JP5238580B2 - Feature extraction device and pattern recognition device - Google Patents

Description

  The present invention relates to a feature extraction device and a pattern recognition device.

 In the pattern recognition methods used in the fields of face recognition and the like shown in Patent Document 1 and Non-Patent Document 1, recognition performance is improved by performing processing that emphasizes the difference between categories to be recognized. In this method, the similarity between two sets of patterns is defined by the angle between linear subspaces generated from the set of patterns by principal component analysis. Therefore, the difference between categories is measured by the angle between the recognized subspaces, and processing for emphasizing the difference between categories is performed by linear transformation that widens these angles.

  On the other hand, in the linear discriminant analysis shown in Non-Patent Document 2, the recognition performance is improved not only by emphasizing the difference between categories but also by projecting to suppress variation within the category. In this method, the difference between categories and the variation within the category are measured by the distance in the vector space between patterns.

JP 2006-221479 A

Tomokazu Kawahara, Masashi Nishiyama, Tatsuo Kozakaya, Osamu Yamaguchi ,: “Face Recognition based on Whitening transformation of Distribution of Subspaces,” Subspace2007 (8th Asian Conference on Computer Vision Workshop) pp. 97-103 “Pattern Identification”, by Richard O. Duda, Peter E. Hart, David G. Stork, directed by Morio Onoe, New Technology Communications

 In the methods shown in Patent Document 1 and Non-Patent Document 1, the angle between subspaces is used as a reference. However, since there is no processing that emphasizes only the difference between categories and suppresses variation within the category, When the angle between the partial spaces between the categories to be expanded is increased, the angle between the partial spaces belonging to the same category is also increased at the same time.

 In addition, the method shown in Non-Patent Document 2 that simultaneously emphasizes the difference between categories and suppresses the variation within the category is based on the fact that the reference for measuring the difference between the categories and the variation within the category is not an angle between the subspaces. Since the distance in the vector space is defined by the angle between the linear subspaces generated by principal component analysis from the set of patterns, the standard is different and can be used. could not.

  The present invention has been made in view of the above-described problems, and an object thereof is to narrow the angle between partial spaces belonging to the same category while widening the angle between the partial spaces of different categories.

 To achieve the above object, the feature extraction apparatus of the present invention includes an acquisition unit that acquires a plurality of partial spaces and a category to which each of the plurality of partial spaces belongs, and a projection matrix that generates a projection matrix from the partial spaces. A plurality of subspaces belonging to the same category among the categories, a variation matrix generation unit within category that generates an intra-category variation matrix, and a plurality of subspaces belonging to different categories among the categories, An intra-category variation matrix generating unit that generates an inter-variation matrix, an eigenvalue problem calculating unit that calculates an eigenvalue and an eigenvector obtained from an eigenvalue problem defined from the intra-category variation matrix and the inter-category variation matrix, and the eigenvalue And a feature extraction calculation unit for calculating a feature extraction matrix used in feature extraction from the eigenvector, The dynamic matrix is calculated by a linear sum of products of the projection matrices generated by the projection matrix generation unit from the subspaces belonging to the same category, and the inter-category variation matrix is calculated from the subspaces belonging to the different categories. It is calculated by a linear sum of products of projection matrices generated by the generation unit.

  Since the angles between the partial spaces belonging to the same category can be narrowed while widening the angles between the partial spaces of different categories, the recognition performance can be improved.

It is a block diagram of a pattern recognition apparatus. It is a block diagram of a feature extraction part. It is a block diagram of a pattern recognition part. It is a figure which shows the flowchart showing operation | movement of the feature extraction part. It is a figure which shows the flowchart showing operation | movement of the pattern recognition part.

 The feature extraction device and the pattern recognition device according to the embodiment of the present invention can be applied to pattern recognition in various fields in which feature amounts are treated as vectors, such as images and sounds. Hereinafter, embodiments of the present invention will be described with reference to FIGS. 1, 2, and 3.

 FIG. 1 is a configuration diagram of a pattern recognition apparatus 10 according to an embodiment of the present invention. The pattern recognition apparatus 10 stores an acquisition unit 101 that acquires data such as a pattern, a feature vector, or a feature extraction matrix, a control unit 102, an output unit 103 that outputs a calculation result, and data acquired by the acquisition unit 101. Storage unit 104. The control unit 102 also includes a feature extraction unit 105 and a pattern recognition unit 106.

 FIG. 2 is a configuration diagram of the feature extraction unit 105. The feature extraction unit 105 includes a learning pattern acquisition unit 201, a feature vector generation unit 202, a learning subspace generation unit 203, a projection matrix generation unit 204, an intra-category variation matrix generation unit 205, and an inter-category variation matrix. A generation unit 206, an eigenvalue problem calculation unit 207, and a feature extraction matrix output unit 208 are provided. The feature extraction unit 105 functions as a feature extraction device.

 FIG. 3 is a configuration diagram of the pattern recognition unit 106. The pattern recognition unit 106 includes a pattern acquisition unit 301, a feature vector generation unit 302, a subspace generation unit 303, a feature extraction application unit 304, a similarity calculation unit 305, and a determination unit 306.

 FIG. 4 is a flowchart illustrating the operation of the feature extraction unit 105.

  In step S <b> 201, the learning pattern acquisition unit 201 sends the pattern to be recognized acquired by the acquisition unit 101 and the category to which the pattern belongs to the storage unit 104 and causes the storage unit 104 to store the pattern. The pattern and category to be input can be realized in advance by being stored in a storage medium such as a hard disk or a memory card, or when the pattern is an image, for example, by a camera connected to a personal computer. When the pattern is voice, it can be realized by a microphone connected to a personal computer, for example.

 In step S <b> 202, the feature vector generation unit 202 generates one or more feature vectors by processing one or more patterns stored in the storage unit 104 and stores the one or more feature vectors in the storage unit 104. Hereinafter, a vector generated by this process is referred to as a “feature vector”. When the input pattern is an image, it is converted into a vector by raster scanning, for example. When the input pattern is speech, for example, a vector in which the frequency components of speech within a certain time are arranged is used.

In step S203, the learning subspace generation unit 203 performs a subspace obtained by performing the following calculation from one or more feature vectors belonging to the same category based on the category information stored in the storage unit 104. Is calculated and stored in the storage unit 104. When there is one feature vector, the length of the vector is normalized to 1 and output to the feature extraction unit 105. In the case of a plurality, the base of the partial space is calculated by the method of Non-Patent Document 1 and output to the feature extraction unit 105. In the method of Non-Patent Document 1, when a plurality of feature vectors are x ₁ ... X _n , the autocorrelation matrix defined by (Formula 1) is calculated, eigenvectors having a large eigenvalue by a predetermined number are selected, and the subspace is selected. The base of. However, ^{x T} is the transpose of the vector x.

  Hereinafter, the base of the subspace generated by this process is referred to as the base of the learning subspace. The category to which the base belongs is the same as the category to which the feature vector used for generation belongs.

  In step S204, the projection matrix generation unit 204 generates a projection matrix from the basis of the learning subspace.

 In step S205, the intra-category variation matrix generation unit 205 uses the bases of the learning subspace stored in the storage unit 104 and the categories to which the bases belong, and the intra-category variation matrix that describes the definition and calculation method below. W (Formula 10) is calculated. In addition, the intra-category variation matrix generation unit 205 stores the calculation result in the storage unit 104.

First, set the symbol. The dimensionality of the feature space C, and the number of category N, the dimension of learning subspace d, each category i (i = 1, ..., N) belongs to _{L i-number} of the subspace _{V i1, ..., V iLi,} Let P _i1,..., P _iLi be the projection matrix onto each subspace. However, a projection matrix P onto a subspace spanned by orthonormal basis Ψ _1... Ψ _d is defined as (Equation 2).

Next, define the average subspace M _i of each category i. _I1 eigenvectors defined by the matrix in (Equation _{3) φ, ..., φ iC} , when the corresponding eigenvalues and _{μ i1 ≧ ... ≧ μ iC,} ' eigenvectors phi _{i1 of, ...,} φ _id' eigenvalues greater d an A base subspace is defined as a d′-dimensional average subspace M _i of each category i. For the dimension d ′ of the average subspace M _i, an appropriate value may be obtained by experiment. Alternatively, d may be the same as the dimension of the learning subspace.

Here, the average subspace Mi of each category _i will be described. The definition of the average subspace M _i for each category i is an extension of the average vector based on the angle. First, the characteristics that characterize the average vector will be described. mean vector x- (x _{bar) = x 1 + ... + x} n / n of n vectors x ₁ ... _{x n} are characterized as vector sum of squares of distances from each vector is minimized. That is, the average vector x− (x bar) is a vector that gives the minimum value of the following function (equation 4) concerning the vector x. However, || ○ || is the norm of the feature space.

Next, the relationship between the angle between two subspaces and the product of its projection matrix will be described. Two d-dimensional subspaces V ₁ ′, V ₂ ′, their projection matrices Q ₁ ′, Q ₂ ′, d canonical angles between subspaces V ₁ ′, V ₂ ′ are θ ⁽¹⁾ _,..., Θ ^(d) , tr are matrix traces, Equation 5 is established between the matrix and the canonical angle. That is, the square sum of cosines of each of a plurality of canons defined between two subspaces can be calculated by tracing the product of projection matrices. The definition of the canonical angle and the derivation of (Formula 5) are detailed in Non-Patent Document 1. The larger the value of (Formula 5), the closer the subspaces V ₁ ′ and V ₂ ′ are.

The minimization problem of (Formula 4) is rewritten to a distance based on the canonical angle (Formula 5). When the vector of (Equation 4) is changed to a subspace and the distance of the feature space is changed to a distance (Equation 5) based on the canonical angle, a problem of obtaining a d′-dimensional subspace V ′ that maximizes (Equation 6) Become. Here, n subspaces are denoted by V _1,..., V _n , projection matrices thereof are denoted by Q _1,..., Q _n , _and projection matrices to d′-dimensional subspace V ′ are denoted by Q.

In order to solve the maximization problem, (Equation 6) is transformed into (Equation 7) below. Here, Φ and Δ are respectively a matrix in which eigenvectors of ΣQ _p (sum from p = 1 to p = n) are arranged, and a diagonal matrix in which eigenvalues are arranged on a diagonal line, and X is a d′-dimensional subspace V ′. Is a matrix in which orthonormal bases are arranged.

(Formula 7) is a problem of the quadratic form defined by ΦΔΦ ^T. Therefore, among the eigenvectors of ΣQ _p (sum of p = 1 to p = n) = ΦΔΦ ^T , X ′ When substituted, it becomes maximum. This indicates that the average subspace of the defined subspaces V _1,..., V _{n is} a subspace that maximizes the value of (Equation 6).

Now, using the average subspace M _i of category i, the intra-category variation matrix W _i of category _i is defined by (Equation 8). Note that P _i is a projection matrix of the average subspace M _i .

The relationship between the intra-category variation matrix W _i (Formula 8) of category i and the angle of the subspace will be described. (Expression 9) is obtained by applying (Expression 5) to (Expression 8). Here, θ _ik ⁽¹⁾ _,..., Θ _ik ^(d) are d canonical angles between the subspaces M _i and V _ik .

As a result, the trace of the intra-category variation matrix W _i (formula 8) of category i is the average of the cosine squares of the canonical angles between the learning subspace belonging to category i and the average subspace.

Category fluctuation matrix W, is defined as follows as an average of the category fluctuation matrix W _i of each category i.

In step S206, the inter-category variation matrix generation unit 206 uses the bases of the learning subspace stored in the storage unit 104 and the categories to which the bases belong, and the inter-category variation matrix that describes the definition and calculation method below. B (Formula 11) is calculated. Further, the inter-category variation matrix generation unit 206 stores the calculation result in the storage unit 104. The inter-category variation matrix is defined by the following (Equation 11) using the projection matrix P _i of the average subspace M _i of each category i.

The right side of (Formula 11) is obtained by transforming the formula using P _i ² ₌ P _i . The relationship between the inter-category variation matrix B (Formula 11) and the angle of the subspace will be described. (Formula 12) is obtained by applying (Formula 5) to (Formula 11). Here, θ _ik ⁽¹⁾ _,..., Θ _ik ^(d) are d canonical angles between the subspaces M _i and V _1k .

Here, τ _ik ⁽¹⁾ _,..., Τ _ik ^{(d ′)} are d ′ canonical angles between the average subspace M _i of category _i and the average subspace M _j of category j. Thus, the trace of the inter-category variation matrix B (Formula 11) is the average of the cosine squares of the canonical angles between the average subspaces of each category.

In step S207, the eigenvalue problem calculation unit 207 calculates eigenvalues and eigenvectors of the following matrix (Formula 13) from the intra-category variation matrix W and the inter-category variation matrix B stored in the storage unit 104. In addition, the eigenvalue problem calculation unit 207 causes the storage unit 104 to store eigenvalues and eigenvectors. Here, α is a weighting coefficient obtained through experiments. Λ is a diagonal matrix in which the eigenvalues of the matrix on the left side of (Equation 13) are arranged diagonally, and H is a matrix in which the eigenvectors are arranged.

 The relationship between the matrix of (Formula 13) and the angle of the subspace will be described. The trace of the matrix of (Equation 13) is obtained from (Equation 9) and (Equation 12) from the average of the cosine square of the canonical angle between the learning subspace belonging to each category and the average subspace. The average of the cosine squares of the canonical angles between the average subspaces is weighted and subtracted. Thereby, the eigenvalue of the matrix of (Equation 13) is a value obtained by subtracting the difference component between the categories from the variation component in each category on the basis of the angle in the corresponding eigenvector direction.

In step S208, the feature extraction matrix output unit 208 calculates the matrix H _D ^T defined below from the D eigenvectors obtained by the eigenvalue problem calculation unit 207 stored in the storage unit 104 in descending order of eigenvalues. To do. The feature extraction matrix output unit 208 stores the calculation result in the storage unit 104 or sends it to the output unit 103. However, _{H D} is, eigenvectors ν ₁ chose D pieces from the larger of the eigenvalues (Equation _{13), ...,} defined as ν _D (vertical vector) using the (Equation 14). T represents transposition of the matrix. The number of eigenvectors D is determined by experiments or the like.

 FIG. 5 is a flowchart illustrating the operation of the pattern recognition unit 106.

 In step S <b> 301, the pattern acquisition unit 301 stores the pattern to be recognized acquired by the acquisition unit 101 in the storage unit 104. The pattern to be acquired can be realized in advance in a storage medium such as a hard disk or a memory card, or when the pattern is an image, for example, with a camera connected to a personal computer. When the pattern is voice, it can be realized by a microphone connected to a personal computer, for example.

  In step S <b> 302, the feature vector generation unit 302 performs the same process as the feature vector generation unit 202.

 In step S <b> 303, the subspace generation unit 303 performs processing similar to that of the learning subspace generation unit 203 from one or more feature vectors stored in the storage unit 104, and stores the calculated subspace bases in the storage unit 104. Remember me.

 In step S304, the feature extraction application unit 304 multiplies the feature extraction matrix stored in the storage unit 104 and the base of the subspace obtained by the subspace generation unit 303 using the feature extraction matrix, and then Gram. -Perform Schmidt orthogonalization and store the obtained base of the subspace in the storage unit 104. As the feature extraction matrix stored in the storage unit 104, a feature extraction matrix output from a different device may be acquired by the acquisition unit 101, sent to the storage unit 104, and stored. Moreover, what was previously stored in a storage medium such as a hard disk or a memory card may be sent from the acquisition unit 101 to the storage unit 104. Hereinafter, the partial space obtained by this processing is referred to as an acquisition partial space.

 In step S305, the similarity calculation unit 305 performs a pattern acquisition unit 301, a feature vector generation unit 302, and a partial space generation unit 303 on the acquired partial space stored in the storage unit 104 and the pattern of the category to be recognized in advance. The processing performed by the feature extraction application unit 304 is performed. The similarity calculation unit 305 calculates the similarity defined below from the base of the generated subspace (hereinafter, this subspace is referred to as “dictionary subspace”), and stores the calculation result in the storage unit 104. Remember. The base of the dictionary subspace stored in the storage unit 104 may be the one stored in advance in a storage medium such as a hard disk or a memory card and sent from the acquisition unit 101 to the storage unit 104.

The similarity can be calculated using the method described in Non-Patent Document 1. That is, the cosine square cos ² θ ₁ of the angle θ ₁ formed by the acquisition subspace and the dictionary subspace is used as the similarity, and this cos ² θ ₁ is calculated as follows. The orthonormal bases of the acquisition subspace and the dictionary subspace are φ _1,..., Φ _M , Ψ _1,..., Ψ _N , respectively, and an M × M matrix X = (x _ij ) having x _ij in (Equation 15) as components. )about,

If the eigenvalues of X are λ _1,..., Λ _M (λ ₁ ≧ _... ≧ λ _M ), the maximum eigenvalue λ ₁ is the similarity obtained (Formula 16).

 In step 306, based on the similarity stored in the storage unit 104, the determination unit 306 has the highest similarity among the registered categories, and if the value is greater than a preset threshold, the determination unit 306 Otherwise, it is determined that there is no corresponding category as the category to which the input pattern belongs. Further, the determination unit 306 outputs the determination result to the output unit 103.

(Modification 1)
The feature extraction matrix output unit 208 may output the feature extraction matrix as Λ _D ^−1/2 H _D ^T. However, Λ _D ^−1/2 is a diagonal matrix in which D eigenvalues are selected from the larger one and the reciprocal of the square root of each eigenvalue is arranged on a diagonal line. At this time, instead of selecting D from the larger eigenvalues, all eigenvalues and eigenvectors may be used. Hereinafter, this conversion is referred to as whitening conversion.

(Modification 2)
As a category between fluctuation matrix B obtained in the category fluctuation matrix W _i and a category variability matrix generator 206 for each category i obtained in the category fluctuation matrix generation unit 205, without using the average subspace M _i for each category i The following may be used. Specifically, the intra-category variation matrix of each category i may be changed to W _i defined by f to (Equation 17), and the inter-category variation matrix may be changed to B to (Equation 18).

 At this time, the feature extraction matrix output unit 208 may output the feature extraction matrix as in (Modification 1).

(Modification 3)
The eigenvalue problem calculation unit 207 solves the eigenvalue problem of the following matrix (Equation 19) instead of the matrix of (Equation 13), and generates a feature extraction matrix output by the feature extraction matrix output unit 208 using the eigenvalue and eigenvector. May be. At this time, the feature extraction matrix of (Modification 1) may be used as the feature extraction matrix. It is also possible to use a W _{i ~} and B~ of the categories in the fluctuation matrix W _i and a category between fluctuation matrix B of each category i, respectively (Modification 2).

(Modification 4)
Instead of solving the eigenvalue problem of (Equation 13) in the eigenvalue problem calculation unit 207, the following generalized eigenvalue problem (Equation 20) is solved, and the feature extraction matrix output unit 208 outputs the feature value using the eigenvalue and eigenvector. A matrix may be generated.

Where λ is the eigenvalue of the generalized eigenvalue problem and ν is its eigenvector. At this time, the feature extraction matrix of (Modification 1) may be used as the feature extraction matrix. It is also possible to use a W _{i ~} and B~ of the categories in the fluctuation matrix W _i and a category between fluctuation matrix B of each category i, respectively (Modification 2).

(Modification 5)
The feature extraction unit 105 may generate a plurality of feature extraction matrices. In the method of generating a plurality of patterns, the learning pattern acquired by the learning pattern acquisition unit 201 may be divided into several groups, and the processes of steps S201 to S207 may be performed for each group. The method of dividing the learning pattern into several groups may be divided for each variation when the variation of the pattern is known in advance. Moreover, you may sample at random.

  When there are a plurality of feature extraction matrices, the feature extraction application unit 304 and the similarity calculation unit 305 perform processing for each feature extraction matrix, and the similarity obtained in each processing is weighted and added to the determination unit 306. . The weight is obtained by experiment. An average may be used instead of weighted addition.

Claims (7)

An acquisition unit for acquiring a plurality of partial spaces and a category to which each of the plurality of partial spaces belongs;
A projection matrix generation unit for generating a projection matrix from the subspace;
Using a plurality of subspaces belonging to the same category among the categories, an intra-category variation matrix generating unit that generates an intra-category variation matrix;
An inter- category variation matrix generating unit that generates an inter-category variation matrix using a plurality of subspaces belonging to different categories among the categories,
An eigenvalue problem calculator for calculating eigenvalues and eigenvectors obtained from eigenvalue problems defined from the intra-category variation matrix and the inter-category variation matrix;
A feature extraction calculation unit for calculating a feature extraction matrix used in feature extraction from the eigenvalue and the eigenvector;
With
The intra-category variation matrix is calculated by a linear sum of products of projection matrices generated by the projection matrix generation unit from subspaces belonging to the same category,
The inter-category variation matrix is calculated by a linear sum of products of projection matrices generated by the projection matrix generation unit from subspaces belonging to the different categories.
 2. The feature extraction apparatus according to claim 1, wherein in the eigenvalue problem, an eigenvalue and an eigenvector of a difference matrix between the intra-category variation matrix and the inter-category variation matrix are obtained.  The feature extraction apparatus according to claim 1, wherein in the eigenvalue problem, an eigenvalue and an eigenvector of a product matrix obtained by multiplying the inverse matrix of the inter-category variation matrix from the left or the right from the intra-category variation matrix are obtained. In the eigenvalue problem, an eigenvalue and an eigenvector obtained from a generalized eigenvalue problem defined by the intra-category variation matrix and the inter-category variation matrix expressed by the following equations are obtained: Feature extraction device.

(Where B is the inter-category variation matrix, W is the intra-category variation matrix, λ is the eigenvalue of the generalized eigenvalue problem, and ν is its eigenvector.)  The feature extraction matrix calculated by the feature extraction calculation unit is a matrix that is a linear map to a space based on the eigenvectors selected in order of decreasing eigenvalues. 5. The feature extraction device according to any one of 4 above. The feature extraction matrix calculated by the feature extraction calculation unit is a matrix that becomes a linear mapping to a space based on N eigenvectors or all eigenvectors in the descending order of the eigenvalues,
5. The feature extraction device according to claim 1, wherein the size of the eigenvector is an eigenvector that is a reciprocal of a square root of an absolute value of a corresponding eigenvalue. A feature vector generation unit that generates a plurality of feature vectors from one or more input patterns;
A subspace generating unit that generates a subspace from the plurality of feature vectors;
A feature extraction unit that performs linear transformation on the partial space using a feature extraction matrix obtained from the feature extraction device according to any one of claims 1 to 6;
A dictionary subspace storage unit that stores, for each category, a dictionary subspace obtained using the feature vector generation unit, the subspace generation unit, and the feature extraction unit in advance for the one or more patterns;
A similarity calculation unit that calculates the similarity between the partial space obtained by the feature extraction unit and the dictionary partial space of each category stored in the dictionary partial space storage unit;
A determination unit that determines a category to which the input pattern belongs from a similarity to each category;
A pattern recognition apparatus comprising:

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