JP2008217246A - Information processor, information processing method, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an information processor, an information processing method, and a program for separating a class having the overlap of the distribution of high density. <P>SOLUTION: This information processor is provided with a node density calculation means 27 for calculating the node density of a node of interest based on a mean distance between the node of interest and the adjacent nodes; a distribution overlap region detection means 28 for dividing a cluster as the group of nodes connected by sides into sub-clusters based on the node density calculated by the node density calculation means 27, and for detecting the overlap region of distribution; a side connection decision means 29 for, if the node where a winner node is positioned is in the distribution overlap region, deciding whether to connect a side between winner nodes based on the node density of the winner nodes; a side connection means 30 for connecting a side between the winner nodes based on the decision result; and a side deletion means 31 for deleting the side between the winner nodes based on the decision result. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an information processing apparatus, an information processing method, and a program for sequentially inputting input vectors belonging to an arbitrary class and learning an input distribution structure of the input vectors.

  As clustering for classifying input data into arbitrary clusters, a technique using a competitive neural network is well known. Competitive neural networks are a typical technique for unsupervised classification in the field of machine learning.

In a competitive neural network, when an input vector, which is training data, is given to the input layer, the distance between the reference vector of each neuron placed in the competitive layer and the input vector is calculated, and the reference closest to the input vector Learning is performed by updating the reference vectors of neurons having vectors and neighboring neurons located in the vicinity thereof so as to approach the input vector.
By sequentially applying the input vector and repeating the learning, a feature map reflecting the phase structure of the input vector is formed in the competitive layer, and unsupervised clustering of the input vector is performed.
Here, the feature map indicates a network composed of neuron groups and edges connecting them.

Kohonen's self-organizing map, which is a representative method of competitive neural networks, has a limited classification ability because it determines the number of neurons in advance and forms a feature map. For this reason, it is difficult to cope with additional learning in which classes to be learned increase during learning (see Non-Patent Document 1).
Further, each time an input vector is given, the reference vector of each neuron is updated, so that the reference vector possessed by the neuron corresponding to the input vector given in the past is gradually destroyed.

On the other hand, the technique disclosed in Non-Patent Document 2 addresses these problems by proliferating neurons as necessary during learning.
Hereinafter, learning by Self-Organizing Incremental Neural Network (hereinafter referred to as “SOINN”), which is a technique disclosed in Non-Patent Document 2, will be briefly described.

  The SOINN has a two-layer network structure and performs the same learning process in the first layer and the second layer. SOINN uses the learning result, which is the output of the first layer, as an input vector to the second layer.

FIG. 16 is a flowchart for explaining learning processing by SOIN which is a conventional technique. Hereinafter, the SOIN process will be described with reference to FIG.
S101: An input vector is given to SOINN.
S102: Search for a node closest to the given input vector (hereinafter referred to as a first winner node) and a second closest node (hereinafter referred to as a second winner node).
S103: Based on the similarity threshold of the first winner node and the second winner node, it is determined whether or not the input vector belongs to the same cluster as at least one of these winner nodes.
Here, the node similarity threshold is calculated based on the idea of the Voronoi region. In the learning process, the position of the node gradually changes to approximate the distribution of the input vector, and the Voronoi region also changes accordingly. That is, the similarity threshold value adaptively changes according to the change in the position of the node.

S104: If the result of determination in S103 is that the input vector belongs to a different cluster from the winner node, the node is inserted at the same position as the input vector, and the process proceeds to S101 to process the next input vector.
This insertion is called interclass insertion.
S105: On the other hand, when the input vector belongs to the same cluster as the winner node, an edge is generated between the first winner node and the second winner node, and the nodes are directly connected by the edge.
S106: Update the weight vectors of the first winner node and the nodes directly connected to the first winner node by edges.

S107: The edge generated in S105 has an age, and an edge having an age exceeding a preset threshold is deleted.
In online learning in which input vectors are given sequentially, the position of the node always changes gradually, so that the adjacency constructed by the initial learning may not be established by subsequent learning. For this reason, a side that is not updated even after a certain period of time is configured so that the age of the side becomes high, thereby deleting a side that is not necessary for learning.

S108: It is determined whether the total number of inputs of the input vector is a preset multiple of λ.
As a result of the determination, if the total number of input vectors is not a multiple of λ, the process returns to S101 to process the next input vector.
On the other hand, when the total number of input vectors is a multiple of λ, the following processing is executed.

S109: A node having the largest local accumulated error is searched, and a new node is inserted in the vicinity of the node. It is determined whether or not the node insertion is successful based on the error radius indicating the average error of the node.
This insertion is called intra-class insertion.
Here, the local accumulated error is calculated by accumulating the error of the node according to the input of the input vector as the error of the node, which is the distance difference between the node and the input vector. The error radius is calculated based on the error of the node and the number of times the node has become the first winner.

S110: When it is determined that the node insertion by the intra-class insertion is successful, the node inserted by the intra-class insertion and the node having the maximum local accumulated error are directly connected by the edge.
On the other hand, if it is determined that node insertion by intra-class insertion has failed, the node inserted by intra-class insertion is deleted, and the process proceeds to S111.

S111: The noise node is deleted based on the number of adjacent nodes and the number of times the node becomes the first winner.
Here, the adjacent node indicates a node that is directly connected to the node by a side, and a node whose number of adjacent nodes is 1 or less is a deletion target. Also, the cumulative number of times of becoming the first winner is compared with a threshold value calculated using a preset parameter c, and a node whose first winner cumulative number is less than the threshold value is targeted for deletion.

S112: It is determined whether or not the total number of inputs of the input vector is a preset multiple of LT.
If it is determined that the total number of input vectors is not a multiple of LT, the process returns to S101 to process the next input vector.
On the other hand, when the total number of input vectors is a multiple of LT, the following processing is executed.

S113: It is determined whether or not learning for the first layer is to be ended.
As a result of the determination, when the process proceeds to the learning of the second layer, the process proceeds to S101, and the node that is the learning result of the first layer is input as an input vector to the second layer.
However, when additional learning is performed, the previous learning result remaining in the second layer is deleted, and then the second layer learning is started.

When the number of inputs to the second layer is a multiple of the preset number of times LT and the learning of the second layer is completed, the nodes are classified into different classes and the number of classes and representative prototype vectors for each class are output. Then stop.
Here, the prototype vector corresponds to a node weight vector.

In this way, SOIN, which is a technique disclosed in Non-Patent Document 2, can learn non-stationary inputs by autonomously managing the number of nodes, and can be used for classes having a complicated shape in the distribution. However, it has many advantages such as the ability to extract the appropriate number of classes and phase structure. As an application example of SOIN, for example, in pattern recognition, after learning a hiragana character class, it is possible to additionally learn a katakana character class.
T. Kohonen, "Self-organized formation of topologically correct feature maps," Biol. Cybern, vol.43, No.1 pp.59-69, Jan 1982 F.Shen and O.Hasegawa, "An incremental network for on-line unsupervised classification and topology learning," Neural Networks, Vol.19, No.1, pp.90-106, 2006

However, in SOINN, when a plurality of classes to which input vectors belong are close to each other and learning data in which high-density input vector distributions exist between classes is learned, different classes are connected to form one cluster. To do.
Although SOIN attempts to solve this problem by performing learning using a two-layer network structure, there is a problem that classes cannot be separated properly when the distribution overlap is high.

  As a specific example, a case is assumed in which an overlapping portion A of the input vector distribution exists between two classes, class 1 and class 2, as shown in FIG. Although SOIN can properly separate two classes when the overlap of such distribution is low density, it cannot be separated when the overlap is high, and multiple classes are connected. One cluster is formed. That is, two classes, class 1 and class 2, are mistakenly connected to form one cluster.

In general, with respect to the input vector of learning data, there are a large number of input vectors in the center region of the class, and they decrease as they approach the boundary region of the class. For this reason, the class can be separated by setting the region where the density of the input vector distribution of the learning data is lower than the predetermined threshold as the class boundary.
However, if there is a high-density input vector distribution overlap between different classes, there is a considerable amount of learning data even in the class boundary region. The class cannot be easily separated.
Further, even if a solution is attempted by simply setting the threshold value to a large value, there is a possibility that an area that is not originally a class boundary may be determined as a boundary area, resulting in a problem that the learning result is not stable.

  On the other hand, by providing the nodes with a density, it is possible to estimate the density of the distribution of the input vectors included in the learning data. Define the density of nodes by the number of input vectors given locally. That is, when many input vectors are given near the node of interest, the density of the input vector distribution in the learning data near the node is considered to be high, and almost no input vector is given near the node of interest. In this case, it is considered that the density of the input vector distribution in the learning data near the node is low.

For this reason, in a competitive neural network including SOINN, the number of winners, which is the number of times a node has become the first winner node, is defined as the node density.
However, although the conventional definition of node density based on the number of winners is a natural definition, there are the following problems.
As a first problem, since a large number of nodes are generally inserted in a region where the distribution of input vectors is high, there is little chance that the node becomes the first winner node in such a region. That is, there is a problem that the number of winners is not always increased as the node is located in a higher density area.
As a second problem, when additional learning is performed, the node generated in the previous learning often does not become the first winner node. That is, there is a problem that the number of times that the node generated in the previous learning is the winner by the additional learning is relatively small, and the result obtained in the previous learning is adversely affected.

  Thus, using the node density based on the number of winners in the past is insufficient to detect the overlapping area of distribution that can be a class boundary. Can not be separated.

  Furthermore, SOIN requires a two-layer network structure to effectively remove noise data contained in the input vector. For this reason, with the extension to the two-layer network structure, it is necessary to determine the end of the learning process in the first layer, and additional learning cannot be realized completely online. That is, there is a problem that noise data cannot be efficiently removed by the one-layer structure.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and a first object of the present invention is to provide an information processing apparatus, an information processing method, and a program that can separate classes having high-density distribution overlap. And
Furthermore, a second object is to provide an information processing apparatus, an information processing method, and a program that can efficiently remove noise data.

  The information processing apparatus according to the present invention has a structure of at least one layer in which nodes described by multidimensional vectors are arranged, sequentially inputs input vectors belonging to an arbitrary class, and inputs distribution of the input vectors In an information processing apparatus that learns the number of classes and the phase structure as a structure, a node having a weight vector closest to the input vector to be input is a first winner node, and a node having a weight vector closest to the second is a second winner When a side is connected between the first winner node and the second winner node, based on the node of interest and the average distance between the node of interest and the node directly connected by the side, Node density calculation means for calculating the node density of the node of interest, and a cluster that is a set of nodes connected by edges A distribution overlapping area detecting means for dividing the sub-cluster which is a subset of the cluster based on the node density calculated by the calculating means and detecting an overlapping area of the distribution which is a boundary of the sub-cluster; the first winner node; When the second winner node is a node located in the distributed overlap area, an edge is formed between the first winner node and the second winner node based on the node density of the first winner node and the second winner node. Based on the determination result, on the basis of the determination result, on the basis of the determination result, on the basis of the determination result, on the side connection means for connecting an edge between the first winner node and the second winner node And an edge deleting means for deleting an edge between the first winner node and the second winner node.

As described above, according to the node density calculated by the node density calculating means, it is possible to estimate the degree of congestion of the node in a certain range of area including the node.
As a result, even if the node is located in a high-density area, the input distribution density of the input vector is approximated compared to the conventional case where the node density is the number of times the node has reached the first winner count. The node density that is the density can be calculated.
Then, the overlapping area of the distribution is detected based on the node density calculated by the node density calculating means, and it is determined whether or not an edge is connected between the first winner node and the second winner node located in the overlapping area of the distribution. By doing so, it is possible to prevent clusters generated from different classes from being connected to each other, and to properly separate the connected clusters even if they are mistakenly connected as one cluster Can do.

  An information processing apparatus that has at least one layer structure in which nodes described by multidimensional vectors are arranged, sequentially inputs input vectors belonging to an arbitrary class, and learns an input distribution structure of the input vectors , The node having the weight vector closest to the inputted input vector is the first winner node, the node having the second closest weight vector is the second winner node, and the first winner node and the second winner node A node density calculation means for calculating a node density of the node of interest based on an average distance between the node of interest and a node directly connected by the edge when the edge is connected between The node of interest is directly determined by the node density calculated by the node density calculating means and the node and edge of interest. Based on the number of connected nodes, but with a noise node deleting means for deleting the node to the attention.

As described above, according to the node density calculated by the node density calculating means, it is possible to estimate the degree of congestion of the node in a certain range of area including the node.
As a result, even if the node is located in a high-density area, the input distribution density of the input vector is approximated compared to the conventional case where the node density is the number of times the node has reached the first winner count. The node density that is the density can be calculated.
Then, by deleting the node of interest based on the node density calculated by the node density calculating unit and the number of nodes directly connected to the node by the side, the noise node can be efficiently deleted. .

  Furthermore, weight vector updating means for updating the weight vector corresponding to the first winner node and the weight vector corresponding to the node directly connected to the first winner node by an edge so as to be closer to the input vector, respectively. You may make it provide further.

  Accordingly, the weight vector corresponding to the first winner node and the weight vector corresponding to the node directly connected to the first winner node by the edge can be updated so as to be closer to the input vector, respectively.

  Furthermore, for the node of interest, noise node deletion that deletes the node of interest based on the node density calculated by the node density calculation means and the number of nodes directly connected to the node of interest by the side You may make it further provide a means.

  Thus, the noise node can be deleted more efficiently by deleting the node based on the node density calculated by the node density calculating means and the number of nodes directly connected to the node by the side. it can.

  Further, the node density calculating means calculates the node density of the first winner node based on an average distance between the first winner node and the first winner node and a node directly connected by an edge. You may make it have a unit node density calculation part calculated as a ratio per.

As described above, the node density can be calculated as the node density of the node per unit input after reflecting the density of the nodes.
As a result, even when additional learning is performed for a long time, the node density of the node can be prevented from becoming relatively small, and the input distribution density of the input vector is approximated compared to the conventional method. The calculated node density can be held and calculated without change.

  Further, the node density calculation means calculates a node density point value of the first winner node based on an average distance between the first winner node and the first winner node and a node directly connected by an edge. The node density point calculation unit to calculate, and the node density points are accumulated until the input number of the input vector reaches a predetermined unit input number, and when the input number of the input vector reaches the predetermined unit input number, A unit node density point calculation unit that calculates the accumulated node density point as a ratio per unit input number and calculates the node density of the node per unit input number may be provided.

Thus, the node density can be calculated as a point reflecting the degree of congestion of the node, and can be calculated as a node density point of the node per unit input number.
As a result, even when additional learning is performed for a long time, the node density of the node can be prevented from becoming relatively small, and the input distribution density of the input vector is approximated compared to the conventional method. The calculated node density can be held and calculated without change.

  Furthermore, the input vector may be input to a neural network, and a self-propagating neural network that automatically increases the nodes arranged in the neural network based on the input vector that is input may be used.

  In this way, by automatically increasing the number of nodes, it is not limited to a stationary environment in which input vectors are randomly given from the input vector space. For example, the class to which the input vector belongs is switched every fixed period. It is possible to deal with a non-stationary environment in which input vectors are randomly given from these classes.

  In addition, when there is a node that is directly connected to the target node by a side with respect to the target node, the node having the maximum distance from the target node among the directly connected nodes If there is no node that is directly connected to the node of interest by a side, the distance between the nodes with the smallest distance from the node of interest is used as the similarity threshold. A similarity threshold calculating means for calculating, whether a distance between the input vector and the first winner node is greater than a similarity threshold of the first winner node, and between the input vector and the second winner node Similarity threshold determination means for determining whether the distance is greater than the similarity threshold of the second winner node, and based on the similarity threshold determination result, the input vector is determined as a node A node insertion means for inserting in the same position as the input vector and may further comprise a.

Thus, the number of nodes can be managed autonomously by determining the insertion of a node based on the similarity threshold.
As a result, the present invention is not limited to a stationary environment in which input vectors are randomly given from the input vector space. For example, the class to which the input vector belongs is switched at regular intervals, and the input vector is randomly given from the switched class. While being able to cope with a stationary environment, additional learning can be performed to additionally learn new classes that are needed in such a non-stationary environment.

  Furthermore, the self-propagating neural network may have a single layer structure.

As described above, the single-layer structure allows additional learning to be performed without specifying the timing for starting learning of the second layer. That is, complete online additional learning can be performed.
Compared with the technique disclosed in Non-Patent Document 2, the number of parameters designated in advance for learning can be reduced, and learning can be performed more easily.

Furthermore, the distribution overlap area detection means, based on the node density calculated by the node density calculation means, a node search unit for searching for a node having a locally maximum node density,
For the searched node, a first label assigning unit that assigns a label different from a label that has already been assigned to another node, and a node that has not been given a label by the first label assigning unit, A second label assigning unit that assigns the same label as the node of the node to which the label is assigned by the first label assigning unit with respect to the node connected by the side to the node to which the label is given by the first label assigning unit A cluster dividing unit that divides a cluster, which is a set of nodes connected by edges, into sub-clusters, which are subsets of clusters composed of nodes with the same label, a node of interest, and the node and edge of interest If the nodes directly connected to each other belong to different sub-clusters, That a region including a node which is directly connected by nodes and edges, may have a distribution overlapping area detection unit detects as the overlapped area of the distribution which is the boundary of the sub-cluster.

  In this way, even if it is difficult to detect by dividing the cluster into sub-clusters based on the node where the node density is locally maximum, simply detecting the low density area as the cluster boundary Thus, it is possible to appropriately detect the overlapping region of the distribution that is the boundary of the subcluster.

  An information processing method according to the present invention has a structure of at least one layer in which nodes described by multidimensional vectors are arranged, and sequentially inputs input vectors belonging to an arbitrary class, and the input distribution of the input vectors In the information processing method for learning a structure, a node having a weight vector closest to the input vector to be input is a first winner node, a node having a weight vector closest to the second is a second winner node, and the first winner is When a side is connected between a node and the second winner node, the node density of the target node is determined based on the average distance between the target node and the target node and the node directly connected by the side. The node density calculation step to calculate and a cluster which is a set of nodes connected by edges are calculated by the node density calculation means. A distributed overlap area detecting step of dividing a sub-cluster which is a subset of the cluster based on a node density and detecting an overlap area of the distribution which is a boundary of the sub-cluster, the first winner node and the second winner node Whether or not an edge is connected between the first winner node and the second winner node based on the node density of the first winner node and the second winner node An edge connection determining step for determining the edge, an edge connecting step for connecting an edge between the first winner node and the second winner node based on the determination result, and the first winner based on the determination result A side deleting step of deleting a side between the node and the second winner node.

  The program according to the present invention causes a computer to execute information processing as described above.

ADVANTAGE OF THE INVENTION According to this invention, the information processing apparatus, the information processing method, and program which can isolate | separate the class with a high-density distribution overlap can be provided.
Furthermore, an information processing apparatus, an information processing method, and a program that can efficiently remove noise data can be provided.

Embodiment 1 of the Invention
FIG. 2 is a diagram illustrating an example of a system configuration for realizing the information processing apparatus according to the first embodiment. The information processing apparatus can be realized by a computer such as a dedicated computer or a personal computer (PC). However, the computer does not need to be physically single, and a plurality of computers may be used when performing distributed processing. As shown in FIG. 2, the computer 10 includes a CPU 11 (Central Processing Unit), a ROM 12 (Read Only Memory), and a RAM 13 (Random Access Memory), which are connected to each other via a bus 14. Although explanation of OS software for operating the computer is omitted, it is assumed that a computer for constructing the information processing apparatus is also provided.

  An input / output interface 15 is also connected to the bus 14. The input / output interface 15 includes, for example, an input unit 16 including a keyboard, a mouse, and a sensor, a display including a CRT and an LCD, an output unit 17 including headphones and speakers, a storage unit 18 including a hard disk, A communication unit 19 including a modem and a terminal adapter is connected.

  The CPU 11 performs various processes according to various programs stored in the ROM 12 or various programs loaded from the storage unit 18 to the RAM 13. In this embodiment, for example, in the node density calculation unit 27 and the distribution overlap region detection unit 28. Execute the process. The RAM 13 also appropriately stores data necessary for the CPU 11 to execute various processes.

  The communication unit 19 performs, for example, communication processing via the Internet (not shown), transmits data provided from the CPU 11, and outputs data received from the communication partner to the CPU 11, the RAM 13, and the storage unit 18. The storage unit 18 exchanges with the CPU 11 to save and erase information. The communication unit 19 also performs communication processing of analog signals or digital signals with other devices.

  The input / output interface 15 is also connected to the drive 20 as necessary. For example, a magnetic disk 201, an optical disk 202, a flexible disk 203, or a semiconductor memory 204 is appropriately mounted, and a computer program read from them is required. Is installed in the storage unit 18 according to

  Subsequently, each process in the information processing apparatus 1 according to the present embodiment will be described with reference to a functional block diagram shown in FIG. In terms of hardware, each processing is actually realized by cooperation of software and hardware resources such as the CPU 11.

The information processing apparatus 1 includes a neural network having a structure of at least one layer in which nodes described by n-dimensional vectors are arranged, and includes an input information acquisition unit 21, a winner node search unit 22, a similarity threshold calculation unit 23, Similarity threshold determination means 24, node insertion means 25, weight vector update means 26, node density calculation means 27, distribution overlap area detection means 28, edge connection determination means 29, edge connection means 30, edge deletion means 31, noise node deletion Means 32, class determination means 33, and output information display means 34 are included.
Note that the information processing apparatus according to the present embodiment further includes a node density calculation unit 27, a distribution overlap region detection unit 28, an edge connection determination unit 29, an edge, as compared with the SOIN disclosed in Non-Patent Document 2. The connecting means 30, the edge deleting means 31, and the noise node deleting means 32 are included.
According to the node density calculation means 27, the distribution overlap area detection means 28, the edge connection determination means 29, the edge connection means 30, and the edge deletion means 31, it is possible to separate classes having a high density overlap in the distribution.
Furthermore, according to the node density calculation unit 27 and the noise node deletion unit 32, the noise node can be deleted efficiently.
This will be described in more detail below.

  In the present embodiment, the neural network constituting the information processing apparatus 1 inputs an input vector to the neural network, and automatically increases the number of nodes arranged in the neural network based on the input vector that is input. This will be described below as a type neural network having a one-layer structure.

As a result, the number of nodes can be automatically increased using a self-propagating neural network, so that the present invention is not limited to a stationary environment in which input vectors are randomly given from the input vector space. It is possible to cope with a non-stationary environment in which the class to which the input belongs is switched and an input vector is randomly given from the switched class.
Furthermore, by adopting a single-layer structure, additional learning can be performed without specifying the timing for starting learning of the second layer. That is, complete online additional learning can be performed.
Further, compared with SOIN, the number of parameters specified in advance for learning can be reduced, and learning can be performed more easily.

  The input information acquisition unit 21 acquires an n-dimensional input vector belonging to an arbitrary class as information given as an input to the information processing apparatus 1. Then, the acquired input vector is stored in a temporary storage unit (for example, the RAM 13), and sequentially input to the neural network stored in the temporary storage unit.

The winner node search means 22 uses the input vector and the node stored in the temporary storage unit as the first winner node with the node having the weight vector closest to the input vector as the second winner. Search as a node, and store the result in a temporary storage unit.
That is, for the n-dimensional input vector ξ, nodes satisfying the following expressions stored in the temporary storage unit are searched as the first winner node a ₁ and the second winner node a ₂ respectively, and the result is temporarily stored. Store in the storage.
Here, a is a node included in the node set A stored in the temporary storage unit, and W _a is a weight vector of the node a stored in the temporary storage unit.

The similarity threshold value calculation means 23 is a node directly connected by a node to which attention is paid and a side (hereinafter referred to as an adjacent node) with respect to the node of interest with respect to the node and node similarity threshold value stored in the temporary storage unit. If there is an adjacent node, the distance to the node having the maximum distance from the node of interest among the adjacent nodes is calculated as a similarity threshold, and the result is stored in the temporary storage unit. Calculates the distance to the node having the smallest distance from the node of interest as the similarity threshold, and stores the result in the temporary storage unit.
Specifically, for example, the similarity threshold value of the node of interest is calculated as follows, and the result is stored in the temporary storage unit.
S201: The similarity threshold calculation means 23 sets the similarity threshold T _i of the node i newly inserted and stored in the temporary storage unit to + ∞ (a sufficiently large value), and stores the result in the temporary storage unit.
S202: For the node stored in the temporary storage unit, when the node i is the closest node or the second closest node from the input vector, it is determined whether or not the node i has an adjacent node, and the result is Store in the temporary storage.
S203: As a result of the determination stored in the temporary storage unit, if there is an adjacent node, the similarity threshold T _i is set as the maximum distance to the adjacent node for the similarity threshold and the node stored in the temporary storage unit, Store the result in the temporary storage.
That is, for the node i, the similarity threshold value T _i is calculated based on the following expression stored in the temporary storage unit, and the result is stored in the temporary storage unit.
Here, c is a node included in the adjacent node set N _i of the node i stored in the temporary storage unit, and W _c indicates a weight vector of the node c stored in the temporary storage unit.
S204: If there is no adjacent node as a result of the determination, the distance from the node i to each of the other nodes excluding the node i is calculated, and the minimum distance among the calculated distances is set as the similarity threshold T _i . To do.
That is, for the node i, the similarity threshold value T _i is calculated based on the following expression stored in the temporary storage unit, and the result is stored in the temporary storage unit.

The similarity threshold determination means 24 has a distance between the input vector and the first winner node greater than the similarity threshold of the first winner node with respect to the input vector, the node, and the node similarity threshold stored in the temporary storage unit. And whether or not the distance between the input vector and the second winner node is larger than the similarity threshold of the second winner node, and the result is stored in the temporary storage unit.
That is, as shown in the following expression stored in the temporary storage unit, it is determined whether or not the distance between the input vector ξ and the first winner node a ₁ is larger than the similarity threshold T _a1, and the result is temporarily stored. While storing in the storage unit, it is determined whether or not the distance between the input vector ξ and the second winner node a ₂ is larger than the similarity threshold value _{Ta 2,} and the result is stored in the temporary storage unit.

  Based on the determination result by the similarity threshold determination unit 24 stored in the temporary storage unit, the node insertion unit 25 uses the input vector stored in the temporary storage unit as a new node and has the same position as the input vector. The result is stored in the temporary storage unit.

The weight vector updating unit 26 updates the weight vector of the first winner node and the weight vector of the adjacent node of the first winner node so that the weight vector of the node stored in the temporary storage unit is closer to the input vector. The result is stored in the temporary storage unit.
Update amount [Delta] W _ai of the weight vectors of the neighboring node i of the update amount [Delta] W _a1, and the first winning node a ₁ of the first weight vector of the winning node a ₁ is, for example, based on the following equation that is stored in the temporary storage unit Calculate and store the result in the temporary storage.
Here, ε ₁ (t) and ε ₂ (t) are respectively calculated based on the following formulas stored in the temporary storage unit, and the results are temporarily stored in 100 million copies.
In the present embodiment, in order to cope with additional learning, instead of the input vector input count t, the cumulative count M in which the first winner node a ₁ stored in the temporary storage unit becomes the first winner node. _{Use a1} .

The node density calculating means 27 calculates the node density of the node of interest based on the average distance between the adjacent nodes for the node of interest and the node stored in the temporary storage unit, and temporarily calculates the result. Store in the storage.
Further, the node density calculating unit 27 includes a unit node density calculating unit, and the unit node density calculating unit corresponds to the additional learning, and therefore, the first winner node and the node density stored in the temporary storage unit are Based on the average distance between the winner node and its adjacent nodes, the node density of the first winner node is calculated as a ratio per unit input number, and the result is stored in the temporary storage unit.
Furthermore, the node density calculation means 27 calculates the node density point value of the first winner node based on the average distance between the first winner node and its adjacent nodes for the nodes and node density points stored in the temporary storage unit. A node density point calculation unit that calculates the number of input vectors, and the node density points are stored and accumulated in a temporary storage unit until the number of inputs of the input vector reaches a predetermined number of unit inputs. In this case, the node density points stored and accumulated in the temporary storage unit are calculated as a ratio per unit input number, the node density of the node per unit input number is calculated, and the result is stored in the temporary storage unit A unit node density point calculation unit.

Specifically, the node density point calculation unit calculates a node density point value p _i given to the node i based on, for example, the following expression stored in the temporary storage unit, and stores the result in the temporary storage unit: To do. The point value p _i given to the node i is given a point value calculated based on the following formula stored in the temporary storage unit when the node i becomes the first winner node. If i is not the first winner node, no points are given to node i.
Here, e _i represents an average distance from the node i to the adjacent node, is calculated based on the following expression stored in the temporary storage unit, and the result is stored in the temporary storage unit.

Incidentally, m represents the number of neighbor nodes of node i that are stored in the temporary storage unit, W _i represents the weight vector of node i that are stored in the temporary storage unit.

Here, when the average distance to the adjacent node is large, it is considered that there are few nodes in the area including the node. Conversely, when the average distance is small, the area has many nodes. it is conceivable that.
Therefore, the node density points so that a high point is awarded when the first winner node is reached in a region with many nodes, and a low point is awarded when the first winner node is found in a region with few nodes. The value calculation method is configured as described above.
As a result, it is possible to estimate the density of nodes in a certain area including the nodes, so even if the nodes are located in a high-density area, the number of nodes is the first winner. Compared with the conventional case where the number of times is a node density, a node density point that is a density approximated by the input distribution density of the input vector can be calculated.

The unit node density point calculation unit calculates the node density density _i per unit input number of the node i based on, for example, the following expression stored in the temporary storage unit, and stores the result in the temporary storage unit.
Here, the number of inputs of consecutively given input vectors is divided into sections for each predetermined number of inputs λ that are set in advance and stored in the temporary storage unit, and the sum of points given to node i in each section is accumulated. It is defined as point s _i . When the total number of input vectors is set to LT that is preset and stored in the temporary storage unit, LT / λ is set to the total number n of sections, and the result is stored in the temporary storage unit. The number of sections in which the total of given points is 0 or more is calculated as N, and the result is stored in the temporary storage unit (note that N and n are not necessarily the same).
The accumulated points s _i are calculated based on, for example, the following expression stored in the temporary storage unit, and the result is stored in the temporary storage unit.
Here, p _i ^{(j, k)} indicates a point given to the node i by the k-th input in the j-th section, is calculated by the node density point calculation unit described above, and the result is stored in the temporary storage unit. To do.
As described above, the unit node density point calculation unit calculates the density density _i of the node i stored in the temporary storage unit as an average of the accumulated points s _i and stores the result in the temporary storage unit.

In this embodiment, N is used instead of n in order to cope with additional learning. This is because, in additional learning, points are often not given to nodes generated by previous learning, and when n is used to calculate the density, the previously learned node density gradually decreases. This is to avoid it. That is, by calculating the node density using N instead of n, even if additional learning is performed for a long time, as long as the added data is not input near the previously learned node, that node Can be maintained without changing the density.
As a result, even when additional learning is performed for a long time, the node density of the node can be prevented from becoming relatively small, and the input distribution density of the input vector is approximated compared to the conventional method. The calculated node density can be held and calculated without change.

  The distribution overlap area detection means 28 calculates a cluster, which is a set of nodes connected by edges, with respect to the nodes stored in the temporary storage unit, the edges connecting the nodes, and the node density. Is divided into sub-clusters that are a subset of the cluster based on the node density, the result is stored in the temporary storage unit, the overlapping area of the distribution that is the boundary of the sub-cluster is detected, and the result is stored in the temporary storage unit Store.

  Further, the distribution overlap area detection unit 28 determines the node density based on the node density calculated by the node density calculation unit 27 for the node stored in the temporary storage unit, the side connecting the nodes, and the node density. A node search unit that searches for a node that is locally maximum, a first label assigning unit that assigns a label different from labels already assigned to other nodes to the searched node, and a first label The second label assignment that assigns the same label as the node of the node to which the label is assigned by the first label assignment unit for the nodes that are connected by the side among the nodes that have not been given the label by the assignment unit. Set of nodes connected by a side when there is a direct connection between the part and a node with a different label A cluster dividing unit that divides a cluster into sub-clusters that are subsets of the cluster, and when the node of interest and its neighboring nodes belong to different sub-clusters, the region including the node of interest and its neighboring nodes is It has a distribution overlap area detection unit that detects a distribution overlap area as a cluster boundary.

Specifically, for the nodes stored in the temporary storage unit, the edges connecting the nodes, and the density of the nodes, for example, the overlapping area of the distribution that is the boundary of the sub-cluster is detected as follows, and the result is Store in the temporary storage.
S301: The node search unit searches for a node whose node density is locally maximum based on the node density calculated by the node density calculation unit 27 for the node and the node density stored in the temporary storage unit, The result is stored in the temporary storage unit.
S302: The first label assigning unit assigns a label different from a label already assigned to another node to the node searched in S301 for the node and the node label stored in the temporary storage unit. The result is stored in the temporary storage unit.
S303: The second label assigning unit is the node stored in the temporary storage unit, the side connecting the nodes, and the label of the node. For the node that has not been given a label by the first label assigning unit in S302, For the node connected by the side and the node to which the label is assigned to the first label giving unit, the same label as the label of the node to which the label is given by the first label giving unit is given, and the result is temporarily stored To store. That is, the same label as the adjacent node having the locally maximum density is assigned.
S304: The cluster dividing unit uses the same cluster, which is a set of nodes connected by the sides stored in the temporary storage unit, for the nodes stored in the temporary storage unit, the sides connecting the nodes, and the labels of the nodes. The data is divided into sub-clusters that are a subset of the cluster composed of nodes to which labels are assigned, and the results are stored in the temporary storage unit.
S305: The distribution overlap area detection unit, when the node stored in the temporary storage unit, the side connecting the nodes, and the label of the node belong to different subclusters, respectively, An area including the node to be processed and its adjacent nodes is detected as an overlapping area of the distribution that is the boundary of the sub-cluster, and the result is stored in the temporary storage unit.

  The edge connection determination means 29 determines the first winner when the first winner node and the second winner node are nodes located in the distribution overlap area with respect to the node, node density, and distribution overlap area stored in the temporary storage unit. Based on the node density of the node and the second winner node, it is determined whether or not an edge is connected between the first winner node and the second winner node, and the result is stored in the temporary storage unit.

  Further, the edge connection determination unit 29 includes a sub-cluster determination unit that determines a sub-cluster to which the node belongs, and a vertex of the sub-cluster to which the node belongs, for the node, node density, and node sub-cluster stored in the temporary storage And an edge connection determination unit for determining whether to connect an edge between the first winner node and the second winner node based on the density of the node and the density of the node.

The edge connecting means 30 is based on the determination result of the edge connection determining means 29 stored in the temporary storage section, and between the first winner node and the second winner node for the nodes stored in the temporary storage section and the edges between the nodes. The sides are connected to and the result is stored in the temporary storage unit.
The edge deleting means 31 is based on the determination result of the edge connection determining means 29 stored in the temporary storage section, and between the first winner node and the second winner node for the nodes stored in the temporary storage section and the edges between the nodes. Are deleted, and the result is stored in the temporary storage unit.

Specifically, for the nodes, node density, node sub-clusters, and sides between nodes stored in the temporary storage unit, for example, the side connection determination unit 29 determines whether to connect the sides as follows. The edge connecting means 30 and the edge deleting means 31 perform edge generation and deletion processing and store the results in the temporary storage unit.
S401: The belonging sub-cluster determining unit determines the sub-cluster to which the first winner node and the second winner node belong for each of the nodes and node sub-clusters stored in the temporary storage unit, and stores the result in the temporary storage unit. To do.
S402: As a result of the determination in S401 stored in the temporary storage unit, when the first winner node and the second winner node do not belong to any subcluster, or the first winner node and the second winner node are the same subcluster The edge connecting means 30 connects the nodes by generating an edge between the first winner node and the second winner node for the node and the edge between the nodes stored in the temporary storage unit. The result is stored in the temporary storage unit.
S403: As a result of the determination in S401 stored in the temporary storage unit, if the first winner node and the second winner node belong to different sub-clusters, the edge connection determination unit, the node stored in the temporary storage unit, For node density and edges between nodes, determine whether to connect edges between the first winner node and the second winner node based on the density of the vertices of the subcluster to which the node belongs and the density of the node, and Store the result in the temporary storage.
S404: If the result of determination by the side connection determination unit in S403 stored in the temporary storage unit determines that there is no need to connect the sides, the node stored in the temporary storage unit and the sides between the nodes are When the first winner node and the second winner node are not connected by an edge and the nodes are already connected by an edge, the edge deleting unit 31 determines the nodes stored in the temporary storage unit and the edges between the nodes. The edge between the first winner node and the second winner node stored in the temporary storage unit is deleted, and the result is stored in the temporary storage unit.
S405: If it is determined that the sides need to be connected as a result of the determination by the side connection determination unit in S403 stored in the temporary storage unit, the side connection unit 30 stores the nodes and nodes stored in the temporary storage unit. For the edges in between, edges are generated between the first winner node and the second winner node to connect the nodes.

Here, the determination process by the edge connection determination unit will be described in detail.
First, the edge connection determination unit determines the minimum node density m among the node density density _win and the second winner node density density _sec-win of the first winner node for the node and node density stored in the temporary storage unit, for example. Calculation is performed based on the following expression stored in the temporary storage unit, and the result is stored in the temporary storage unit.
Next, with regard to the nodes stored in the temporary storage unit, the node density of the nodes, and the subclass of the nodes, the subcluster A and the subcluster B to which the first winner node and the second winner node belong respectively, The density A _max and the density B _max of the vertices of the sub-cluster B are calculated, and the result is stored in the temporary storage unit.
Of the nodes included in the subcluster, the node density having the highest node density is defined as the density of the vertices of the subcluster.
Then, regarding the density A _max and B _max of the vertices of the subcluster to which the node stored in the temporary storage unit belongs, and the density m of the node, m is smaller than α _A A _max and m is smaller than α _B B _max. And the result is stored in the temporary storage unit. That is, it is determined whether or not the following inequality stored in the temporary storage unit is satisfied, and the result is stored in the temporary storage unit.
As a result of the determination, when m is smaller than α _A A _max and m is smaller than α _B B _max , the first winner node and the second winner are determined for the node and the edge between the nodes stored in the temporary storage unit. It is determined that no edge is required between the nodes, and the result is stored in the temporary storage unit.
On the other hand, as a result of the determination, if m is greater than or equal to α _A A _max or m is greater than or equal to α _B B _max , the first winner node and the first It is determined that an edge is necessary between the two winner nodes, and the result is stored in the temporary storage unit.

Thus, by comparing the minimum node density m of the first winner node and the second winner node with the average node density of the sub-cluster including the first winner node and the second winner node, respectively, the first winner node And the size of the unevenness of the node density in the region including the second winner node can be determined. That is, when the node density m between the valleys of the distribution existing between the sub-cluster A and the sub-cluster B is larger than the threshold value α _A A _max or α _B B _max , the node density shape is determined to be small unevenness. can do.

Here, α _A and α _B are calculated based on the following expressions stored in the temporary storage unit, and the results are stored in the temporary storage unit. Since α _B can be calculated in the same manner as α _A , description thereof is omitted here.
i) When A _max / mean _A −1 ≦ 1, α _A = 0.0.
ii) When 1 <A _max / mean _A −1 ≦ 2, α _A = 0.5.
iii) If 2 <A _max / mean _A -1, then α _A = 1.0.
In the case of i) where the value of A _max / mean _A is 1 or less, the values of A _max and mean _A are similar, and it is determined that the unevenness in density is due to the influence of noise. Then, the sub-cluster is integrated by setting the value of α to 0.0.
When the value of A _max / mean _A exceeds iii), it is determined that A _max is sufficiently larger than mean _A and that there are irregularities with clear density. Then, the sub-cluster is separated by setting the value of α to 1.0.
Then, in the case of ii) where the value of A _max / mean _A is other than the case described above, by setting the value of α to 0.5, the sub-clusters are integrated or separated according to the size of the density unevenness. To be.
Here, mean _A indicates the average value of the node density density _i of the node i belonging to the sub-cluster A, and N _A is calculated based on the following formula stored in the temporary storage unit, where N _A is the number of nodes belonging to the sub-cluster A. The result is stored in the temporary storage unit.

In this way, when separating into sub-clusters, the degree of unevenness of the node density included in the sub-cluster is determined, and two sub-clusters that satisfy a certain standard are integrated into one, thereby overlapping the distribution. It is possible to prevent instability due to excessive division of sub-clusters in area detection.
For example, for the two subclusters A and B shown in FIG. 4, it is assumed that the density of the vertices of the subcluster A is A _max and the density of the vertices of the subcluster B is B _max .
As shown in FIG. 4, many fine irregularities may be formed in the density distribution due to a small amount of noise and learning samples.
In such a case, when the first winner node and the second winner node are located in the overlapping region of the distribution between the sub-clusters A and B, the two that satisfy certain criteria when connecting between the nodes By integrating the sub-clusters into one, the density distribution can be smoothed as shown in FIG. 1 even when the density distribution includes many fine irregularities as shown in FIG. .

  The noise node deletion unit 32 is configured to calculate the node density calculated by the node density calculation unit 27 and the node of interest with respect to the node of interest, the number of nodes, the node density, the sides between the nodes, and the number of adjacent nodes stored in the temporary storage unit Based on the number of adjacent nodes, the node of interest is deleted, and the result is stored in the temporary storage unit.

Further, the noise node deleting unit 32 includes a node density comparison unit that compares the node density of the node of interest with a predetermined threshold for the number of nodes, node density, sides between nodes, and adjacent nodes stored in the temporary storage unit; It has an adjacent node number calculation unit that calculates the number of adjacent nodes of the node of interest, and a noise node deletion unit that deletes the node of interest as a noise node.
Specifically, for example, the nodes, the node density, the sides between the nodes, and the number of adjacent nodes stored in the temporary storage unit as described below are based on the node density and the number of adjacent nodes of the target node. The node to be deleted is deleted, and the result is stored in the temporary storage unit.

The noise node deletion means 32 calculates the number of adjacent nodes by the adjacent node number calculation unit for the node i of interest with respect to the nodes stored in the temporary storage unit, the sides between the nodes, and the number of adjacent nodes, and the result Is stored in the temporary storage unit. Then, the following processing is performed according to the number of adjacent nodes stored in the temporary storage unit.
i) When the number of adjacent nodes stored in the temporary storage unit is 2, the node density comparison unit compares the node density density _i of the node _i with a threshold value calculated based on the following formula stored in the temporary storage unit, for example. The result is stored in the temporary storage unit.
For the comparison result stored in the temporary storage unit, when the node density density _i is smaller than the threshold, the noise node deletion unit deletes the node for the node stored in the temporary storage unit, and the result is stored in the temporary storage unit. To store.
ii) When the number of adjacent nodes stored in the temporary storage unit is 1, the node density comparison unit compares the node density density _i of the node _i with, for example, a threshold value calculated based on the following formula stored in the temporary storage unit. The result is stored in the temporary storage unit.
If the node density density _i is smaller than the threshold for the comparison result stored in the temporary storage unit, the noise node deletion unit deletes the node for the node stored in the temporary storage unit, and temporarily stores the result. Store in the department.
iii) Regarding the number of adjacent nodes stored in the temporary storage unit, when there is no adjacent node, the noise node deletion unit deletes the node for the node stored in the temporary storage unit, and stores the result in the temporary storage unit To do.
Here, by adjusting predetermined parameters c ₁ and c ₂ that are set in advance and stored in the temporary storage unit, the behavior of noise node deletion by the noise node deletion unit 32 can be adjusted.

  The class determination means 33 determines the class to which the node belongs based on the side generated between the nodes, the side between the nodes, and the node class stored in the temporary storage unit, and temporarily stores the result. Store in the department.

Specifically, for the nodes stored in the temporary storage unit, the sides between the nodes, and the node class, for example, the class to which the node belongs is determined as follows, and the result is stored in the temporary storage unit.
S501: With respect to the nodes and node classes stored in the temporary storage unit, all the nodes do not belong to any class, and the result is stored in the temporary storage unit.
S502: For nodes and node classes stored in the temporary storage unit, node i is randomly selected from nodes that do not belong to any class, a new class label is assigned, and the result is stored in the temporary storage unit. To do.
S503: Search for all nodes connected to node i by a path for nodes, edges between nodes, and node classes stored in the temporary storage unit, assign the same label as node i, and temporarily store the result. Store in the storage.
S504: If there is a node that does not belong to any class of nodes and node classes stored in the temporary storage unit, the process proceeds to S502, and processing is performed until class labels are assigned to all nodes. Continue.
Here, that the node a and the node b are connected by a path indicates that two nodes are connected through some sides between the node a and the node b.
That is, for the node a, node b, and node x _i (i = 1, 2,..., N) included in the node set A, the sides between the node a and the node x ₁ are indicated (a, x ₁ ), (X ₁ , x ₂ ) indicating the side between the node x ₁ and the node x ₂ ,..., (X _n , b) indicating the side between the node x _n and the node b exists. In some cases, the node a and the node b are connected by a path.

  The output information display means 34 outputs the number of classes to which the node belongs and the prototype vector of each class for the nodes and node classes stored in the temporary storage unit.

Next, an overall processing flow in the information processing apparatus according to the present embodiment will be described with reference to the flowchart of FIG. FIG. 5 is a flowchart illustrating an outline of a learning process performed by the information processing apparatus according to the present embodiment.
S601: The input information acquisition unit 21 acquires two input vectors at random, initializes the node set A as a set including only two nodes corresponding to them, and stores the result in the temporary storage unit. Also, the edge set C⊂A × A is initialized as an empty set, and the result is stored in the temporary storage unit.
S602: The input information acquisition unit 21 inputs a new input vector ξ and stores the result in the temporary storage unit.
S603: The winner node search means 22 has the first winner node a ₁ having the weight vector closest to the input vector ξ and the second winner having the second closest weight vector for the input vector and node stored in the temporary storage unit. The node a ₂ is searched, and the result is stored in the temporary storage unit.

S604: The similarity threshold determination unit 24 determines that the distance between the input vector ξ and the first winner node a ₁ is the first winner node a ₁ for the input vector, node, and node similarity threshold stored in the temporary storage unit. It is determined whether or not it is greater than the similarity threshold T ₁ and whether the distance between the input vector ξ and the second winner node a ₂ is greater than the similarity threshold T ₂ of the second winner node a ₂ , and the result Is stored in the temporary storage unit.
Here, the similarity threshold T ₂ of the similarity threshold T ₁ and the second winning node a ₂ of the first winning node a ₁ stored in the temporary storage unit, similarity threshold as shown in S201 to S204 described above Calculated by the calculation means 23 and the result is stored in the temporary storage unit.
S605: As a result of the determination in S604 stored in the temporary storage unit, the distance between the input vector ξ and the first winner node a ₁ is greater than the similarity threshold T ₁ of the first winner node a ₁ , or the input vector ξ when the distance between the second winning node a ₂ is greater than the similarity threshold T ₂ of the second winning node a _2, the node insertion means 25, the input vector and node stored in the temporary storage unit, an input vector ξ Is inserted at the same position as the input vector ξ as a new node i, and the result is stored in the temporary storage unit.

S606: On the other hand, as a result of the determination in S604 stored in the temporary storage unit, the distance between the input vector ξ and the first winner node a ₁ is equal to or less than the similarity threshold T ₁ of the first winner node a ₁ and the input When the distance between the vector ξ and the second winner node a ₂ is equal to or less than the similarity threshold T ₂ of the second winner node a ₂ , the edge connection determination unit 29 determines the node and node density stored in the temporary storage unit. for edges between nodes, based on the node density of the first winning node a ₁ and the second winning node a _2, whether to connect the edges between the first winning node a ₁ and the second winning node a ₂ The determination is made, and the result is stored in the temporary storage unit.

S607: As a result of the determination in S606 stored in the temporary storage unit, when the side is generated and connected between the first winner node a ₁ and the second winner node a ₂ , the side connection unit 30 includes the temporary storage unit Are connected between the first winner node and the second winner node, and the result is stored in the temporary storage unit.
Then, the information processing device determines the age of the side and the age of the side stored in the temporary storage unit, the side of the newly generated side, and the side of the side if the side has already been generated between the nodes. The result is set to 0, the result is stored in the temporary storage unit, the age of the side directly connected to the first winner node a ₁ is incremented (increased by 1), and the result is stored in the temporary storage unit.
On the other hand, the result of determination in S606 stored in the temporary storage unit, when not connected to edges between the first winning node a ₁ and the second winning node a _2, although the process proceeds to S608, already between nodes When the side has been generated, the side deletion unit 31 deletes the side between the first winner node a ₁ and the second winner node a ₂ for the node stored in the temporary storage unit and the side between the nodes. The result is stored in the temporary storage unit. In addition, as shown in above-mentioned S401 thru | or S405, the edge connection determination means 29, the edge connection means 30, and the edge deletion means 31 implement a process.
Next, with respect to the node and node density point values stored in the temporary storage unit, for the first winner node a ₁ , the node density calculation means 27 calculates the node density of the first winner node a ₁ stored in the temporary storage unit. By calculating the point value and storing the result in the temporary storage unit, by adding the point value of the node density calculated and stored in the temporary storage unit to the point value previously calculated and stored in the temporary storage unit, Accumulate as node density points and store the result in the temporary storage.
Next, the information processing apparatus increments (accumulates by 1) the cumulative number of times M _a1 at which the first winner node a ₁ stored in the temporary storage unit has become the first winner node, and stores the result in the temporary storage unit.

S608: The weight vector updating means 26 inputs the weight vector of the first winner node a _{1 and} the weight vector of the adjacent node of the first winner node a ₁ for the nodes and node weight vectors stored in the temporary storage unit, respectively. Update it so that it is closer to ξ, and store the result in the temporary storage.
S609: the information processing apparatus, the stored edge in the temporary storage unit, delete the edges with a exceeds a preset threshold age _t stored in the temporary storage unit age, and stores the result in the temporary storage unit . The age _t is used to delete a side that is erroneously generated due to the influence of noise or the like. By setting a small value for age _t , edges can be easily deleted and the effect of noise can be prevented. However, if the value is extremely small, edges are frequently deleted and the learning result becomes unstable. Become. On the other hand, if excessively set to a large value age _t, it can not be removed edges generated by influence of noise appropriately. Taking these into account, the parameter age _t is calculated in advance by experiments and stored in the temporary storage unit.

S610: The information processing apparatus determines whether or not the total number of input vectors ξ stored in the temporary storage unit is a multiple of λ set in advance and stored in the temporary storage unit. And the result is stored in the temporary storage unit. As a result of the determination stored in the temporary storage unit, if the total number of input vectors is not a multiple of λ, the process returns to S602 to process the next input vector ξ.
On the other hand, when the total number of input vectors ξ is a multiple of λ, the following processing is executed.
Note that λ is a period for deleting a node regarded as noise. Although it is possible to frequently perform noise processing by setting a small value to λ, if the value is extremely small, nodes that are not actually noise are erroneously deleted. On the other hand, if an extremely large value is set to λ, a node generated due to noise cannot be removed appropriately. In consideration of these, the parameter λ is calculated in advance through experiments and stored in the temporary storage unit.

S611: The distribution overlap area detection means 28 detects the distribution overlap area that is the boundary of the subcluster as shown in S301 to S305 above for the subcluster and distribution overlap area stored in the temporary storage unit. The result is stored in the temporary storage unit.
S612: The node density calculation unit 27 calculates the node density points stored in the temporary storage unit and accumulated as a ratio per unit input number, stores the result in the temporary storage unit, and stores the node nodes per unit input number. The density is calculated and the result is stored in the temporary storage unit.
S613: The noise node deleting unit 32 deletes a node regarded as a noise node from the nodes stored in the temporary storage unit, and stores the result in the temporary storage unit. In S613, the parameters c ₁ and c ₂ used by the noise node deletion unit 32 are used to determine whether or not the node is regarded as noise. Normally, a node having two adjacent nodes is often not a noise, and therefore c ₁ uses a value close to 0. Further, since a node having the number of adjacent nodes of 1 is often noise, c ₂ is assumed to use a value close to 1, and these parameters are set in advance and stored in the temporary storage unit.
S614: The information processing apparatus determines whether the total number of given input vectors ξ is a preset multiple of LT stored in the temporary storage unit with respect to the total number of input vectors ξ stored in the temporary storage unit. And the result is stored in the temporary storage unit. If the total number of input vectors is not a multiple of LT as a result of the determination stored in the temporary storage unit, the process returns to S602 to process the next input vector ξ.
On the other hand, when the total number of input vectors ξ is a multiple of LT, the following processing is executed.

  S615: The class determination unit 33 performs the above processing on the nodes stored in the temporary storage unit, the sides between the nodes, and the class of the nodes based on the sides generated between the nodes as shown in S501 to S504 above. The class to which the node belongs is determined, and the result is stored in the temporary storage unit. And the output information display means 34 outputs the class number of the class to which the node belongs and the prototype vector of each class for the node and the class of the node stored in the temporary storage unit. After completing the above processing, learning is stopped.

Subsequently, a learning result for input data will be described below as a specific example of the present embodiment.
First, using the artificial data set shown in FIG. 7, a comparative experiment is performed on the conventional technique, SOIN, and the information processing apparatus of the present embodiment.

FIG. 7 is a diagram showing an artificial data set of input vectors used in a comparison experiment between the conventional technique SOIN and the information processing apparatus of the present embodiment.
The artificial data set is constituted by a total of five classes: two Gaussian distributions A and B with overlapping distributions, two concentric circles C and D, and sine curves E1, E2, and E3. In addition, assuming a real-world environment, 10% uniform noise is added to the artificial data set.
FIG. 6 is a table showing an input environment of input vectors from the artificial data set shown in FIG. 7 in a non-stationary environment. In a stationary environment, an input vector is randomly given from the entire artificial data set. In an unsteady environment, the artificial data set is divided into seven regions A, B, C, D, It is assumed that the input environment is divided into E1, E2, and E3, and the input environment is given while switching the input environment at regular intervals according to the table shown in FIG. Experiments in such non-stationary environments are conducted assuming online additional learning.
Experiments using the same artificial data set were performed for the conventional technique, SOINN, and it was shown that 5 classes and topological structures of each class were appropriately output in both stationary and non-stationary environments. Has been.

FIG. 8 is a diagram showing an output result of the information processing apparatus of the present embodiment for the artificial data set shown in FIG.
As shown in FIG. 8, the information processing apparatus according to the present embodiment can appropriately output the five classes and the phase structure of each class in both the stationary environment and the non-stationary environment. That is, the information processing apparatus according to the present embodiment has the same level of learning function as compared with the conventional SOIN.
The parameters set in advance were λ = 100, age _t = 100, c ₁ = 0.001, and c ₂ = 1.0, and these were determined by experiment.

Next, FIG. 9 is a diagram showing an artificial data set of input vectors used in a comparison experiment between the conventional technique SOINN and the information processing apparatus of the present embodiment.
The artificial data set shown in FIG. 9 is composed of three Gaussian distributions with overlapping distributions, and 10% uniform noise is added. The artificial data set shown in FIG. 9 has a higher density of distribution between classes than the artificial data set shown in FIG.
In a stationary environment, input vectors are randomly selected from the entire artificial data set shown in FIG. 9, and in an unsteady environment, learning is performed by selecting input vectors 10,000 times in order from each class. carry out.

FIG. 10 is a diagram showing an output result of the conventional SOIN for the artificial data set shown in FIG.
As shown in FIG. 10, in either a stationary environment or a non-stationary environment, the conventional technique SOINN cannot separate high-density overlapping classes.
For the preset parameters, λ = 200, age _t = 50, and c = 1.0 are determined by experiment, α ₁ = 1/6, α ₂ = 1/4, α ₃ = 1/4, For β = 2/3 and γ = 3/4, the same values as those disclosed in Non-Patent Document 2 were used.

On the other hand, as shown in FIG. 11, the information processing apparatus according to the present embodiment can appropriately output the three classes and the phase structure of each class in both the stationary environment and the non-stationary environment. That is, the information processing apparatus according to the present embodiment can separate classes having high density overlap.
The parameters set in advance were λ = 200, age _t = 50, c ₁ = 0.001, and c ₂ = 1.0, and these were determined by experiments.

  Subsequently, using the actual data set, a comparison experiment between the conventional technique SOINN and the information processing apparatus of the present embodiment is performed.

First, a comparative experiment using the AT & T database (http://www.uk.research.att.com) is performed.
The data set used for the experiment uses 10 classes selected from the AT & T_FACE database (each class contains 10 samples). The original image included in the data set has 92 × 112 pixels and 256 gray scales (see FIG. 11 in Non-Patent Document 2 for details).
Here, in the experiment, an original image is reduced to 23 × 28 pixels (interpolated by the nearest neighbor method), and an image subjected to smoothing processing by a Gaussian distribution (size 4, variance 2) is used. The feature vector obtained by these processes is used as an input vector for the experiment (for details, see FIG. 12 in Non-Patent Document 2).
In a stationary environment, learning is performed by selecting an input vector randomly from the entire data set, and in an unsteady environment, selecting an input vector 1,000 times in order from each class.

As for the experimental results for the data set, the information processing apparatus according to the present embodiment outputs 10 classes as the number of output classes in both the stationary environment and the non-stationary environment.
The parameters set in advance were λ = 25, age _t = 25, c ₁ = 0.0, and c ₂ = 1.0, and these were determined by experiments.

Further, using one of the prototype vectors output by the information processing apparatus of the present embodiment, the original data set is identified in the same manner as the SOIN experiment in Non-Patent Document 2.
As a result, the information processing apparatus of the present embodiment can obtain a recognition rate of 90% in a stationary environment and a recognition rate of 86% in a non-stationary environment.
These recognition rates are similar to those of SOINN, and the information processing apparatus of this embodiment has a recognition function similar to that of SOINN.
The reason why the recognition rate comparable to that of SOINN could be obtained is that the number of samples included in the data set is small and the distribution overlap between classes is low density.

Next, in order to compare the stability of the output results of the conventional technique SOINN and the information processing apparatus of the present embodiment, experiments are performed 1,000 times to confirm the frequency of the number of output classes.
FIG. 12 is a diagram showing the frequency of the number of output classes, which is the output result of SOIN. FIG. 13 is a diagram illustrating the frequency of the number of output classes, which is an output result of the information processing apparatus according to the present embodiment.
From FIG. 12 and FIG. 13, the number of times that the information processing apparatus of this embodiment outputs around 10 classes as compared with SOIN in both the stationary environment (stationary) and the non-stationary environment (non-stationary). There are many. That is, the output result of the information processing apparatus of this embodiment is more stable than that of SOIN.

  Subsequently, a comparative experiment is performed using another actual data. As data used in the experiment, Optical Recognition of Handwritten Digits database (Optdigits) is used (http://www.ics.uci.edu/~mlearn/MLRepository.html). This data set is composed of 10 classes of handwritten numerals, and includes 3,823 samples as learning data and 1,797 samples as test data. The number of dimensions of the sample is 64.

FIG. 14 is a diagram illustrating an example of a prototype vector that is an output result of SOIN, which is a conventional technique, with respect to the Optdigits data set.
As a result of the experiment on the data set, SOINN outputs 10 classes as the number of output classes in both the stationary environment and the non-stationary environment.
When the test data is classified using one of the prototype vectors output by SOINN, the recognition rate is 92.2% in a stationary environment and 90.4% in a non-stationary environment. Recognition rate can be obtained.
Furthermore, when 100 experiments are performed for SOINN and the variation in the number of classes is confirmed, 6 to 13 classes are output in both the stationary environment and the non-stationary environment.
For the preset parameters, λ = 200, age _t = 50, and c = 1.0 are determined by experiment, α ₁ = 1/6, α ₂ = 1/4, α ₃ = 1/4, For β = 2/3 and γ = 3/4, the same values as those disclosed in Non-Patent Document 2 were used.

FIG. 15 is a diagram illustrating an example of a prototype vector that is an output result of the information processing apparatus of the present embodiment for the Optdigits data set.
As for the experimental results for the data set, the information processing apparatus according to the present embodiment outputs 12 classes as the number of output classes in both the stationary environment and the non-stationary environment.
Then, when test data is classified using one of the prototype vectors output by the information processing apparatus of the present embodiment, a recognition rate of 94.3% is obtained in a non-stationary environment. Can obtain a recognition rate of 95.8%, and can obtain a recognition rate higher than that of SOINN.
Furthermore, when the experiment of 100 times is performed on the information processing apparatus according to the present embodiment and the change in the number of classes is confirmed, 10 to 13 classes are output in both the stationary environment and the unsteady environment. The output result is more stable than that of SOINN.
The parameters set in advance were λ = 200, age _t = 50, c ₁ = 0.001, and c ₂ = 1.0, and these were determined by experiments.

Here, comparing the prototype vector examples shown in FIGS. 14 and 15, although the SINN cannot extract samples such as “1 ′” and “9 ′”, the information processing apparatus of the present embodiment is “1 ′”. ”And“ 9 ′ ”can be extracted. That is, it can be confirmed that the number “1” is output as one class in SOINN, whereas the information processing apparatus of the present embodiment outputs “1” as two classes (similarly, The information processing apparatus in the form also divides the number “9” into two classes.)
This is because, in the original data set, a large difference is recognized between samples such as “1” and “1 ′” shown in FIG. 15, so that the information processing apparatus of this embodiment separates “1 ′”. ("9" and "9 '" are considered to be the same).
Therefore, the information processing apparatus of the present embodiment can separate classes with overlapping distributions such as “1” and “1 ′” shown in FIG. 15, for example. Can be stored properly.
As described above, from the experimental results using the actual data Optdigits, the information processing apparatus according to the present embodiment can separate classes having overlapping distributions as compared to SOIN.
Furthermore, the information processing apparatus according to the present embodiment can obtain a high recognition rate and has high output result stability.

The following effects can be achieved by the information processing apparatus according to the present invention described above.
First, classes with high-density overlap in distribution can be separated. In addition, in the process of detecting the overlapping region of the distribution, since a smoothing method is introduced, the operation can be performed more stably than the SOIN.
Furthermore, since the noise node can be efficiently deleted even in the single-layer structure, complete online additional learning can be realized.
Furthermore, since the operation is performed with fewer parameters compared to SOIN, the processing can be executed more easily.
As a result, for example, by mounting the information processing apparatus according to the present invention on a robot, the robot uses various information acquired from the surroundings as input data, even for complicated data that has been difficult to classify conventionally. Recognize stably in real time while eliminating data.

Other Embodiments of the Invention
An object of the present invention is to supply a recording medium (or storage medium) that records a program code of software that realizes the functions of the above-described embodiments to a system or apparatus, and a computer (or CPU or MPU) of the system or apparatus. Of course, this can also be achieved by reading and executing the program code stored in the recording medium. In this case, the program code itself read from the recording medium realizes the functions of the above-described embodiment, and the recording medium on which the program code is recorded constitutes the present invention.

  Further, by executing the program code read by the computer, not only the functions of the above-described embodiments are realized, but also an operating system (OS) operating on the computer based on the instruction of the program code. Of course, a case where part or all of the actual processing is performed and the functions of the above-described embodiments are realized by the processing is included.

  Further, after the program code read from the recording medium is written into a memory provided in a function expansion card inserted into the computer or a function expansion unit connected to the computer, the function expansion is performed based on the instruction of the program code. Naturally, a case where the CPU or the like provided in the card or the function expansion unit performs part or all of the actual processing and the functions of the above-described embodiments are realized by the processing is included.

  When the present invention is applied to the recording medium, program code corresponding to the above-described flowchart shown in FIG. 5 is stored in the recording medium.

  As mentioned above, although this invention was demonstrated by the embodiment, this invention can be variously deformed in the range of the meaning.

It is a figure which shows the example of the distribution overlap area | region between classes. It is a figure which shows the structural example for implementing this invention. It is a figure which shows the functional block for implementing this invention. It is a figure which shows the example of the distribution overlap area | region between the classes containing a fine unevenness | corrugation. It is a flowchart which shows the process outline | summary of the learning process by the Example which concerns on this invention. It is a table | surface which shows the input environment of the input vector in non-stationary environment. It is a figure which shows the artificial data set of the input vector used for the comparison experiment. It is a figure which shows the output result of the Example which concerns on this invention with respect to an artificial data set. It is a figure which shows the artificial data set containing the overlap of distribution and containing noise. It is a figure which shows the output result of SOINN with respect to an artificial data set. It is a figure which shows the output result of the Example which concerns on this invention with respect to an artificial data set. It is a figure which shows the frequency of the number of output classes which is an output result of SOIN. It is a figure which shows the frequency of the number of output classes which is an output result of the Example which concerns on this invention. It is a figure which shows the prototype vector which is an output result of SOIN. It is a figure which shows the prototype vector which is an output result of the Example which concerns on this invention. It is a flowchart which shows the process outline | summary of the learning process by SOIN.

Explanation of symbols

1 Information processing apparatus 10 Computer 11 CPU
12 ROM
13 RAM
14 bus 15 input / output interface 16 input unit 17 output unit 18 storage unit 19 communication unit 20 drive 201 magnetic disk 202 optical disk 203 flexible disk 204 semiconductor memory 21 input information acquisition unit 22 winner node search unit 23 similarity threshold calculation unit 24 similarity Threshold determination means 25 Node insertion means 26 Weight vector update means 27 Node density calculation means 28 Distribution overlap area detection means 29 Edge connection determination means 30 Edge connection means 31 Edge deletion means 32 Noise node deletion means 33 Class determination means 34 Output information display means

Claims (21)

Having a structure of at least one layer in which nodes described by multidimensional vectors are arranged;
In an information processing apparatus for sequentially inputting input vectors belonging to an arbitrary class and learning an input distribution structure of the input vectors,
A node having a weight vector closest to the input vector to be input is a first winner node, a node having a weight vector closest to the second is a second winner node, and between the first winner node and the second winner node. When the side is connected to
Node density calculating means for calculating the node density of the node of interest based on the node of interest and the average distance between the node of interest and nodes directly connected by the sides;
A cluster that is a set of nodes connected by edges is divided into sub-clusters that are subsets of clusters based on the node density calculated by the node density calculation means, and an overlapping region of distribution that is a boundary of the sub-cluster A distribution overlap area detecting means for detecting
When the first winner node and the second winner node are nodes located in the distributed overlap area, the first winner node and the second winner node are determined based on the node density of the first winner node and the second winner node. Edge connection determination means for determining whether to connect an edge between two winner nodes;
Based on the determination result, side connection means for connecting a side between the first winner node and the second winner node;
An information processing apparatus comprising: an edge deleting unit that deletes an edge between the first winner node and the second winner node based on the determination result. Having a structure of at least one layer in which nodes described by multidimensional vectors are arranged;
In an information processing apparatus for sequentially inputting input vectors belonging to an arbitrary class and learning an input distribution structure of the input vectors,
A node having a weight vector closest to the input vector to be input is a first winner node, a node having a weight vector closest to the second is a second winner node, and between the first winner node and the second winner node. When the side is connected to
Node density calculating means for calculating the node density of the node of interest based on the node of interest and the average distance between the node of interest and nodes directly connected by the sides;
Noise node deletion means for deleting the node of interest based on the node density calculated by the node density calculation means and the number of nodes directly connected to the node of interest by sides. An information processing apparatus characterized by that. Weight vector updating means for updating the weight vector corresponding to the first winner node and the weight vector corresponding to the node directly connected to the first winner node by an edge so as to be closer to the input vector, respectively. The information processing apparatus according to claim 1 or 2. Noise node deletion means for deleting the node of interest based on the node density calculated by the node density calculation means and the number of nodes directly connected to the node of interest by sides. The information processing apparatus according to claim 1, further comprising: The node density calculation means includes:
Unit node density for calculating the node density of the first winner node as a ratio per unit input based on the average distance between the first winner node and the node directly connected to the first winner node by an edge The information processing apparatus according to claim 1, further comprising a calculation unit. The node density calculation means includes:
A node density point calculation unit that calculates a point value of a node density of the first winner node based on an average distance between the first winner node and a node directly connected to the first winner node by an edge;
Node density points are accumulated until the number of inputs of the input vector reaches a predetermined number of unit inputs, and when the number of inputs of the input vector reaches a predetermined number of unit inputs, the accumulated node density points are input as units. 5. The information processing apparatus according to claim 1, further comprising: a unit node density point calculation unit that calculates a ratio per number and calculates a node density of the node per unit input number. 6. 2. The self-propagating neural network that inputs the input vector to a neural network and automatically increases the number of nodes arranged in the neural network based on the inputted input vector. 6. The information processing apparatus according to any one of claims 6. When there is a node that is directly connected to the node of interest by a side with respect to the node of interest, among the nodes that are directly connected, between the nodes having the maximum distance from the node of interest If the distance is a similarity threshold and there is no node that is directly connected to the node of interest by a side, the distance between the nodes with the smallest distance from the node of interest is calculated as the similarity threshold. Similarity threshold calculation means;
Whether the distance between the input vector and the first winner node is greater than the similarity threshold of the first winner node, and the distance between the input vector and the second winner node is similar to the second winner node A similarity threshold determination means for determining whether or not it is greater than the degree threshold;
8. The information processing apparatus according to claim 7, further comprising node insertion means for inserting the input vector as a node at the same position as the input vector based on the similarity threshold determination result. The information processing apparatus according to claim 7, wherein the self-propagating neural network has a one-layer structure. The distribution overlap area detecting means includes:
Based on the node density calculated by the node density calculation means, a node search unit for searching for a node having a locally maximum node density;
A first label assigning unit for assigning a label different from a label already assigned to another node to the searched node;
For a node that has not been given a label by the first label giving unit, a label is given by the first label giving unit for a node that is connected by a side to a node that has been given a label by the first label giving unit. A second label assigning unit that assigns the same label as the label of the given node;
A cluster dividing unit that divides a cluster, which is a set of nodes connected by edges, into sub-clusters, which are subsets of a cluster of nodes having the same label;
An area including a node of interest and a node directly connected by the edge of interest and the node of interest when the node of interest and a node directly connected by the edge belong to different sub-clusters The information processing apparatus according to claim 1, further comprising: a distribution overlap region detection unit that detects a distribution overlap region that is a boundary of subclusters. Having a structure of at least one layer in which nodes described by multidimensional vectors are arranged;
In an information processing method for sequentially inputting input vectors belonging to an arbitrary class and learning an input distribution structure of the input vectors,
A node having a weight vector closest to the input vector to be input is a first winner node, a node having a weight vector closest to the second is a second winner node, and between the first winner node and the second winner node. A node density calculating step of calculating a node density of the node of interest based on an average distance between the node of interest and the node directly connected by the edge when the edge is connected to
A cluster that is a set of nodes connected by edges is divided into sub-clusters that are subsets of clusters based on the node density calculated by the node density calculation step, and an overlapping region of distribution that is a boundary of the sub-cluster A distribution overlap area detecting step for detecting
When the first winner node and the second winner node are nodes located in the distributed overlap area, the first winner node and the second winner node are determined based on the node density of the first winner node and the second winner node. An edge connection determination step of determining whether to connect an edge between two winner nodes;
An edge connection step of connecting an edge between the first winner node and the second winner node based on the determination result;
An information processing method comprising: an edge deletion step of deleting an edge between the first winner node and the second winner node based on the determination result. Having a structure of at least one layer in which nodes described by multidimensional vectors are arranged;
In an information processing method for sequentially inputting input vectors belonging to an arbitrary class and learning an input distribution structure of the input vectors,
A node having a weight vector closest to the input vector to be input is a first winner node, a node having a weight vector closest to the second is a second winner node, and between the first winner node and the second winner node. A node density calculating step of calculating a node density of the node of interest based on an average distance between the node of interest and the node directly connected by the edge when the edge is connected to
For a node of interest, a noise node deletion step of deleting the node of interest based on the node density calculated by the node density calculation step and the number of nodes directly connected to the node of interest by a side An information processing method characterized by the above. A weight vector update step of updating the weight vector corresponding to the first winner node and the weight vector corresponding to the node directly connected to the first winner node by an edge so as to be closer to the input vector, respectively. 13. The information processing method according to claim 11 or 12, wherein: For the node of interest, a noise node deletion step of deleting the node of interest based on the node density calculated by the node density calculation step and the number of nodes directly connected to the node of interest by sides The information processing method according to claim 11, further comprising: The node density calculating step includes:
Unit node density for calculating the node density of the first winner node as a ratio per unit input based on the average distance between the first winner node and the node directly connected to the first winner node by an edge 15. The information processing method according to claim 11, further comprising a calculation step. The node density calculating step includes:
A node density point calculating step of calculating a point value of the node density of the first winner node based on an average distance between the first winner node and a node directly connected to the first winner node by an edge;
Node density points are accumulated until the number of inputs of the input vector reaches a predetermined number of unit inputs, and when the number of inputs of the input vector reaches a predetermined number of unit inputs, the accumulated node density points are input as units. 15. The information processing method according to claim 11, further comprising a unit node density point calculation step of calculating a node density per unit input and calculating a node density of the node per unit input number. 12. The self-propagating neural network that inputs the input vector to a neural network and automatically increases the number of nodes arranged in the neural network based on the input vector that is input. 16. The information processing method according to any one of items 16. When there is a node that is directly connected to the node of interest by a side with respect to the node of interest, among the nodes that are directly connected, between the nodes having the maximum distance from the node of interest If the distance is a similarity threshold and there is no node that is directly connected to the node of interest by a side, the distance between the nodes with the smallest distance from the node of interest is calculated as the similarity threshold. A similarity threshold calculation step;
Whether the distance between the input vector and the first winner node is greater than the similarity threshold of the first winner node, and the distance between the input vector and the second winner node is similar to the second winner node A similarity threshold determination step for determining whether or not it is greater than the degree threshold;
18. The information processing method according to claim 17, further comprising a node insertion step of inserting the input vector as a node at the same position as the input vector based on a similarity threshold determination result. The information processing method according to claim 17, wherein the self-propagating neural network has a one-layer structure. The distribution overlap area detection step includes:
Based on the node density calculated by the node density calculation step, a node search step for searching for a node having a locally maximum node density;
A first label assigning step for assigning a label different from a label already assigned to another node to the searched node;
For a node that has not been given a label by the first label assigning unit, a node that is connected by a side to a node that has been given a label by the first label assigning step is labeled by the first label assigning step. A second labeling step of assigning the same label as the label of the assigned node;
A cluster dividing step of dividing a cluster, which is a set of nodes connected by edges, into sub-clusters, which are subsets of a cluster of nodes having the same label;
An area including a node of interest and a node directly connected by the edge of interest and the node of interest when the node of interest and a node directly connected by the edge belong to different sub-clusters 12. The information processing method according to claim 11, further comprising a distribution overlap region detecting step of detecting the region as a distribution overlap region that is a boundary of sub-clusters.   A program for causing a computer to execute the information processing according to any one of claims 11 to 20.