
According to this configuration, by changing the feature amount of the image and the weight of the position information, it is possible to adjust which information is prioritized and ranked higher according to the user's preference.

According to another aspect of the present invention, a system for searching for an image having metadata and displaying the image based on a ranking, the input receiving unit receiving an input including location information, and the input based on the input A search unit for searching for the image, a matrix generation unit for extracting a feature vector of the searched image and generating a similarity matrix, position information in the metadata of the searched image, and the input A bias creation unit that creates a bias vector based on the distance to the position, a ranking calculation unit that creates a ranking by repeatedly calculating the following equation (1) using the similarity matrix and the bias vector; A display unit that displays the image based on the ranking, and the bias creating unit gives a larger bias as the distance is smaller. Image display system is provided, wherein the door.
Where R is a ranking value, S is a normalized similarity matrix, P is a normalized bias vector, and α is a parameter for adjusting the bias strength (0 <= α <= 1).
R = α (S × R) + (1−α) P (1)
According to this configuration, it is possible to provide a system that retrieves a large amount of image information and displays an image that seems to be of interest to the user at the top.

  As described above, according to the present invention, it is possible to display an image considered to be of interest to the user from a large amount of image information.

The flowchart of the method of producing the ranking in 1st Embodiment of this invention. User interface used in Experimental Example 1-1. The noun list of 250 words used for Experimental example 1-1. List of adjectives of 100 words used in Experimental Example 1-1. The list of the city name and latitude / longitude of the attention point used in Experimental Example 1-1. The image which shows the result of Experimental example 1-1. The query is “pyramid” and the points of interest are (a) Cairo, (b) Paris, (c) New York, and (d) Sydney. The image which shows the result of Experimental example 1-1. The query is “traditional” and the points of interest are (a) Tokyo, (b) Sydney, (c) Rio de Janeiro, and (d) Delhi. The image which shows the result of Experimental example 1-2. When “house” is a query and the value of α is 1.0. The image which shows the result of Experimental example 1-2. When “house” is a query and the value of α is 0.9. The image which shows the result of Experimental example 1-2. When “house” is a query and the value of α is 0.8. The image which shows the result of Experimental example 1-2. When “house” is a query and the value of α is 0.5. The image which shows the result of Experimental example 1-2. When “house” is a query and the value of α is 0.0. The image which shows the result of Experimental example 2 at the time of using the similarity degree by metadata feature-value in 2nd Embodiment. The image which shows the result of Experimental example 2 at the time of using the similarity degree by visual feature-value in 2nd Embodiment. The image which shows the result of Experimental example 3-1. The query is “phone” and the point of interest is Paris. (a) When similarity based on tag features is used. (b) When similarity based on visual features is used. (c) When the similarity based on the tag feature and the similarity based on the visual feature are combined and used. The image which shows the result of Experimental example 3-2. The query is “cat” and the point of interest is Tokyo. (a) When similarity based on tag features is used. (b) When similarity based on visual features is used. (c) When the similarity based on the tag feature and the similarity based on the visual feature are combined and used. The image which shows the result of Experimental example 4. When the query is “insect” and the points of interest are Sydney, Delhi, and Cape Town. The image which shows the result of Experimental example 5-1. The query is “castle”, the focus is on Tokyo, and a positive bias is used. The image which shows the result of Experimental example 5-1. The query is “castle”, the focus is on Tokyo, and a negative bias is used. The image which shows the result of Experimental example 5-2. The query is “arc de triomphe”, the focus is Paris, and a negative bias is used. The block diagram of the image display system in 6th Embodiment.

<First Embodiment>
Hereinafter, a method, an apparatus, and the like according to each embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a flowchart of a method for creating a ranking in the present embodiment. In the flowchart, “S” indicates a step of each process.

First, an input of an image query to be searched and location information is received from the user (S100).
An image query typically consists of a language and can include any text information, such as nouns, adjectives, sentences, etc., depending on the image search function described below. An image may be input using an image matching technique.

  The image to be searched has additional information regarding the image, that is, metadata. The metadata includes GPS (Global Positioning System) information, date / time, direction, comments, and the like of the location where the image was taken, attached to the image. Typically, it refers to various information added to an image as in the Exif (Exchangeable Image File Format) standard for image files for digital cameras.

  The place information to be input is information indicating the geographical position of a land such as a region, a region, a country, and a city, and can be expressed as language, map information, or position information. The position information refers to a physical quantity in a two-dimensional plane or a three-dimensional space expressed by a coordinate system, and is typically GPS information including latitude, longitude, height, and the like.

  An image with metadata related to the accepted query is searched (S110). This step is a step of collecting images that are a population of subsequent steps, and the image search method itself is not particularly specified. Typically, a Web service using an API (Application Programming Interface) search function provided by Flickr (registered trademark), Google (registered trademark), or Yahoo (registered trademark) may be used. Of course, it is also possible to search for an image that has its own image data and that hits the accepted query from the original mechanism, and use the image of the result set as the population of the subsequent steps.

Next, a visual feature amount is extracted from the searched image, and a similarity matrix is created (S120).
As a method of expressing the visual feature amount from the searched image, the Bag of Features method using a color histogram and a SIFT descriptor is used. However, the present invention is not limited to this, and for example, an edge histogram or a Gabor feature histogram can be used. The color histogram is a histogram showing which color appears in what ratio in the image, and the histogram is created by dividing the normal RGB color space into 64 equal parts. As a result, the image is represented by a 64-dimensional vector.

  The Bag of Features method is a method of extracting a local feature amount from an image and expressing the image with a histogram of its appearance frequency. The local feature amount is a feature amount that describes a feature of a part of the image, and is extracted from a plurality of locations in the image. The SIFT method is an algorithm for detecting feature points and describing feature amounts. For each detected feature point, a feature amount that is invariant to image changes due to rotation, scale change, or illumination change is described for each pixel. Therefore, it is effective not only for specific object recognition but also as a feature quantity for image classification.

  Specifically, this is performed as follows. First, for each collected image, a location for extracting a local feature is determined. Various methods such as Difference of Gaussian (DoG), random sampling, and grid sampling can be used. Note that random sampling is employed in the experimental examples described later. Then, local features are extracted from the determined portions by a feature description method using the SIFT method.

  Next, the extracted feature descriptor is created. Specifically, each center of the cluster of feature descriptors obtained by the clustering of the k-means method is set as a codebook element for the Bag of Features method.

  Then, the feature descriptor extracted from the image is allocated to the nearest codebook element, and a histogram is created. The appearance frequency histogram of the feature quantity obtained in this way is an image expression vector in the Bag of Features method, and a histogram indicating the ratio of the feature quantity close to which codebook element appears in the image. It will be expressed in.

Next, based on the color histogram and the feature quantity appearance frequency histogram obtained as described above, the similarity between the images is obtained by histogram intersection. With the histogram intersection, the smaller value is adopted for each element of the histograms of the two images to be compared, and the sum is obtained over all the elements. If the sum is large, the value is large. Is evaluated as high. Specifically, as shown in Expression 10, a similarity matrix is obtained for each of the color histogram and the feature quantity appearance frequency histogram, and a similarity matrix in which both feature quantities are mixed by combining the linear sums of them. Can be requested. In Equation 10, Scombine is a synthesized similarity matrix, Scolor is a similarity matrix based on a color histogram, and Sbof is a similarity matrix based on a feature amount appearance frequency histogram.

  Next, in the present embodiment, a bias vector for correcting the feature amount is created from the position information included in the searched image metadata and the position of the input location (S130). Specifically, this is performed as follows.

  The position information included in the metadata of the image is typically GPS information, and the position where the image is captured is represented by latitude and longitude. Further, the position of the input place is information indicating a geographical position as a place of interest (attention point) in which the user is interested, and at the time of input, as the language, map information, or position information. Although it is expressed, in order to obtain the distance on the earth between two points, it is finally expressed by latitude and longitude. Of course, when the distance between two points is included as data, it goes without saying that the distance data may be used without performing the following calculation.

When the distance between two points is represented by latitude and longitude, the distance on the earth between the two points can be calculated by spherical trigonometry, assuming that the earth is a perfect sphere with a radius of 1, as shown in Equation 11.

Based on the distance between the above two points, a bias vector is created according to Equation 12.

This bias vector is an element corresponding to the image i, and increases as the image i is closer to the point of interest A, that is, as the distance between the two is smaller. Preferably, this bias vector is used after being normalized.
In addition, even if the geographical distance is close, the distance may be increased (the weight is reduced) if it is culturally different. In this case, it can be realized by a known method as appropriate, such as separately providing a weight table for cultural differences.

Next, using the created similarity matrix and bias vector, VisualRank is executed to obtain image ranking (S140). Specifically, executing VisualRank and obtaining the ranking means performing the iterative calculation of Equation 1 to converge the column vector R.

  The ranking value is updated by multiplying the similarity matrix S by the vector of the ranking value R, which is the VisualRank value, and this updating is repeated until the ranking value R converges. It becomes.

  R is a VisualRank vector in which VisualRank values of each image are arranged. The initial value is the same for all images, and may be 1.0, for example. S is obtained by normalizing each column of the image similarity matrix obtained above. The reason why S normalizes the similarity matrix for each column is that the total VisualRank value is not changed during the update.

  When a uniform vector is given as the bias vector P, correction is applied in the direction of equalizing the VisualRank value of each image. On the other hand, if a non-uniform vector is given, correction for enhancing a part of the image is applied.

<Experimental Example 1-1>
FIG. 2 is a user interface that receives an image query and location information input from a user. Since the population was created by the method described later, a query is created by selecting specific nouns and adjectives. In addition, the place of interest can be selected in a menu format. Of course, you may provide the field which a user can input freely.

  Using the search function API of Flickr's online album service, we searched for 250 nouns, 100 adjectives and a total of 350 words shown in FIGS. 3 and 4, and collected 2000 images with position information. In addition, in Flickr, some users may post a lot of similar images, so the number of images posted by the same user is limited. Further, as shown in FIG. 5, ten cities of interest are selected, and the latitude and longitude thereof are used as position information of the point of interest.

  After collecting the images, the Visual Rank value was calculated for each word. At that time, the color histogram was 64 dimensions in the RGB space, and the number of elements by the SIFT descriptor was 500 dimensions.

  6A to 6D show the results of using “pyramid” as a query. FIG. 6A shows the result of the Cairo as a point of interest, and the image of the Egyptian pyramid is the upper image. In FIG. 6b, Paris is a notable point, and a pyramid type building in front of the Louvre is displayed at the top. In FIG. 6c, the attention point is New York, and an image of a building photographed in the eastern United States is displayed at the top. In FIG. 6d, the attention point is Sydney, and an image regarding “pyramid” taken in Australia is displayed at the top.

7A to 7D show the results of using “traditional” as a query. 7a is Tokyo, FIG. 7b is Sydney, FIG. 7c is Rio de Janeiro, and FIG. 7d is Delhi. Images of people wearing traditional costumes for each region were obtained. That is, for example, in the case of “traditional” and “Tokyo”, images of people wearing kimonos are ranked higher.
As described above, it is possible to provide a ranking method for searching a large amount of image information and displaying an image considered to be of interest to the user at the top. Further, by using GPS information, it is possible to exclude images of the same object.

<Experimental example 1-2>
In addition, when α in Expression 1 is changed, as shown below, a change occurs in the image displayed at the upper level by changing the weight of the image feature amount and the location information. Therefore, which information has priority. It is possible to adjust the ranking according to the user's preference.

  8A to 8E, “house” is a query, and the values of α are (a) 1.0, (b) 0.9, (c) 0.8, (d) 0.5, (e) 0. This is changed to 0. In (a), since α = 1, there is no weight of location information “Sydney”, and an image of a Western house is displayed at the top. In (b), α = 0.9, so the weight of the location information Sydney is 10%, and the image of the Australian house is at the top. In (c), α = 0.8, and the weight of the location information “Sydney” is further increased, and an image taken in a location close to Sydney in Australia is ranked high. In (d), α = 0.5, that is, the weight of the image feature amount and the location information is 50:50, and an image that does not look like “house” just because it was taken in a place close to Sydney In. In (e), α = 0, no image feature weights are included, and only the location information “Sydney” is used, and the shooting locations are displayed in the order closest to Sydney, regardless of “house”.

Second Embodiment
In the present embodiment, a tag in metadata attached to an image or a text sentence similarity for explanation is used. In addition, not only the text sentence directly attached to the image but also a text sentence of a Web page including the image may be used. In this case, the similarity matrix S is obtained by the following equation 2. Sv is a visual feature vector, St is a metadata feature vector, β is a parameter for adjusting the weight of the visual feature vector and the metadata feature vector.

Specifically, the text attached to the image is aggregated for each query, and the higher-ranked texts, for example, 500 kinds of texts are used as a code book (however, the query itself is not included in the code book). As a feature vector of an image, a 500-dimensional vector related to the codebook is created for each image. In each image, the element corresponding to the attached text is 1, and the element not attached is 0. The similarity between images uses the cosine similarity of binary vectors. For example, since the element corresponding to the text attached to the image is 1 and the others are 0, the similarity between the images X and Y is expressed by the following Expression 13.

<Experimental example 2>
FIG. 9 shows the results when the similarity by text is used, “napoleon” is a query, and location information is “Sydney”. Most of the upper images are related to Napoleon Fish. In contrast, when only the visual feature amount is used, irrelevant images are also included as shown in FIG. It is considered that the content of the text is attached by a person and is often directly related to the feature of the image.

<Third Embodiment>
In the present embodiment, visual feature amounts and metadata feature amounts (tag feature amounts) of a plurality of images are mixed. For example, in order to obtain a similarity matrix in which all are mixed from the visual feature amount and the metadata feature amount of two images, it can be calculated as shown in Equation 14. Sv1 and Sv2 are similarity matrixes of the respective visual feature quantities, and St is a similarity matrix of the metadata feature quantities.

<Experimental example 3-1>
11a to 11c show the results when “phone” is a query and Paris is location information.
In (a), the similarity is obtained using the tag feature, and the image of the British red telephone box is the upper image. Tags such as “london”, “red”, and “phonebooth” were commonly assigned to these images.
In (b), the degree of similarity is obtained using visual feature amounts, and a dark image showing the city is the upper image.
(c) is a case where the similarity obtained by the tag feature and the visual feature is combined and used.
An image of the entire red telephone box is the main high-level image.
It is considered that the image of the entire telephone box was selected by the visual feature amount while the image of the red telephone box was ranked high by the tag feature amount.

<Experimental Example 3-2>
12A to 12C show the results when “cat” is a query and Tokyo is location information.
In (a), the similarity is obtained by using the tag feature amount, and the cat image taken indoors is the main upper image. Tags such as “pets” and “cute” were commonly assigned to these images.
In (b), the degree of similarity is obtained using the visual feature amount, and the cat image taken outdoors is the main upper image. This is considered to be due to the similarity of the background region.
(c) is a case where the similarity obtained by the tag feature and the visual feature is combined and used.
The balance between images taken indoors and images taken outdoors is improved, and the diversity of higher-order images is improved.
These indicate that combining the visual feature value and the tag feature value can lead to a higher-level image that is likely to be obtained from a more diverse viewpoint, and the diversity of the higher-level image can be improved. ing.

<Fourth embodiment>
In this embodiment, a bias vector is obtained based on a plurality of pieces of location information. It can be obtained from the average, maximum value, minimum value, etc. of bias vectors of a plurality of location information.

<Experimental example 4>
FIG. 13 shows the results when “insect” is used as a query, and Sydney, Delhi, and Cape Town are used as location information as location information. A bias vector is created for each of the three pieces of location information, and the average vector is used. By using three cities that surround the Indian Ocean, insect images taken in a wide area surrounding the Indian Ocean are obtained as high-order images.

<Fifth Embodiment>
In this embodiment, a large value is given to an image having position information at a position far from the position given by the location information, that is, a negative bias vector is obtained. It can be found by Equation 15. For example, when searching for a triumphal arch image other than Paris, “Paris” can be given as an input value of location information.
<Experimental Example 5-1>
FIG. 14A shows the result when “castle” is a query and Tokyo is location information.
The image of a Japanese castle became the top image because a large bias value was given to images taken near Tokyo.
FIG. 14B shows the result when a large bias value is given to an image photographed at a point far from Tokyo. The images of buildings mainly made up of castles, taken in various locations away from Japan, are at the top.
<Experimental example 5-2>
FIG. 15 shows the results when “arc de triomphe” is used as a query and a negative bias vector is used for Paris. The image of Thailand's Arc de Triomphe (Patusai) and the imitation of the French Arc de Triomphe in Shenzhen, China, are at the top, and an “Arch of Triumph Image outside Paris” has been obtained.

  The above-described method for creating a ranking can be realized as a program for causing a computer to execute, or can be provided as a storage medium that is read by a computer and stored as an executable program.

<Sixth Embodiment>
FIG. 16 is a block diagram of an image display system that implements the above-described ranking creation method.

  The input receiving unit 10 of the image display system 1 in the present embodiment receives an image query and location information that the user 99 is interested in as an input to the image display system 1. Specifically, as described above with reference to FIG.

The search unit 20 searches the image data 100 in the database and the image data 200 on the Internet based on the image query received by the input receiving unit 10. The matrix creation unit 30 extracts feature amounts from the images found by the search unit 20 that match the search conditions, and creates a similarity matrix. In addition, the bias creation unit 40 calculates a bias vector for correcting the feature amount from the position information included in the metadata of the image found by the search unit 20 and the position of the location information input by the input receiving unit 10. create. The ranking calculation unit 50 executes VisualRank using the similarity matrix created by the matrix creation unit 30 and the bias vector created by the bias creation unit 40 to obtain image rankings. The display unit 60 displays images to the user 99 according to the display order based on the ranking calculated by the ranking calculation unit 50.
According to this, it is possible to provide a system that retrieves a large amount of image information and displays an image that seems to be of interest to the user at the top.

DESCRIPTION OF SYMBOLS 1 Image display system 10 Input reception part 20 Search part 30 Matrix preparation part 40 Bias preparation part 50 Ranking calculation part 60 Display part 99 User 100 Image data 200 in database 200 Image data on the internet

Claims (10)

A method of an apparatus for searching for an image having at least position information attached as metadata and creating a ranking of the searched image,
Receiving input including a query and location information for the image to be searched;
Searching the image based on the query;
Extracting a feature amount of the searched image and obtaining a similarity between the searched images based on the extracted feature amount;
Calculating a distance between a position indicated by the position information in the metadata of the searched image and a position indicated by the input location information;
Creating the ranking using the similarity and the distance. A method for creating a ranking. A system that searches for images having at least position information as metadata and creates a ranking of the searched images,
An input accepting unit that accepts an input including a query about the image to be searched and location information;
A search unit for searching for the image based on the query;
Extracting a feature amount of the searched image, and calculating a similarity between the searched images based on the extracted feature amount; and
A distance calculation unit that calculates a distance between the position indicated by the position information in the metadata of the searched image and the position indicated by the input location information;
A ranking creation system comprising: a ranking calculation unit that creates the ranking using the similarity and the distance.   The ranking creating system according to claim 2, wherein the input receiving unit further receives an input of the similarity and the weighting of the distance when the ranking is created. The input receiving unit receives a plurality of input of the location information,
The distance calculation unit calculates the distance for each of the plurality of location information,
4. The ranking creation system according to claim 2, wherein the ranking calculation unit creates the ranking using the similarity and the plurality of calculated distances.   The ranking creation system according to claim 2, wherein a larger bias is applied to the ranking as the distance is smaller.   The ranking creation system according to claim 2, wherein a larger bias is applied to the ranking as the distance is larger.   The similarity generation unit extracts a visual feature amount of the searched image, extracts a text feature amount vector from text information in the metadata of the searched image, and extracts the extracted visual feature. The ranking creation system according to any one of claims 2 to 6, wherein the similarity is obtained based on a quantity and the text feature quantity.   The system for creating a ranking according to any one of claims 2 to 7, wherein the similarity creation unit obtains the similarity from a plurality of images. The similarity creation unit creates a similarity matrix,
A bias creating unit that creates a bias vector based on the distance calculated by the distance calculating unit;
9. The ranking calculation unit according to claim 2, wherein the ranking calculation unit creates a ranking by repeatedly calculating the following equation (1) using the similarity matrix and the bias vector. A system for creating rankings described in.
R = α (S × R) + (1−α) P (1)
However,
R is the ranking value,
S is a similarity matrix,
P is a bias vector,
α is a parameter (0 <= α <= 1) for adjusting the strength of the bias.   The program for functioning a computer as a system which produces the ranking in any one of Claim 2 thru | or 9.