JP5284530B2 - Information processing method and information processing apparatus - Google Patents

Description

  The present invention relates to a highly efficient data representation technique with reduced redundancy and a processing technique using this data.

  In recent years, nonlinear dimensional compression techniques represented by Isomap of Non-Patent Document 1 and Locally Linear Embedding (LLE) of Non-Patent Document 2 have been proposed. These map the data considered to be on the lower dimensional hypersurface (Manifold) in the higher dimensional space to a new lower dimensional space where the surface shape unique to Manifold is acceptable. Provide a method.

  Such a technique has succeeded in highly efficient pattern expression in the sense that data can be expressed in a lower dimensional space. However, information about which class the data belongs to is not used, and it is not optimal in terms of efficiently representing the data classification.

  On the other hand, in the method disclosed in Patent Document 1, a method for representing an image for pattern classification by extending the conventional Isomap method using a kernel Fisher linear discriminant function or a Fisher linear discriminant function. providing.

  Non-Patent Document 3 proposes a method for constructing a map that increases the degree of separation between classes by forcibly increasing the geodesic distance between data belonging to other classes as an improvement of the conventional Isomap method. Has been.

Thus, there is a demand for a method that can store the surface shape unique to Manifold to an acceptable level and can represent data for pattern classification.
Special table 2005-535017 No. Joshua B. Tenenbaum, Vin de Silva, John C. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction”, Science, Vol. 290, pp. 2319-2323, 2000 Sam T. Roweis, Lawrence K. Saul, “Nonlinear Dimensionality Reduction by Locally Linear Embedding”, Science, Vol. 290, pp. 2323-2326, 2000 Bisser Raytchev, Ikushi Yoda, Katsuhiko Sakaue, “Multi-View Face Recognition By Nonlinear Dimensionality Reduction And Generalized Linear Models”, Proceedings of the 7th International Conference on Automatic Face Gesture Recognition, pp. 625-630, 2006

  The present invention has been made in view of the above problems. A data representation method that preserves the unique surface shape of Manifold to an acceptable level and is suitable for pattern classification, and pattern identification using the representation method. It aims at providing the technique concerning a method.

  More specifically, in a plurality of data labeled with a certain class, a data representation method in which a data set of the same class is represented as one cluster, and the distance between each cluster can be set to a desired distance, And a pattern identification method using the expression method.

  In order to achieve the object of the present invention, for example, an information processing method of the present invention comprises the following arrangement.

That is, an information processing method performed by the information processing apparatus,
An input process in which input means inputs process data belonging to different classes;
A first calculation step in which a first calculation means obtains a geodesic distance relationship between the respective processing data input in the input step;
A setting step for obtaining a distance between the classes, and setting a degree of separation between classes so that the distance between the classes is increased when the distance between the classes is smaller than a predetermined value;
The updating means determines that the geodesic distance between the processing data belonging to the same class is based on the geodesic distance with the processing data belonging to another class based on the set inter-class separation degree of the class to which each of the processing data belongs. Updating step of updating the geodesic distance relationship between the processing data,
The second calculation means includes a second calculation step for obtaining information indicating a data mapping relationship that approximates the Euclidean distance relationship using the geodesic distance relationship updated in the updating step.

  According to the configuration of the present invention, there is provided a data expression method that preserves the unique surface shape of Manifold to an acceptable level and is suitable for pattern classification, and a technique related to a pattern identification method using the expression method. be able to.

It is a block diagram which shows the function structural example of the information processing apparatus which performs the data expression process using the pattern image by which labeling (labeling) was carried out about the area | region of the person's face. It is a flowchart of the data expression process performed using a pattern image. It is a flowchart which shows the process of approximate geodesic distance calculation. It is the block diagram which showed the function structure only about each part which operate | moves at the time of learning mode among each part which comprises the information processing apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart of the process which the information processing apparatus which concerns on the 2nd Embodiment of this invention performs at the time of learning mode. It is a flowchart of the process which the approximate system construction process part 46 performs in step S56. It is the block diagram which showed the function structure only about each part which operate | moves at the time of identification mode among each part which comprises the information processing apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart of the process which the information processing apparatus which concerns on the 2nd Embodiment of this invention performs at the time of identification mode. It is the block diagram which showed the function structure only about each part which operate | moves at the time of learning mode among each part which comprises the information processing apparatus which concerns on the 3rd Embodiment of this invention. It is a flowchart of the process which the information processing apparatus which concerns on the 3rd Embodiment of this invention performs at the time of learning mode. FIG. 10 is a block diagram illustrating a hardware configuration example of a computer that executes a computer program when the units illustrated in FIGS. 1, 4, 7, and 9 are implemented by a computer program.

  First, an outline of the present embodiment will be described.

  In this embodiment, when the label data indicating the class to which the process data belongs are input together with the process data belonging to different classes, the distance relationship between the input process data is obtained (first calculation). Then, the inter-class separation degree between the classes is set, and when the information indicating the distance relationship is updated based on the label data and the information indicating the inter-class separation degree, the distance relationship indicated by the updated information is approximated. Information indicating the data mapping relationship is obtained (second calculation).

  Here, the distance relationship to be obtained is the geodesic distance relationship, and the distance relationship approximated using information indicating the data mapping relationship is the Euclidean distance relationship.

It is assumed that the graph distance dG (x ₁ , x ₂ ) between the _two processing data x ₁ and x ₂ is ∞ when x ₁ and x ₂ are not in the vicinity. At this time, the geodesic distance dM (ξ, ζ) between the two processing data ξ and ζ is dG (ξ, ζ) or dG (ξ, a) + dG () passing through the processing data a different from the processing data. a, ζ), whichever is smaller.

Here, the graph distance is a graph distance dG (x ₁ , x ₂ ) between the _two processing data x ₁ and x ₂ , such as Euclidean distance and Manhattan distance when x ₁ and x ₂ are nearby. This is the so-called Minkowski distance. Or a statistical distance such as Mahalanobis distance.

  What is necessary is just to set the isolation degree between classes according to the isolation degree between the classes defined beforehand. When the degree of separation between the two classes is large, that is, when the relationship between the classes is to be expressed largely separated, for example, to emphasize the difference between two classes, the degree of separation between the two classes. Increase On the other hand, when the degree of separation is small, for example, when it is not necessary to express the relationship between classes so much that the two classes do not need to be clearly distinguished, Reduce the degree of separation between classes.

  The interclass separation degree may be obtained by obtaining a distance between classes and setting the interclass separation degree based on the distance between the classes. In this case, when the distance between classes is small, it is preferable to set the degree of separation between classes large. By doing so, it is possible to efficiently separate and express two classes that are relatively difficult to separate. Distances between classes can be obtained by using the shortest distance method, longest distance method, group average method, centroid method, median method, Ward method, variable method, etc., which are common in cluster analysis. Should be requested.

Whether or not the _two processing data x ₁ and x ₂ are in the vicinity is determined when the processing data x ₂ exists in the processing data up to a preset number in order from the closest to the processing data x _1. Further, it is characterized in that it is determined that the _two data x ₁ and x ₂ are in the vicinity. Alternatively, when the distance between the _two processing data x ₁ and x ₂ is within a preset distance, it may be determined that the two processing data x ₁ and x ₂ are in the vicinity.

  Also, in updating the distance relationship, the distance between the processing data is updated in proportion to the class separation of the class to which each of the two processing data belongs, and the distance from the processing data belonging to the same class is changed to the other class. Update to be smaller than the distance to the processing data to which it belongs.

  As a method of updating so that the distance to the processing data belonging to the same class becomes smaller than the distance to the processing data belonging to the other class, the distance to the processing data belonging to the same class is multiplied by a positive number smaller than 1. A method is mentioned. Further, the distance from the processing data belonging to the same class may be a positive number that is smaller than the distance from the processing data belonging to another class.

  The method for obtaining the data mapping relationship is a method for obtaining a mapping that minimizes an error between the distance relationship in the post-mapping space and the updated distance relationship. As such a method, there is a method for obtaining a correspondence relationship after processing data is mapped using a multidimensional scaling method. Alternatively, a method may be used in which a correspondence relationship after processing data is mapped using a multidimensional scaling method and then a neural network in which the obtained correspondence relationship is trained as teacher data is constructed. As this neural network, a multilayer feedforward type neural network can be used.

なる誤差関数Ｊ（Ａ）を最小化する線形写像行列Ａを求める手法が挙げられる。 As a method for obtaining the data mapping relationship, a method for obtaining a linear mapping that minimizes the error between the distance relationship in the mapped space and the updated distance relationship may be used. Examples of such methods include the following. That is, when the i-th and j-th processing data are x _i and x _j and the updated distance relationship between the i-th and j-th processing data is d _d (i, j),

A method for obtaining a linear mapping matrix A that minimizes the error function J (A) is given.

As a method for obtaining the data mapping relationship, there is a method for obtaining a nonlinear mapping φ (x) that minimizes an error between the distance relationship in the post-mapping space and the updated distance relationship. Here, the nonlinear mapping φ (x) is obtained by using the kernel function K (ξ, ζ) that is a real symmetric function satisfying the semi-definite value and the processing data x _i (i = 1, 2,...) (X) = Σα _i · K (x, x _i )

なる誤差関数Ｊ（Γ）を最小化する行列Γを求め、求めた行列Γのｉ行目の行ベクトルを、α_ｉとすることにより求められる。または、更に、λを正の定数、｜γ_ｋ｜_Ｌ１を行列Γのｋ番目の列ベクトルのＬ１ノルムとした時、

なる誤差関数Ｊ（Γ）を最小化する行列Γを求め、求めた行列Γのｉ行目の行ベクトルを、α_ｉとするようにして求めてもよい。これらの写像を求める際に、少なくとも、写像後の距離関係の順序が、更新後の距離関係の順序を満たすようにしてもよい。 The non-linear mapping phi (x) is a vector kappa _i, kernel function value _{K (x} i, _{x j)} of the process data _{x j} for processing data _{x i} and a vector whose j-th element, processing the data _{x i} And d _d (i, j) is the updated distance relationship between the processing data y _i and the processing data y _i

The matrix Γ that minimizes the error function J (Γ) is obtained, and the row vector of the i-th row of the obtained matrix Γ is obtained as α _i . Or, further, when λ is a positive constant and | γ _k | _L1 is the L1 norm of the k-th column vector of the matrix Γ,

The matrix Γ that minimizes the error function J (Γ) is obtained, and the row vector of the i-th row of the obtained matrix Γ may be obtained as α _i . When obtaining these mappings, at least the order of the distance relations after mapping may satisfy the order of the updated distance relations.

  Furthermore, to apply to pattern identification, information indicating identification rules for identifying different classes that can be defined in the space mapped by the data mapping relationship is generated, and identification target data is input (second input). The data is mapped using the data mapping rule indicated by the generated information. And the label of identification object data is identified using the mapped data and the data mapping rule which the produced | generated information shows.

  Hereinafter, several embodiments of the present invention will be described in detail with reference to the accompanying drawings. Note that some of the technical matters described below may be selected as appropriate and used in appropriate combination.

[First Embodiment]
The image handled in the present embodiment is an extracted image (pattern image) having a size of 20 pixels in length and 20 pixels in width obtained by cutting out an area of this face from an original image including a human face, and is a grayscale image. Suppose that Of course, when a plurality of human faces are included in the original image, there are a plurality of pattern images (data). In addition, a label indicating who the face is is attached to the face area (pattern) in each pattern image (labeling processing is completed). That is, the description will be made on the assumption that the pattern image handled in the present embodiment includes the data of the label.

  In the present embodiment, a data expression method (technology) for mapping such a pattern onto a new space will be described.

  An extracted image having a size of 20 pixels in length and width can be regarded as a 20 × 20 = 400-dimensional vector in which pixel values are arranged as elements in a raster scan. In this case, one pattern is one point in the 400-dimensional space. In general, a set of patterns of a specific category such as “person's face” forms a lower-dimensional hypersurface than a 400-dimensional space. That is, in order to express “a person's face”, the 400th dimension is redundant and can be expressed in a lower-dimensional space.

  As a most general method for reducing this redundancy, there is a method using principal component analysis (PCA). However, in PCA that assumes that the pattern distribution is a normal distribution for a set of patterns that include essentially non-linear variations such as “face of a person”, such as variations in face orientation, Cannot expect sufficient redundancy reduction.

  Therefore, in Isomap proposed in Non-Patent Document 1, first, for any two points of data on the nonlinear hypersurface, a geodesic curve that is the shortest distance between the two points of data along the hypersurface Approximate distance. Then, using a multidimensional scaling (MDS), a mapping that approximates the geodesic distance relationship estimated for all data combinations as the Euclidean distance is obtained. This makes it possible to represent a set of essentially non-linear distributions in a more compact space with reduced redundancy.

  However, PCA is the same, but Isomap aims to express the category of “person's face” in a compact space, and therefore, for example, it always expresses a classification such as who the image is. It may not be a suitable space. Therefore, in the present embodiment, an expression in a space suitable for classification such as the type of person, for example, is performed using a label added in advance to data.

  FIG. 1 is a block diagram illustrating an example of a functional configuration of an information processing apparatus that performs data expression processing using a pattern image that is labeled (labeled) with respect to a human face area. FIG. 2 shows a flowchart of data expression processing performed by the information processing apparatus using the pattern image. Hereinafter, the data expression process will be described with reference to FIGS. Note that the following description is substantially the same even if the size of the pattern image is another size or the labeling target is other than a human face.

  In step S <b> 20, the data input unit 10 inputs one or more pattern images 5 as described above and transfers them to the subsequent image normalization unit 11. The pattern image input by the data input unit 10 may be performed by receiving a pattern image transmitted from the outside via a network such as the Internet. Alternatively, the pattern image stored in a large-capacity information storage device such as a hard disk drive device may be read out. In any case, the form of inputting the pattern image to the information processing apparatus is not particularly limited.

Here, the 400-dimensional vectors each pixel arranged in a raster scan manner constituting the i th input to the data input unit 10 pattern images is ~ x _i, to the label and y _i. Therefore, “inputting N pattern images to the data input unit 10” is equivalent to inputting a set of _˜xi and y _i to the N set data input unit 10 (i = 1, 2, ..., N).

The label value may be any value as long as the same value is set for the same person. Here, for the sake of simplicity, when using a data set in which m types (m> 1) exist, y _i ∈ {1, 2,..., M} and m class labels are set. It should be expressed using.

  Here, among the data input to the data input unit 10, a set of data having the same label is defined as one class. In the following, a set of data whose label is c is referred to as class c.

Next, in step S21, the image normalization unit 11 normalizes ~ x _i corresponding to the pattern image in the data transferred from the data input unit 10, x _i = (~ x _i -u _i · 1). / Σ _i is obtained for all pattern images (i). Then, each obtained _xi is held.

Here, u _i is the average value of each element of the _˜xi vector. Also, 1, all elements are 1, ~ x _i and the same dimension, i.e. a 400-dimensional vector. Σ _i is the standard deviation of each element of the _˜xi vector. The normalization process here is not essential, but generally, when the data input to the data input unit 10 is an image or the like as in the present embodiment, the strength of the overall signal (here, each pixel value) is weak. Since it is necessary to eliminate factors caused by fluctuations, normalization as described above may be performed.

Through the processing so far, N sets of normalized pattern images x _i and their labels y _i are stored in a memory included in the image normalization unit 11 and the like.

In step S22, the geodesic distance relationship matrix generation unit 12 first extracts two pattern images from the N pattern images normalized by the image normalization unit 11. The number of combinations for selecting two pattern images from N pattern images is N! / 2! (N-2)! Since there are (= M) ways, M sets of two pattern images are obtained. For each of the M sets, the geodesic distance dM (i, j) between the two pattern images (where dM (i, j) is the i-th pattern image x and _i, to calculate the geodesic distance) between the j-th pattern image x _j. When M geodesic distances dM (i, j) are obtained, a geodesic distance relation matrix DM is obtained.

  The geodesic distance relationship matrix DM is an N-th order square matrix because the component of i rows and j columns is a matrix of dM (i, j) and the number of input pattern images is N. Further, since the geodesic distance dM (i, j) as a component is dM (i, j) = dM (j, i), the geodesic distance relation matrix DM is a symmetric matrix and dM (i, i) = Since it is 0, all diagonal components are 0.

  As described above, the geodesic distance is the shortest distance between data along the surface of the manifold formed by a large number of input data. Here, the approximate calculation method of the geodesic distance in this embodiment performed in step S22 is demonstrated using the flowchart shown in FIG. FIG. 3 is a flowchart showing an approximate geodesic distance calculation process. Note that the processing according to the flowchart of FIG. 3 is performed by the geodesic distance relationship matrix generation unit 12.

First, in step S320, the Euclidean distance dx (i, j) between any two points of the N pattern images is calculated for all combinations to obtain the Euclidean distance relation matrix Dx. Here, dx (i, j) is the Euclidean distance between the i-th pattern image x _i and the j-th pattern image x _j .

  The Euclidean distance relationship matrix Dx is a symmetric matrix in which the component of i rows and j columns is a matrix of dx (i, j), and the diagonal component of the Nth order square is 0, like the geodesic distance relationship matrix DM. is there. In this embodiment, the Euclidean distance is used in step S320. However, the present invention is not limited to this. For example, a Minkowski distance such as a Manhattan distance, a statistical distance such as a Mahalanobis distance, and other general distance axioms such as symmetry and non-negativeity are satisfied. An indicator may be used.

Subsequently, in step S321, the graph distance dG (i, j) between any two points of the input N pattern images is calculated for all combinations, and the graph distance relationship matrix DG is calculated. Ask. Here, dG (i, j) is a graph distance between the i-th pattern image x _i and the j-th pattern image x _j .

Here, the graph distance is, for example, dG (i, j) = dx (i, j) when the i-th pattern image x _i and the j-th pattern image x _j are close to each other. If the two points are not in the vicinity, the distance is dG (i, j) = ∞. In a realistic calculation, since the numerical value ∞ cannot be used, a sufficiently large constant may be used instead of ∞, compared to the Euclidean distance between any two pattern images. The graph distance relationship matrix DG is a matrix whose component of i rows and j columns is dG (i, j), and is also a symmetric matrix whose N-order square diagonal component is 0 as well.

  In the present embodiment, whether or not two points are in the vicinity is determined in accordance with k pattern images (k ≧ 1) from which each of the pattern images itself is removed in order from the closest distance obtained in step S320 ( Including itself, it is determined that (k + 1) pieces of data) are in the vicinity. If it is determined that neither of the two points is adjacent in the pattern image of two points, it is determined that the two points are not close. As described above, in the present embodiment, the k pattern images are arranged in the order of the shortest distance except for itself. For example, a pattern image having a relationship whose distance is within the positive value ε may be set as the vicinity. good. In this case, ε needs to be set to a value that is large enough that at least one pattern image other than itself is regarded as a neighborhood in each of all pattern images. However, if ε is too large, even a pattern image that should not be regarded as a neighborhood is regarded as a neighborhood, so it is not preferable to make the value too large. Although it depends on the number of input pattern images and the like, it is usually preferable to set ε to a size that allows several pattern images to be regarded as neighboring.

In step S322, the above-mentioned geodesic distance dM (i, j between any two points of the input N pattern images is used by using the Floyd-Warshall method for the graph distance relation matrix DG obtained in step S321. ) Is calculated for all combinations. Thereby, a geodesic distance relationship matrix DM is obtained. The geodesic distance dM (i, j) between two points of the i-th pattern image x _i and the j-th pattern image x _j by the Floyd-Warshall method is dM (i, j) = min {dG (i, j), dG (i, k) + dG (k, j)}, k ≠ i, j.

  The geodesic distance relationship matrix DM can be obtained by the processing from step S320 to step S322.

  Next, in step S23, the interclass separation degree setting unit 13 performs an interclass separation degree setting process. Hereinafter, the processing performed by the inter-class separation setting unit 13 will be described in detail.

  The interclass separation degree setting unit 13 sets the interclass separation degree ν (cp, cq). Here, cp and cq are class labels, and in the present embodiment, since a pattern image set in which m types exist is used, cp, cqε {1, 2,... There are m × m combinations of the class separation ν (cp, cq). The class separation degree ν (cp, cq) represents the degree of separation expression between the class cp and the class cq, and is set according to a desired degree of separation between the classes. Specifically, when it is desired to increase the degree of separation, this class separation degree is set to be larger than 1, and when it is desired to reduce the degree of separation, it is set to be smaller than 1. Further, when there is no need to change the separation degree, the class separation degree is set to 1. The degree of separation here is, as described above, the degree of emphasis on the difference between classes. For example, when the difference between the class cp and the class cq is to be expressed with emphasis, between the classes between the two classes. The degree of separation ν (cp, cq) may be set larger than 1.

  As in this definition, the degree of separation between classes is set by the relationship between two commutative classes, and therefore satisfies the symmetry ν (cp, cq) = ν (cq, cp). Further, the inter-class separation degree ν (cp, cp) between the same classes is arbitrary because it is not actually used, and may be simply set to 1.

  Next, a method for setting the class separation degree according to this embodiment will be described. In this embodiment, in order to promote the separated expression of each class, the class separation degree between similar classes is set to be larger than 1 by the following method, and the class separation degree between dissimilar classes is 1. Set to.

  First, in all combinations in which two classes are selected from all classes, it is determined whether or not the two classes are similar. Various methods can be considered as a method for determining whether two classes are similar. In this embodiment, the distance between classes is calculated using a general shortest distance method in cluster analysis, and between the classes. If the distance is smaller than the threshold, it is determined that the two classes are similar. Then, the degree of class separation between two classes determined to be similar is set to be greater than one. In the present embodiment, specifically, a value obtained by dividing the threshold value by the obtained distance between classes is set as the degree of class separation. Since the distance between classes determined to be similar is smaller than the above threshold, this value is always greater than 1. Further, the degree of class separation between two classes that are not determined to be similar is set to 1.

  For the threshold value, for example, a value that is determined to be similar for faces of similar persons such as siblings may be experimentally obtained in advance and used. In this embodiment, the distance between classes is calculated using the shortest distance method, but the distance between other classes such as the longest distance method, group average method, centroid method, median method, Ward method, variable method, etc. You may use the method of calculating. Further, as a degree of class separation between similar classes, a value obtained by dividing the above threshold value by the obtained distance between classes is set. Any other method may be used.

  As described above, in the present embodiment, the degree of class separation is set based on the distance between classes. However, the present invention is not limited to this, and the degree of class separation is determined based on information given to class labels in advance. You may make it set. For example, if information that Mr. A and Mr. B are twins is given in advance, the degree of class separation between two classes, Mr. A and Mr. B, may be set to an appropriate value greater than 1. Good.

  Further, the setting of the degree of class separation is not limited to the setting method of increasing the degree of class separation between similar classes, and other setting methods can be used. For example, if a predetermined class cp is to be clearly expressed separately from other classes cq (q ≠ p), ν (cp, cq) [、 q, q ≠ p] are all set to a value greater than 1. However, there is a setting method in which all others are set to 1. Further, when there is no need to clearly distinguish between classes cp and cq, a setting method may be used in which only ν (cp, cq) is set to a value smaller than 1 and all others are set to 1. Absent. As described above, in the data expression method described in the present embodiment, it is possible to arbitrarily set the degree of separation between classes according to the desired degree of separation between classes.

Next, in step S24, the geodesic distance relationship matrix update unit 14 calculates a distorted geodesic distance dd (i, j) and calculates a distorted geodesic distance relationship matrix Dd. Here, dd (i, j) indicates a distorted geodesic distance between the i-th pattern image x _i and the j-th pattern image x _j obtained by the geodesic distance relationship matrix generation unit 12. Further, the distorted geodesic distance dd (i, j) is obtained by converting the geodesic distance dM (i, j) between the i-th pattern image x _i and the j-th pattern image x _j into labels y _i and y. _j and updated based on the class separation ν (y _i , y _j ).

In the present embodiment, this distorted geodesic distance dd (i, j) is expressed as dd (i, j) = dM (i, j). [Ν (y _i , y _j ) − {ν (y _i , y _j )-[Beta]}. _{Delta.yi, yj} ]. Here, δ _{i, j} is the Kronecker δ symbol. When i = j, δ _{i, j} = 1, and when i ≠ j, δ _{i, j} = 0. The coefficient β is a positive number smaller than 1. That is, the distorted geodesic distance dd (i, j) is dd (i, j) when the i-th data x _i and the j-th data x _j belong to the same label, that is, the same class. = Β · dM (i, j), which is smaller than the geodesic distance dM (i, j).

On the other hand, when they are not the same label, that is, belong to different classes, dd (i, j) = dM (i, j) · ν (y _i , y _j ). Accordingly, the distorted geodesic distance dd (i, j) is obtained by multiplying the geodesic distance dM (i, j) by the interclass separation ν (y _i , y _j ).

Further, the coefficient β to be multiplied when the two data are of the same class is obtained by setting a value satisfying the following condition. This condition is that dd (i, j) = β · dM () in any two pattern images x _i and x _j of the same class and in any pattern image x _c of a class different from the two pattern images. i, j) <dd (i, c) = dM (i, c) · ν (y _i , y _c ). That is, the distorted geodesic distance between two pattern images of the same class may be made smaller than the distance from any pattern image of a different class. Ultimately, by setting β = 0, the above relationship can be satisfied, but β> 0 because there is a high possibility of causing inconvenience in processing in the data mapping relationship generation unit 15 described later. Try to set a value.

  In the data expression method according to the present embodiment, as described above, the distance relationship between pattern images is set so that the distance between pattern images that are the same class is smaller than the distance between pattern images that are different classes. Update. Further, under the above conditions, the distance between pattern images of different classes is updated based on the set degree of separation between classes. As a result, continuous fluctuations within the class of pattern images, for example, if the pattern image is a “person's face” image, non-linear and continuous fluctuations in the original feature space that change from front to side A distance relationship is constructed by agglomerating in the axial direction of fluctuation. As for the relationship between the classes, a distance relationship based on the desired degree of class separation is constructed. In the present embodiment, the distance relationship between pattern images of the same class is updated by multiplying the distance between pattern images of the same class by a coefficient β.

  However, the updating of the distance relationship between pattern images is not limited to this, and any updating method in which the distance between pattern images of the same class is smaller than the distance between pattern images of different classes. For example, other methods may be used. For example, the distance between all pattern images of the same class may be updated to a constant ρ that is smaller than the distance from pattern images of different classes.

Next, in step S25, the data mapping relationship generation unit 15 uses the distorted geodesic distance relationship matrix Dd calculated by the geodesic distance relationship matrix update unit 14, and is a mapping destination corresponding to each of all pattern images x _i . Find the output vector z _i .

Hereinafter, the output vector z _i corresponding to the i-th pattern image x _i calculated by the geodesic distance relationship matrix update unit 14 is denoted as the i-th output vector z _i . Here, the output vectors are the i-th output vector z _i and the Euclidean distance dz (i, j) between the j-th output vector z _j and the i-th pattern image x _i and the j-th pattern image x _j . It is determined so as to approximate the distorted geodesic distance dd (i, j). In the present embodiment, similar to the above-described Isomap, such an output vector is obtained by using a multidimensional scaling method (MDS) (refer to Non-Patent Document 1 for an output vector calculation method using MDS). .

  Usually, when MDS is used for the purpose of visualization, the output vector is three dimensions or less. However, since the data representation method according to the present embodiment is not particularly intended for visualization, the output vector is four dimensions or more. It does not matter. If the dimension of this output vector is made very high, the distance can be approximated relatively accurately. However, for the purpose of reducing data redundancy, it is better to make the dimension of the output vector as small as possible so as to be smaller than the dimension of the input data (pattern image) (400 dimensions in this embodiment).

  Therefore, in the present embodiment, an output vector is obtained with a minimum dimension in which the maximum distance error rate is equal to or less than a predetermined value among the distance error rates of all pairs of input pattern images. Here, the distance error rate between the i-th data and the j-th data is | dd (i, j) −dz (i, j) | / dd (i, j). The allowable range of the maximum distance error rate used here depends on the category or the like of the input pattern image, but may be set to 10% or less, for example. In the present embodiment, the minimum dimension such that the maximum distance error rate is equal to or less than a preset value is used as the dimension of the output vector. However, the present invention is not limited to this. For example, the minimum dimension such that the sum of the distance error rates is not more than a preset value may be set as the dimension of the output vector.

By the processing in each unit from the data input unit 10 to the data mapping relationship generation unit 15 described above, it is possible to obtain a correspondence relationship of ~ x _i → x _i → z _i for each labeled pattern image. As a result, for all pattern images, the output vector z _i approaches between the pattern images of the same class in the space of the dimension of the output vector z _i with reduced redundancy. That is, it is possible to express a cluster that is expressed as one cluster and that corresponds to each class with a desired degree of separation.

The data mapping relationship generation unit 15 then stores information indicating a correspondence relationship _{~ x i → x i → z} i obtained for each pattern image labeled the memory 16. Is not particularly limited for representation of such information, for example, the file name of ~ x _i, the file name of the x _i, the file name of the z _i may be created a file associated with this order.

  In the present embodiment, as the pattern image, a grayscale image obtained by cutting out a person's face and a label indicating which person it is are used. However, the present invention is not limited to this. For example, instead of the pattern image, voice data that utters a preset word and data with the word as a label may be used. Furthermore, a web page described in HTML and its content category may be used as a label. That is, the present embodiment can be applied to any data as long as it can define some distance that reflects the similarity between the labeled original data.

[Second Embodiment]
In the present embodiment, the data expression method shown in the first embodiment is applied. In the present embodiment, a pattern image which is an extracted image (pattern image) having a size of 20 pixels in the vertical direction and 20 pixels in the horizontal direction obtained by cutting out the face area from the original image including the face of the person, and is a grayscale image. To identify which person it contains. Of course, the input pattern image is not subjected to the labeling process as described in the first embodiment.

  This embodiment includes two modes, a learning mode and an identification mode.

  In the learning mode, the data mapping relationship is approximately constructed using the pattern images handled in the first embodiment, that is, the pattern images that have been labeled, and the class corresponding to each label is mapped in the mapping destination space. Generate a model.

  In the identification mode, first, a pattern image that has not been labeled is mapped using the data mapping relationship constructed in the learning mode. In the mapping destination space, a model of a class corresponding to each label generated in the learning mode is used to identify which person's face image the image is.

<Learning mode>
FIG. 4 is a block diagram illustrating the functional configuration of only the units that operate in the learning mode among the units that configure the information processing apparatus according to the present embodiment. In FIG. 4, the same reference numerals are given to portions common to the configuration shown in FIG. 1, and description thereof is omitted.

  FIG. 5 is a flowchart of processing performed by the information processing apparatus according to the present embodiment in the learning mode. In FIG. 5, the same reference numerals are given to portions common to the configuration shown in FIG. 2, and description thereof is omitted.

  Hereinafter, the processing in the learning mode will be described with reference to FIGS.

  In the present embodiment, N pattern images (the same as the pattern images handled in the first embodiment, which have been subjected to labeling processing) are input, and each input pattern image is the same as in the first embodiment. Perform the process. Thereby, an output vector for each pattern image (in this embodiment, the number of dimensions of the output vector is h) is obtained. Since the processing so far is the same as the processing in the first embodiment, the description thereof is omitted.

By the processing up to the data mapping relationship generation unit 15, the label y _i at any i up to i = 1, 2,..., N, the normalized vector x _i , and the output vector z _i are configured. Data set (training data set) is obtained. Using this training data set, the approximate system construction processing unit 46 constructs a system that approximates the mapping x _i → z _i . In this embodiment, a three-layer feedforward neural network (three-layer NN) is used as a system that approximates this mapping.

  The three-layer NN has a three-layer structure of an input layer, an intermediate layer, and an output layer, and each layer has a plurality of neurons.

  The number of neurons in the input layer is 400, which is the same as the 400-dimensional dimension of the normalized vector, and these input layer neurons have each element value of the 400-dimensional vector as input data to the 3-layer NN. , Each state value.

  The number of neurons in the intermediate layer is determined by the processing in the data mapping relationship generation unit 15, and these neurons in the intermediate layer are connected to all neurons in the input layer.

  Here, the connection has a certain weight and receives as input the state value of the connection destination neuron (in the case of an intermediate layer, the neuron of the input layer) multiplied by the weight. The neurons in the intermediate layer take the sum of all received inputs, and use a value obtained by performing a preset nonlinear transformation as a value obtained by subtracting a preset value (threshold value) from the sum. Random values are set for these weight values and threshold values in the initial state, and the values are determined in the processing in the approximate system construction processing unit 46 described later. Further, the non-linear transformation is generally a transformation using a so-called sigmoid function, and in this embodiment, a hyperbolic tangent function (f (u) = tanh (u)) is used as the non-linear transformation.

  The number of neurons in the output layer is the same as the number of dimensions of the output vector, and these output layer neurons are connected to all the neurons in the intermediate layer. As described above, the number of dimensions of the output vector is determined by the processing in the data mapping relation generation unit 15. Here, since the number of dimensions of the output vector is h as described above, the number of neurons in the output layer is h. It becomes.

  Similarly to the intermediate layer neuron, the output layer neuron receives, as an input, a value obtained by multiplying the state value of the connection destination neuron (here, the intermediate layer neuron) by the weight for each connection. Then, the sum of all received inputs is taken, and a value obtained by subtracting the threshold value from the sum is used as a state value, that is, an output value. Thus, unlike the neurons in the intermediate layer, the neurons in the output layer do not perform nonlinear conversion.

  As for the connection weight value and threshold value from the neurons in the intermediate layer, as in the case of the neurons in the intermediate layer, a random value is set in the initial state, and the value is set in the processing by the approximate system construction processing unit 46. Determine.

  Using the above three-layer arithmetic system, each element value of a 400-dimensional vector is set as the state value of each of the 400 neurons in the input layer (hereinafter simply described as being input to the three-layer NN). The state values of h neurons in the output layer are obtained. If the state values of the h neurons are considered as the element values of the h-dimensional vector, it can be regarded that the mapping from the 400-dimensional vector to the h-dimensional vector is performed by the calculation using the three-layer NN.

Here, as described above, it is known that an arbitrary mapping can be approximated with an arbitrary accuracy, depending on the number of neurons in the intermediate layer, by variously changing the value of the connection weight and the threshold. Yes. Therefore, in the present embodiment, by using the three-layer NN and adjusting the value of the connection weight and the threshold value, the mapping of the training data set x _i → z _{i at} an arbitrary i, that is, the normalized vector Approximate the mapping from to the output vector.

  In FIG. 5, in step S56, the approximate system construction processing unit 46 performs processing for constructing a system that approximates the mapping.

  In the following, the processing performed by the approximate system construction processing unit 46 in step S56, that is, the adjustment of the connection weight value and threshold value of the three-layer NN and the determination of the number of neurons in the intermediate layer, is shown in FIG. Will be described.

  First, in step S660, the above-described training data set (N sets of data including three of the label, the normalized vector, and the output vector) obtained by the processing up to the data mapping relation generation unit 15 is obtained. Divide into two sets. Of these two sets, one is used to adjust the value of the connection weight and the threshold, and hereinafter this set is referred to as an adjustment set. The other set is used for a test in step S664 described later, and this set is hereinafter referred to as a test set.

  At the time of division, M sets (0 <M <N) are randomly selected from N sets of training data, and these are set as a test set. The remaining (N−M) pairs are adjustment sets. Although the value of M is arbitrary, in this embodiment, it is 30% of N. Here, in both of these two sets, it is preferable that there is at least one data of each label. Therefore, in this embodiment, if there is no data of a certain label in either set, the selection is performed again at random.

  In step S661, the number of intermediate layer neurons is set. Initially, the number of neurons in the intermediate layer is set to a predetermined number. Then, when the process returns to step S661 again by the determination in step S666 described later, the number of neurons in the intermediate layer is increased by one. The number of neurons in the intermediate layer to be initially set is arbitrary, but it is preferable to initially set the number as small as possible. Therefore, in the present embodiment, the number of neurons in the initial intermediate layer is two.

  In step S662, the weight values and threshold values of all the connections are initialized to random values. Here, in order to reduce the dependency on the initial value in the subsequent processing in step S663, it is preferable to set all values to a value that can be regarded as almost zero.

  In step S663, the value of the connection weight and the threshold value initialized in step S662 are started, the value of the connection weight and the threshold value are adjusted using the adjustment set, and the normalized vector in the adjustment set is used. A three-layer NN approximating the mapping of output vectors is constructed. Here, when all the normalized vectors in the adjustment set are input to the third layer NN, the state values of the h neurons in the output layer are changed to the element values of the corresponding output vectors. The values of the connection weight and the threshold are adjusted so as to approach each other. In this adjustment, a general error back-propagation method is used as a learning method for the multilayer feedforward neural network. See S. Haykin, “Neural Networks A Comprehensive Foundation 2nd Edition”, Prentice Hall, pp. 156-255, July 1998, for details on how to adjust the value of the connection weight and threshold using the backpropagation method. I want.

  Then, this adjustment is performed with the state values of the h neurons in the output layer obtained when all the normalized vectors in the adjustment set are input to the third layer NN, and the element values of the corresponding output vectors. The process ends when the error between and has converged. In the present embodiment, as this error, the sum of square errors of the state values of h neurons in the output layer and each element value of the corresponding output vector is used. Further, whether or not the error has converged is determined when the error is almost not reduced in the adjustment of the preset number of steps using the error back propagation method (for example, the error reduction rate is 1% or less). It is determined that the error has converged. The “preset number of steps” used for the determination may be arbitrarily set. However, if the number is too small, there is a high possibility that it is determined that the convergence has been erroneously performed although it has not originally converged. However, if this is too large, there is a high possibility that the convergence determination will not be made. Therefore, it is only necessary to experimentally determine and set a value that ensures the convergence determination.

  By the processing in step S663 described above, the mapping of the output vector from the normalized vector in the adjustment set using the three-layer NN when the number of neurons in the intermediate layer is the number set in step S661 is approximated 3 The construction of the layer NN is completed.

  In step S664, the mapping performance of the three-layer NN constructed in step S663 is evaluated using the test set. Here, first, all normalized vectors in the test set are input to the three-layer NN constructed in step S663, and the state values of h neurons in the output layer corresponding to the respective inputs are obtained. Then, the sum of square errors between the obtained h state values and each element value of the output vector in the test set corresponding to the input normalized vector is obtained. It can be said that the smaller this square error is, the higher the performance of performing a desired mapping on unknown post-normalization data. Therefore, this sum of square errors is used as an evaluation value of the mapping performance of the three-layer NN constructed in step S663. That is, it can be determined that the smaller the evaluation value, the higher the mapping performance.

  In step S665, the number of neurons in the intermediate layer of the three-layer NN constructed in step S663, the values of all connection weights, the threshold value, and the evaluation value of the mapping performance obtained in step S664 are respectively used as approximate system construction processing. It records in the memory which the part 46 has.

  In step S666, it is determined whether or not the mapping performance of the three-layer NN is deteriorated using the evaluation values recorded in the memory so far. As a result of such determination, if it is determined that the condition has deteriorated, the process proceeds to step S667. On the other hand, if it is determined that the condition has not deteriorated, the process returns to step S661, and as described above, the number of neurons in the intermediate layer is increased by one, and the processes after step S662 are performed.

  Here, in step S666, the evaluation values of the three layers NN thereafter are all deteriorated compared to the evaluation values of the three layers NN recorded in step S665 a number of steps set in advance, that is, the sum of square errors is reduced. When it is larger, it is determined that the mapping performance is deteriorated. If the “preset number of steps” is too small, there is a high possibility of erroneous determination as to whether or not it has deteriorated, so a large value may be set to a practical level. In the initial stage, since there is no evaluation value before “the preset number of steps”, it is not possible to determine the deterioration. In that case, the process always returns to step S661.

  In step S667, the evaluation value with the smallest evaluation value is selected from the evaluation values of the mapping performance recorded so far in step S665. Then, together with the selected evaluation value, the number of neurons in the intermediate layer, the values of all connection weights, and threshold values recorded in step S665 are output to the class model generation unit 47 described later.

  By the processing from step S660 to step S667 described above, a three-layer NN having an appropriate number of neurons in the intermediate layer is constructed as a system that approximates the mapping from the normalized vector to the output vector with high generalization performance. The

  In the present embodiment, a three-layer NN that approximates the mapping from the normalized vector to the output vector is constructed using the above method. However, the present embodiment is not limited to this, and a general three-layer NN construction method may be used. Furthermore, in the present embodiment, the three-layer NN is used as a system for approximating the mapping from the normalized vector to the output vector, but the present invention is not limited to this. For example, the nonlinear mapping may be approximated by a nonlinear mapping system such as a feedforward neural network having three or more layers or a support vector regression method using a kernel method.

Next, in step S57, the class model generation unit 47 generates a class model corresponding to each label using the three-layer NN constructed in the processing by the approximate system construction processing unit 46 and the training data set. The class model generated here is used in an identification mode, which will be described later, and corresponds to the generation of parameters of a classifier for class identification in a space mapped by the three-layer NN. For example, when class identification using a linear discriminant function is performed in the discriminant mode, a linear discriminant function coefficient vector w _c and a bias value b _c (c is a class label) may be generated.

  In this embodiment, since the nearest neighbor method is used in class identification in the identification mode, at least one prototype data is generated for each class. Specifically, first, the normalized vector in the training data set is input to the constructed three-layer NN, and the state values of h neurons in the output layer of the three-layer NN at that time are calculated. Then, the h-dimensional post-mapping vector having the state value as each element value and the corresponding label set, that is, the data after mapping by the three-layer NN and the label are recorded in the memory 48 as prototype data. Process. The recording of the prototype data may be performed on data randomly selected from the training data set, but in this embodiment, it is performed on all data.

  With the above processing, the three-layer NN constructed in the processing in the approximate system construction processing unit 46 and the plurality of prototype data recorded in the class model generation unit 47 are obtained, and the processing in the learning mode is completed. In other words, in the learning mode, if the input data is data of the same class with reduced redundancy, they are approached and mapped to a space where the degree of separation between classes becomes a desired degree of separation, and the mapping is approximated. Build the system. Then, a model of each class is generated at the mapping destination.

<Identification mode>
FIG. 7 is a block diagram illustrating the functional configuration of only the units that operate in the identification mode among the units that configure the information processing apparatus according to the present embodiment.

  FIG. 8 is a flowchart of processing performed by the information processing apparatus according to the present embodiment in the identification mode.

  Hereinafter, processing in the identification mode will be described with reference to FIGS.

  First, in step S80, the data input unit 70 inputs a pattern image 75 (a pattern image that has not been subjected to labeling processing) that is an object for identifying who the image is.

  Next, in step S81, the image normalization unit 71 performs the same image normalization processing as the image normalization unit 11 described in the first embodiment on the pattern image 75, and each pixel of the image after normalization is performed. A 400-dimensional vector in which values are arranged in a raster scan is generated. This vector obtained here is assumed to be a normalized vector x.

  In step S87, the data mapping processing unit 77 calculates a post-mapping vector z using the three-layer NN obtained in the learning mode. The post-mapping vector z is an h dimension in which the normalized vector x is input to the three-layer NN obtained in the learning mode, and the state values of h neurons in the output layer of the three-layer NN at that time are used as element values. Vector.

  In step S88, since the identification processing unit 78 performs class identification using the nearest neighbor method, first, the post-mapping vector z calculated by the data mapping processing unit 77 and the mapping of all prototype data recorded in the learning mode. The Euclidean distance from the back vector is calculated. Then, the post-mapping vector having the smallest calculated distance is selected, and the label recorded corresponding to it is obtained.

  In step S89, the identification result output unit 79 outputs information indicating the type of person corresponding to the label obtained by the identification processing unit 78. The type of person corresponding to the label may be stored in advance in a memory included in the identification result output unit 79 as a table. Such information is not particularly limited, but may be text document data describing information about a person such as a person name. Further, it may be audio data for causing the information processing apparatus to utter a person name. In this case, the information processing apparatus needs to be provided with a configuration for generating an audio signal based on the audio data and an audio speaker that outputs audio in accordance with the audio signal.

  With the processing described above, it is possible to identify who the face image is from the pattern image to be identified. In the present embodiment, since the input pattern image (face image) is assumed to be a person included in the data used in the learning mode in advance, the identification result is always the data used in the learning mode. One of the persons included in the inside. If an image of a person not included in the data used in the learning mode is input, if the smallest distance obtained by the identification processing unit 78 is greater than or equal to a preset value, it is unknown. What is necessary is just to make it the identification result that it is a person's image. The “preset value” used here may be obtained experimentally so that an image of a person not included in the data is input and it is determined that the image is an unknown person.

  By the processing in the learning mode and the identification mode described above, it is possible to input a pattern image to which no label is attached and to identify which person it is. In the present embodiment, the nearest neighbor method is used for the identification processing by the identification processing unit 78 in the identification mode. However, the present invention is not limited to this, and other general identification methods such as a k-nearest neighbor method and a support vector machine. It is clear that this can also be realized using. In this case, the modeling process for each class in the class model generation unit 47 in the learning mode may be changed to a so-called parameter learning process or data collection process necessary for the identification process to be used.

  As described above, in the pattern identification method according to the present embodiment, first, if data of the same class are used, the distance between the data is closer than the distance between the data of other classes, and the relationship between the classes is a desired degree of separation. A data mapping system represented by Then, a classifier for class identification is generated in the mapping destination space mapped by the constructed data mapping system. Newly input data is mapped using this data mapping system, and the data after mapping is identified using the generated classifier. It is possible to perform pattern identification that is robust against essentially non-linear fluctuations.

  When the class separation degree is set in the same manner as in the first embodiment, the degree of separation between similar classes is increased, so that it is possible to obtain an identification characteristic that increases the degree of separation of similar classes. it can. This is a characteristic realized by constructing a mapping system to a space in which differences between similar classes are emphasized. This makes it possible to obtain a good identification result even for an object that is relatively difficult to identify.

In addition, various identification characteristics can be obtained by the method for setting the degree of class separation described in the description of the first embodiment. For example, a class c _p, is set to all 1 value greater than the interclass separation degree of other classes c _{q (q} ≠ p), when, as set all other 1, newly entered class c _q ( The probability of erroneously determining that data of q ≠ p) is class c _p can be reduced.

The above characteristics are useful, for example, in the construction of a strong security system using face images. Specifically, the class of persons having elevated privileges, by treating as described above class c _p, to reduce the possibility of being determined to be a person with a higher authority incorrectly ordinary person It is possible to build a highly reliable security system. Further, when considering a similar security system, even if persons having the same level of authority are mistakenly determined by mistaken those persons, there is little actual harm. For this reason, such classes of persons do not need to be clearly distinguished, and thus the degree of separation between classes may be set to a value smaller than 1. By doing so, it is possible to relatively increase the degree of separation between classes with different authorities, and to reduce the probability of misidentifying persons with different authorities. Thus, in the pattern identification method according to the present embodiment, a pattern identification method having desired identification characteristics can be realized by setting the degree of separation between classes.

[Third Embodiment]
In this embodiment, as a modification of the pattern identification method shown in the second embodiment, as in the second embodiment, a pattern image that has not been subjected to labeling processing is input, and which person it is is determined. An example of a pattern identification method for identifying is shown.

  Similar to the second embodiment, the present embodiment also includes two modes, a learning mode and an identification mode. The processing performed in each mode in this embodiment is almost the same as in the second embodiment, but the portions corresponding to the processing in the data mapping relationship generation unit 15, the approximate system construction processing unit 46, and the class model generation unit 47, And only the part corresponding to the processing in the data mapping processing unit 77 is different. Therefore, only this different part will be described below, and description of parts that are similar in processing will be omitted.

<Learning mode>
FIG. 9 is a block diagram illustrating the functional configuration of only the units that operate in the learning mode among the units that configure the information processing apparatus according to the present embodiment. In FIG. 9, the same reference numerals are given to portions common to the configuration shown in FIG. 1, and description thereof is omitted.

  FIG. 10 is a flowchart of processing performed by the information processing apparatus according to the present embodiment in the learning mode. In FIG. 10, parts common to those shown in FIG. 2 are given the same reference numerals, and descriptions thereof are omitted.

  Hereinafter, the processing in the learning mode will be described with reference to FIGS.

  Also in this embodiment, N pattern images (the same as the pattern images handled in the first embodiment, which have been labeled) are input, and each input pattern image is the same as in the first embodiment. Perform the process. Thereby, an output vector for each pattern image (in this embodiment, the number of dimensions of the output vector is h) is obtained. Since the processing so far is the same as the processing in the first embodiment, the description thereof is omitted.

  In the second embodiment, a mapping system to a new space that approximately stores the obtained distorted geodesic distance relationship is constructed by two steps of construction of MDS and three-layer NN.

  In the present embodiment, a linear mapping system is used as the mapping system, and the linear mapping system construction processing unit 96 uses the distortion geodesic distance relationship matrix and the set of normalized vectors normalized by the image normalization unit 11. Build a linear mapping system. This process corresponds to step S106 in FIG.

First, the process performed by the linear mapping system construction processing unit 96 in step S106 will be described. Here, the linear system to be constructed is A as a matrix notation. Since A is the dimension of the normalized vector, that is, 400 dimensions here, A is a 400 × h matrix, where h is the dimension of the space after mapping. When a 400-dimensional vector x is input to this system, a vector z obtained as an output can be expressed as z = A ^T x, which is an h-dimensional vector. Here, ^AT is a transposed matrix of A. At this time, the Euclidean distance between output vectors z _i and z _j (= A ^T x _i and A ^T x _j ) obtained by mapping arbitrary i and j-th normalized vectors x _i and x _j , respectively. A linear mapping system that approximates the distorted geodesic distance dd (i, j) is constructed. Therefore, in the present embodiment, this linear mapping A is obtained as a minimization problem of the error function J (A) shown in the following Expression 1.

In the present embodiment, A that minimizes this is obtained by the steepest descent method. Here, the column vector of the k-th column of A is a _k (a _k is a 400-dimensional vector, k = 1, 2,..., H). In the steepest descent method, first, all components of A are initialized at random. And based on Formula 2, the component of A is updated sequentially.

Here, a ′ _k is a column vector of the k-th column of A after being updated once, and η is a positive proportionality constant that determines the update amount in the one-time update. Also, ∇ _ak is a partial differentiation with respect to the vector _ak , and ∇ _ak J (A) is obtained by Equation 3.

  In the present embodiment, the update shown in Expression 2 is sequentially performed until the value of the error function J (A) in Expression 1 converges to obtain a converged matrix A. Convergence here is determined to be that the error has converged when the error does not substantially decrease in the update for the preset number of steps, as in the error convergence determination of the third layer NN in the second embodiment. do it. The value of η is related to this convergence. If this value is too large, there is a high possibility that the error does not converge well, but if it is too small, many updates are required before convergence. Therefore, it is preferable to set η to a value that is small enough to converge with a practically allowable number of updates.

  By the above method, the linear mapping matrix A can be obtained as a minimization problem of the error function J (A). In the above description, the number of columns of A is generalized as h, but it is necessary to determine the value of h. In general, the larger h is, the higher the approximation performance is, that is, the value of the error function J (A) can be reduced. However, a smaller h can be mapped to a space with reduced redundancy. Therefore, in the present embodiment, A is obtained by the above method for various values of h, and A having the smallest value of h is selected from among those satisfying preset conditions. Specifically, first, the initial value of h is set to 1, and the value of h is increased by 1 each time A is obtained. Then, it is verified whether or not the condition shown in the following Expression 4 is satisfied in A obtained by the value of each h.

  Equation 4 means a condition as to whether or not the distance relationship between any three points in the mapped space satisfies at least the order of the distorted geodesic distance relationship. h is incremented by 1 to obtain A, and when A satisfying the relationship of the above equation 4 is obtained, the operation is terminated, and the linear mapping to be obtained in this linear mapping system construction processing unit 96 is obtained. As a system, it is recorded and retained in its own memory. In the present embodiment, an error function as defined in Equation 1 is defined, and a linear map A that minimizes the error function is obtained by the steepest descent method. However, the present invention is not limited to this, and any other error function may be used or A may be obtained analytically if the method is to obtain a linear mapping that preserves the distorted geodesic distance relationship as much as possible, particularly preserves the order. It doesn't matter.

  In step S107, the class model generation unit 97 uses the linear mapping system constructed in the processing of the linear mapping system construction processing unit 96 and the all normalized vectors normalized by the image normalization unit 11, A class model corresponding to the label is generated.

  Here, as in the second embodiment, first, a normalized vector is input to the constructed linear mapping system A, and an output vector of the linear mapping system at that time is calculated. Then, the h-dimensional output vector is used as a post-mapping vector, and is recorded in the memory 98 as prototype data used in an identification mode, which will be described later, together with the corresponding label. As in the second embodiment, the recording of the prototype data may be performed on data randomly selected from the training data set, but in this embodiment, it is performed on all data.

  With the above processing, the linear mapping system A constructed in the processing in the linear mapping system construction processing unit 96 and a plurality of prototype data recorded in the class model generation unit 97 are obtained, and this completes the processing in the learning mode. To do. In other words, in the learning mode, a linear mapping system A is constructed in which the input data is close to the same class data with reduced redundancy, and mapping is performed in a space where the degree of separation between classes becomes a desired degree of separation. Then, a model of each class is generated at the mapping destination.

<Identification mode>
In the identification mode according to the present embodiment, the basic configuration of the processing unit is the same as the configuration of the identification mode in the second embodiment, and the processing contents in the processing unit corresponding to the data mapping processing unit 77 in FIG. Only the difference. Therefore, the configuration of the processing unit is not particularly illustrated here, and only the processing contents in the processing unit corresponding to the data mapping processing unit 77 will be described, and description of other processing will be omitted.

  Similar to the second embodiment, this embodiment also inputs data and normalizes the image. Then, the data mapping processing unit of the present embodiment calculates a post-mapping vector z using the linear mapping system A obtained in the learning mode. The post-mapping vector z is an h-dimensional vector obtained when the normalized vector x is input to the linear mapping system A obtained in the learning mode. That is, in the second embodiment, the difference is that a post-mapping vector obtained using a three-layer NN is obtained using a linear mapping system. Subsequent processing corresponding to the identification processing unit 78 and the identification result output unit 79 in the second embodiment searches for the nearest prototype and outputs the result, as in the second embodiment.

  In the above, the difference of the process in 3rd Embodiment from the process in 2nd Embodiment was demonstrated. As for the method used in the identification processing, various methods can be applied as in the second embodiment, and the correspondence to an unexpected input pattern may be the same as the method described in the second embodiment. .

[Fourth Embodiment]
In this embodiment, as a modification of the pattern identification method shown in the third embodiment, an example of a pattern identification method when the linear mapping in the third embodiment is expanded to a nonlinear mapping using a kernel function is shown.

  In the third embodiment, a linear map is used to store a distorted geodesic distance relationship between data as much as possible (particularly in the order of distances), and a map that can reduce redundancy is constructed. When the linear mapping is used, the above object can be achieved if the data distribution is relatively simple (even non-linear). However, if the data distribution has a very complicated shape, there is a high possibility that a target mapping cannot be constructed.

Therefore, in this embodiment, the linear mapping portion in the third embodiment, that is, the portion mapping input data using the linear mapping matrix A is changed to a non-linear mapping using a kernel function. Here, the kernel function is a real symmetric function having a domain of χ × χ when a certain set χ is targeted, and a function satisfying the semi-definite property. Examples of such kernel functions include polynomial kernel K (x, x ′) = (x · x ′ + 1) ^p and Gaussian kernel K (x, x ′) = exp (− | x−x ′ | ² / σ ² ) is common.

  In this embodiment, such a kernel function is used to construct a nonlinear mapping system from input data x to output data z. As described above, this embodiment differs from the third embodiment only in whether the mapping system portion is a linear mapping or a nonlinear mapping using a kernel function. Therefore, in the description of the present embodiment, only the construction of the nonlinear linear mapping using the kernel function and the nonlinear mapping using the kernel function will be described, and description of other portions will be omitted.

In the third embodiment, a linear mapping z = A ^T x is used as a mapping system from input data x to output data z. On the other hand, the non-linear mapping of the present embodiment is based on the input N number of h-dimensional vectors α _n (n = 1, 2,..., N) and the corresponding input vectors x _n , and Using the kernel function K (x, x ′), z = Σα _n · K (x, x _n ). Here, Σ means the sum from n = 1 to n = N.

This mapping depends on what kernel function is used (selection of the function itself and parameters such as p and σ in the above kernel function example). It is determined only by the dimension vector α _n . Therefore, in the present embodiment, the Gaussian kernel is used as a kernel function, and the mapping of geodesic distance between data as much as possible is preserved as much as possible, and the construction of a map that can reduce redundancy is optimized for N h-dimensional vectors α _n. By doing. The parameter σ of the Gaussian kernel may be an arbitrary constant, but is preferably a constant in the order of the Euclidean distance between the input data.

The optimization of the N h-dimensional vectors α _n is obtained as a solution to the minimization problem of the error function J (Γ) shown in Equation 5.

Here, Γ is a matrix of N rows and h columns where the column vector of the kth column is an N-dimensional vector γ _k (k = 1, 2,..., H). Also, κ _i in the equation is an N-dimensional vector having K (x _i , x _k ) as the k-th element, and κ _i = {K (x _i , x ₁ ), K (x _i , x _2). ),..., K (x _i , x _N )} ^T. Also in this embodiment, Γ that minimizes this error function is obtained by the steepest descent method. First, all components of Γ are initialized at random. Then, based on Expression 6, the component of Γ is sequentially updated.

Here, γ ′ _k is a column vector of the kth column of Γ after being updated once, and η is a positive proportionality constant that determines the update amount in the one-time update, as in the third embodiment. Further, γ _γk is a partial differentiation with respect to the vector γ _k , and ∇ _γk J (Γ) is obtained by Expression 7 as in the third embodiment.

Also in this embodiment, as in the third embodiment, the update shown in Expression 6 is sequentially performed until the value of the error function J (Γ) in Expression 5 converges to obtain a converged matrix Γ. The row vector of the nth row of the converged matrix Γ is the h-dimensional vector α _n to be obtained. The determination of convergence and the setting of η may be performed in the same manner as in the third embodiment, and thus description thereof is omitted.

The number h of columns of Γ may be obtained by the same method as in the third embodiment, but the cross-validation method similar to the method for determining the number of neurons in the intermediate layer of the three-layer NN used in the second embodiment is used. Is preferred. In this case, first, the data is divided into an adjustment set and a test set, and Γ is obtained by the above method at various values of h using the adjustment set as in the third embodiment. Then, the mapping z = Σα _k · K (x, x _k ) determined by Γ obtained by the value of each h is applied to the test set, and among those satisfying a preset condition, h Γ having the smallest value may be selected. The conditions used here include the condition of Equation 4 shown in the third embodiment and the maximum distance error among the respective distance error rates of all input data pairs used in the first embodiment. A condition that the rate is equal to or less than a preset value may be used.

  Also in the present embodiment, an error function such as Equation 5 is defined, and a matrix Γ that minimizes the error function is obtained by the steepest descent method. However, the present invention is not limited to this, and any other error function can be used or analyzed as long as it is a method for obtaining a matrix Γ that determines a nonlinear transformation to be mapped so as to preserve the order of the distorted geodesic distance. Alternatively, the matrix Γ may be obtained. In particular, with respect to the error function shown in Equation 5, in order to obtain a sparse solution, the L1 norm for Γ may be added as a regularization term, and Equation 8 may be used.

Here, | γ _k | _L1 is the L1 norm of γ _k , and Σ _{k in} the second term means the sum from k = 1 to k = h. Λ is a positive parameter that determines the effect of regularization, and is a constant that determines the effect of regularization. Increasing the value of λ increases the effect of regularization, but the actual value to be used may be determined experimentally according to the required sparseness and the final mapping performance. When the error function is represented by Expression 8, ∇ _γk J (Γ) illustrated in Expression 7 is represented by Expression 9.

Here, Λ _k is a case _where the n-th element of γ _k is γ _kn , the diagonal component of the n th row and the n th column of this matrix Λ _k is λ / | γ _kn |, and all other components are It is an Nth-order diagonal matrix that becomes zero. Therefore, in order to obtain a more sparse solution, using Equation 9, the update shown in Equation 6 is sequentially performed until the value of the error function J (Γ) in Equation 8 converges, and the converged matrix Γ is obtained. You can get it.

In the processing in this embodiment corresponding to the class model generation unit 97 and the data mapping processing unit 77 in the third embodiment, the linear mapping z = A ^T x in the third embodiment is expressed as a kernel function in the learning mode. Using K, it is only necessary to replace z = Σα _k · K (x, x _k ).

  By the above method, the linear mapping in the third embodiment can be replaced with a non-linear mapping using a kernel function, and it is possible to deal with a more complicated pattern distribution. In the present embodiment, the kernel function is described as fixed. However, the mapping is constructed using various kernel functions (including selection of the function itself and parameters such as p and σ in the kernel function example) Among them, the one with the smallest error function value in cross-validation may be selected.

  In the example of the pattern identification method of the second to fourth embodiments described above, a grayscale image obtained by cutting out a person's face is used as input data. However, the present invention is not limited to this, and it is obvious that the present invention can be applied to other categories of image data and audio data. For example, even in the case of general data such as Web contents, the mapping of the data to the multidimensional space determined by the distance of each data and some parameters can be defined in the second to fourth embodiments. It can be used as input data. In this case, an error function as shown in Expression 1, 5 or Expression 8 is used, and a parameter for determining mapping may be determined so that the error function is minimized.

[Fifth Embodiment]
1, 4, 7, and 9 have been described as being configured by hardware in the above embodiment. However, these parts may be implemented by software. That is, you may implement as a computer program for making a computer perform the process corresponding to each part.

  FIG. 11 is a block diagram showing a hardware configuration example of a computer that executes a computer program when the units shown in FIGS. 1, 4, 7, and 9 are implemented by the computer program.

  The CPU 1101 controls the entire computer using programs and data stored in the RAM 1102 and the ROM 1103 and executes each process performed by each unit shown in FIGS.

  The RAM 1102 has an area for temporarily storing programs and data loaded from the external storage device 1106 and programs and data received from the outside via the I / F 1107. The RAM 1102 has a work area used when the CPU 1101 executes various processes. That is, the RAM 1102 can provide various areas as appropriate. The RAM 1102 also functions as the memories 16, 48 and 98.

  The ROM 1103 stores setting data and a boot program for the computer.

  The operation unit 1104 is configured by a keyboard, a mouse, and the like, and can input various instructions and data when operated by a user of the computer. For example, in the “setting process” in each of the above explanations, a user input using the operation unit 1104 may be accepted.

  The display unit 1105 is configured by a CRT, a liquid crystal screen, or the like, and can display a processing result by the CPU 1101 using an image, text, or the like. For example, an identification result as a processing result in the identification mode can be displayed with an image or a character. In addition, a list of pattern images is displayed on the display screen of the display unit 1105, and a pattern image to be processed in the computer is selected from the pattern image group displayed in the list by the operation unit 1104. Also good.

  The external storage device 1106 is a large-capacity information storage device represented by a hard disk drive device. Here, an OS (Operating System), a program and data for causing the CPU 1101 to execute the functions of the respective units shown in FIGS. 1, 4, 7, and 9, and a function program described as being set in advance, Data etc. are also saved. Further, data to be processed such as a pattern image is also stored in the external storage device 1106. Note that the external storage device 1106 may also function as the memories 16, 48, and 98.

  Programs and data stored in the external storage device 1106 are appropriately loaded into the RAM 1102 under the control of the CPU 1101. The CPU 1101 executes processing using the loaded program and data. As a result, the computer can execute processing by each unit shown in FIGS.

  The I / F 1107 is for connecting the computer to an external device. For example, by connecting the I / F 1107 to a network such as a LAN or the Internet, for example, a pattern image or the like can be downloaded from a device on the network via the I / F 1107. The processing result by the computer can be transmitted to a device on the network via the I / F 1107.

  A bus 1108 connects the above-described units. Note that the configuration shown in FIG. 11 is an example, and the computer may have any configuration as long as the computer program described above can be executed.

[Other Embodiments]
Needless to say, the object of the present invention can be achieved as follows. That is, a computer-readable recording medium (or storage medium) that records software program codes for realizing the functions of the above-described embodiments is supplied to the system or apparatus. Then, the computer (or CPU or MPU) of the system or apparatus reads and executes 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, an operating system (OS) or the like running on the computer performs part or all of the actual processing based on the instruction of the program code. Needless to say, the process includes the case where the functions of the above-described embodiments are realized.

  Furthermore, it is assumed that the program code read from the recording medium is written in a memory provided in a function expansion card inserted into the computer or a function expansion unit connected to the computer. After that, based on the instruction of the program code, the CPU included in the function expansion card or function expansion unit performs part or all of the actual processing, and the function of the above-described embodiment is realized by the processing. Needless to say.

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

Claims (25)

An information processing method performed by an information processing apparatus,
An input process in which input means inputs process data belonging to different classes;
A first calculation step in which a first calculation means obtains a geodesic distance relationship between the respective processing data input in the input step;
A setting step for obtaining a distance between the classes, and setting a degree of separation between classes so that the distance between the classes is increased when the distance between the classes is smaller than a predetermined value;
The updating means determines that the geodesic distance between the processing data belonging to the same class is based on the geodesic distance with the processing data belonging to another class based on the set inter-class separation degree of the class to which each of the processing data belongs. Updating step of updating the geodesic distance relationship between the processing data,
The second calculation means comprises a second calculation step for obtaining information indicating a data mapping relationship that approximates the Euclidean distance relationship using the geodesic distance relationship updated in the updating step. Processing method. When the graph distance dG (x ₁ , x ₂ ) between the _two processing data x ₁ and x ₂ is ∞ when x ₁ and x ₂ are not nearby,
The geodesic distance dM (ξ, ζ) between the two processing data ξ and ζ is dG (ξ, ζ) or dG (ξ, a) + dG (a, passing through the processing data a different from the processing data. The information processing method according to claim 1, which is smaller of ζ). The graph distance dG (x ₁ , x ₂ ) between the _two processing data x ₁ and x ₂ is a Euclidean distance when x ₁ and x ₂ are close to each other. Information processing method. The graph distance dG (x ₁ , x ₂ ) between the _two processing data x ₁ and x ₂ is a Minkowski distance or Mahalanobis distance when x ₁ and x ₂ are close to each other. Information processing method described in 1.   5. The information processing method according to claim 1, wherein, in the setting step, the interclass separation is set according to a predefined separation between classes.   The distance between the classes is obtained in the setting step using any one of a shortest distance method, a longest distance method, a group average method, a center of gravity method, a median method, a Ward method, and a variable method. 6. The information processing method according to any one of 5 above. Whether or not the _two processing data x ₁ and x ₂ are in the vicinity is determined when the processing data x ₂ exists in the processing data up to a preset number in order from the closest distance from the processing data x _1. 5. The information processing method according to claim 2, wherein the two pieces of data x ₁ and x ₂ are determined to be close to each other. Whether or not the _two processing data x ₁ and x ₂ are in the vicinity is determined when the distance between the _two processing data x ₁ and x ₂ is within a preset distance. _1, an information processing method according to any one of claims 2 to 4 x _2, characterized in that the determined to be near.   9. The information processing method according to claim 1, wherein in the updating step, a positive number smaller than 1 is multiplied by a distance from the processing data belonging to the same class.   In the updating step, the distance between the processing data is updated in proportion to the class separation degree of the class to which each of the two processing data belongs, and the distance from the processing data belonging to the same class is changed to the processing belonging to the other class. The information processing method according to claim 1, wherein the information is a positive number that is smaller than a distance to the data.   11. The information processing according to claim 1, wherein, in the second calculation step, a mapping that minimizes an error between the distance relationship in the space after mapping and the updated distance relationship is obtained. Method.   4. The information processing method according to claim 1, wherein in the second calculation step, a correspondence relationship after mapping of the processing data is obtained using a multidimensional scaling method. 5.   13. The information processing method according to claim 12, wherein, in the second calculation step, a neural network in which the obtained correspondence relationship is trained as teacher data is constructed.   The information processing method according to claim 13, wherein the neural network is a multilayer feedforward neural network.   2. The information processing method according to claim 1, wherein, in the second calculation step, a linear mapping that minimizes an error between a distance relationship in the space after mapping and an updated distance relationship is obtained. In the second calculation step, the i-th and j-th processing data are x _i and x _j , and the updated distance relationship between the i-th and j-th processing data is d _d (i, j). Time,

The information processing method according to claim 15, wherein a linear mapping matrix A that minimizes the error function J (A) is calculated. In the second calculation step, a nonlinear mapping φ (x) that minimizes an error between the distance relationship in the space after mapping and the updated distance relationship is obtained, and the nonlinear mapping φ (x) has a semi-definite property. Using the kernel function K (ξ, ζ) which is a real symmetric function to be satisfied and the processing data x _i (i = 1, 2,...), Φ (x) = Σα _i · K (x, x _i ) and The information processing method according to claim 1, wherein the information processing method is represented. Wherein in the second calculation step, the vector kappa _i, wherein the processing data _{x j} for processing data _{x i} kernel function value _{K (x} i, _{x j)} to a vector whose j-th element, processing the data _{x i} And d _d (i, j) is the updated distance relationship between the processing data y _i and the processing data y _i

18. The information processing method according to claim 17, wherein a matrix Γ that minimizes the error function J (Γ) is obtained, and a row vector of the i-th row of the obtained matrix Γ is set to the α _i . Wherein in the second calculation step, the vector kappa _i, wherein the processing data _{x j} for processing data _{x i} kernel function value _{K (x} i, _{x j)} to a vector whose j-th element, processing the data _{x i} And the processed data y _i is the updated distance relationship d _d (i, j), λ is a positive constant, | γ _k | _L1 is the L1 norm of the k-th column vector of the matrix Γ,

18. The information processing method according to claim 17, wherein a matrix Γ that minimizes the error function J (Γ) is obtained, and a row vector of the i-th row of the obtained matrix Γ is set to the α _i .   The information processing method according to any one of claims 11 to 19, wherein in the second calculation step, at least the order of distance relations after mapping satisfies the order of distance relations after update. An information processing method performed by an information processing apparatus,
An input process in which input means inputs process data belonging to different classes;
A first calculation step in which a first calculation means obtains a geodesic distance relationship between the respective processing data input in the input step;
A setting step for obtaining a distance between the classes, and setting a degree of separation between classes so that the distance between the classes is increased when the distance between the classes is smaller than a predetermined value;
The updating means determines that the geodesic distance between the processing data belonging to the same class is based on the geodesic distance with the processing data belonging to another class based on the set inter-class separation degree of the class to which each of the processing data belongs. Updating step of updating the geodesic distance relationship between the processing data,
A second calculation step in which a second calculation means obtains information indicating a data mapping relationship that approximates the Euclidean distance relationship using the geodesic distance relationship updated in the updating step;
A generating step for generating information indicating identification rules for identifying the different classes definable in a space mapped by the data mapping relationship;
A second input step in which the second input means inputs identification target data;
A mapping step in which mapping means maps the identification target data using a data mapping relationship indicated by information obtained in the second calculation step;
The identification means comprises: an identification step of identifying a label of the identification target data using the data mapped in the mapping step and the identification rule indicated by the information generated in the generation step. Processing method.   A computer program for causing a computer to execute the information processing method according to any one of claims 1 to 21.   A computer-readable storage medium storing the computer program according to claim 22. An information processing apparatus,
Input means for inputting processing data belonging to different classes,
First calculation means for obtaining a geodesic distance relationship between processing data input by the input means;
A setting means for obtaining a distance between the classes, and setting a degree of separation between classes so that the distance between the classes is increased when the distance between the classes is smaller than a predetermined value;
Based on the set class separation degree of the class to which each of the processing data belongs, the geodesic distance between the processing data belonging to the same class is smaller than the geodesic distance with the processing data belonging to another class. Updating means for updating a geodesic distance relationship between the processing data;
An information processing apparatus comprising: second calculation means for obtaining information indicating a data mapping relation that approximates the Euclidean distance relation using the geodesic distance relation updated by the updating means. An information processing apparatus,
Input means for inputting processing data belonging to different classes,
First calculation means for obtaining a geodesic distance relationship between processing data input by the input means;
A setting means for obtaining a distance between the classes, and setting a degree of separation between classes so that the distance between the classes is increased when the distance between the classes is smaller than a predetermined value;
Based on the set class separation degree of the class to which each of the processing data belongs, the geodesic distance between the processing data belonging to the same class is smaller than the geodesic distance with the processing data belonging to another class. Updating means for updating a geodesic distance relationship between the processing data;
Second calculation means for obtaining information indicating a data mapping relation approximating the Euclidean distance relation using the geodesic distance relation updated by the updating means;
Generating means for generating information indicating identification rules for identifying the different classes definable in a space mapped by the data mapping relationship;
A second input means for inputting identification target data;
Mapping means for mapping the identification target data using a data mapping relationship indicated by information obtained by the second calculation means;
An information processing apparatus comprising: data mapped by the mapping unit; and an identification unit that identifies a label of the identification target data using an identification rule indicated by information generated by the generation unit.

Images