CN111325275B - Robust image classification method and device based on low-rank two-dimensional local identification map embedding - Google Patents

Robust image classification method and device based on low-rank two-dimensional local identification map embedding Download PDF

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CN111325275B
CN111325275B CN202010105990.0A CN202010105990A CN111325275B CN 111325275 B CN111325275 B CN 111325275B CN 202010105990 A CN202010105990 A CN 202010105990A CN 111325275 B CN111325275 B CN 111325275B
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吴其阳
万鸣华
杨国为
詹天明
杨章静
张凡龙
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NANJING AUDIT UNIVERSITY
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Abstract

The invention discloses a robust image classification method and device based on low-rank two-dimensional local identification map embedding, which construct an image library unit: the method comprises the steps of obtaining a standard image library and constructing a new standard image library to be classified; a first calculation unit: in-class divergence matrix S for calculating new standard images to be classified w And an inter-class divergence matrix S b A difference J (P); a first image processing unit: the method comprises the steps of performing low-rank matrix decomposition on an acquired image X to obtain a low-rank matrix A and a sparse matrix E; a second calculation unit: combining the results of the first computing unit and the first image processing unit to obtain a final objective function: a feature matrix calculation unit: obtaining a feature matrix Y; nearest neighbor classifier unit: the method is used for classifying the images by utilizing the nearest neighbor classifier and outputting the classification result of the images. The invention solves the technical problems of lower classification precision, noise points and singular points in the existing image classification based on the 2DLPP learning model, and improves the recognition precision.

Description

Robust image classification method and device based on low-rank two-dimensional local identification map embedding
Technical Field
The invention relates to a robust image classification method and device based on low-rank two-dimensional local identification map embedding.
Background
In recent decades, to solve the "dimension disaster" problem in machine learning, image processing, computer vision and pattern recognition, many projection-based linear feature extraction techniques have been developed, including Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) and their extended versions, such as two-dimensional PCA (2 DPCA), two-dimensional LDA (2 DLDA), and the like. However, linear techniques may not find basic non-linear data structures, in practical applications, non-linear data includes non-gaussian and manifold value data, and therefore representative non-linear manifold learning techniques have been proposed to reveal hidden semantics while preserving manifold geometry. Among manifold learning theory and techniques, local Linear Embedding (LLE), ISOMAP, and Laplacian feature mapping (LE) are the most popular manifold learning techniques, however, all of these nonlinear techniques have generalization ability problems.
The graph embedding framework emphasizes the importance of constructing a similarity matrix, and a new graph embedding formula is provided, and linearization of Local Preserving Projection (LPP), laplace feature mapping, such as Neighborhood Preserving Projection (NPP) and LLE, such as Neighborhood Preserving Embedding (NPE), is provided to solve the sample generalization problem. Based on 2DPCA and 2DLDA directly acting on a two-dimensional image matrix, two-dimensional office-keeping projection (2 DLPP) is proposed for linear dimension reduction, however, 2DLPP has the following problems, firstly, the method is an unsupervised method, and the discrimination information of the recognition task is not considered; second, 2DLPP is very sensitive to outliers because it uses the L2 norm criterion to measure the similarity of pairs of projection data; finally, it has singularities, with the problem of not solving eigenvalues.
In addition, in practical applications, the data is often corrupted by noise or outliers, which may negatively affect the key information and reduce the performance of the algorithm. However, the one-dimensional vector-based method and the two-dimensional matrix-based method described above use the L2 norm as a metric, and are sensitive to noise or outliers. In the prior art, a number of dimension reduction methods using the L1 norm as a distance criterion have been proposed. For example, the sensitivity of noise and outliers in the data is overcome by solving an optimization problem instead of the L2 norm to search for local extrema; for example, the rotation invariant L1-norm PCA (R1-PCA) has some properties that are not shared with PCA-L1, generalizing the L1-norm based 2DPCA (2 DPCA-L1) to a two-dimensional case. For example, in order to improve the robustness of 2DLPP to outliers and corrosion, two-dimensional local preserving projection (2 DLPP-L1) is proposed, and the two-dimensional discriminant LPP method (2D-DLPP-L1) based on L1 norms effectively preserves the spatial topology of the image.
The method based on the L1 norm is superior to the method based on the L2 norm in terms of robust feature extraction, and the method based on the L1 norm searches sparse representation to ensure that test points can be represented by training samples of the same type. However, they cannot recover a clean matrix from noisy data. In contrast, low rank representation shows good performance in matrix recovery. A 2DPCA (N-2 DPCA) method based on a kernel norm uses the kernel norm to describe the reconstruction error, and an improved representation of the image is proposed, however, in practical applications, most of the above methods are susceptible to illumination, corrosion or noise.
In recent years, many Low Rank Representation (LRR) methods have received attention for their robustness to noise data. The method assumes that the data points are located on a low-dimensional subspace, then the representation matrix of the data points is low-rank, the problem of single subspace clustering is introduced into multi-subspace clustering, the proposed LRR can better capture the global structure of the data, and the lowest-rank representation of the data is restored. For example, patent application No. 201811269217.7 discloses a hyperspectral image classification method based on a low-rank-sparse information combined network, which takes low-rank information and sparse information into consideration and performs preprocessing to obtain a certain recognition accuracy, but the disclosed method does not take noise of a data sample into consideration, and the recognition accuracy is affected to a certain extent. The patent with application number 201510884791.3 discloses a robust face image principal component feature extraction method and a robust face image principal component feature recognition device, noise is removed by considering low rank and sparse characteristics of face image training sample data, and a good face recognition effect is achieved. However, the disclosed method is an unsupervised algorithm, and does not consider the class of data.
Disclosure of Invention
Aiming at the problems, the invention provides a robust image classification method and device based on low-rank two-dimensional local discrimination map embedding, which comprehensively considers discrimination information in map embedding and low rank of data in image classification, and is used for solving the technical problems of low classification precision, noise points and singular points in the existing image classification based on a 2DLPP learning model, solving the noise of a sample and considering the category of the sample.
In order to achieve the technical purpose and the technical effect, the invention is realized by the following technical scheme:
a robust image classification method based on low-rank two-dimensional local discrimination map embedding comprises the following steps:
1) Acquiring a standard image library and constructing a new standard image library to be classified;
2) The following processing is carried out on the new standard image to be classified:
21 Calculating an intra-class divergence matrix S of a new standard image to be classified w And an inter-class divergence matrix S b Difference J (P):
Figure GDA0004117608160000031
wherein, P is a projection matrix,
Figure GDA0004117608160000032
representing the value of the projection matrix P when the loss function is minimal, gamma being the adjustment parameter and 0 < gamma < 1;
22 Low-rank matrix decomposition is carried out on the acquired image X to obtain a low-rank matrix A and a sparse matrix E):
Figure GDA0004117608160000033
s.t.X=A+E,
wherein s.t. represents a constraint sign,
Figure GDA0004117608160000034
indicating that when the loss function is at a minimum, the values of the low rank matrix a and the sparse matrix, I.I * The number of kernels is represented by a kernel norm, I.I 1 Represents an L1 norm, β represents an adjustable parameter;
23 Combining the results according to 21) and 22) above to obtain the final objective function:
Figure GDA0004117608160000035
s.t.X=A+E
wherein α represents an adjustable parameter; rank (a) represents the rank of matrix a;
24 From Y) i =P T X i Obtaining a feature matrix Y= (Y) 1 ,…,Y i ,…,Y N ) T
wherein ,PT Representing the transposed matrix of P, Y i Representing an ith post-projection sample matrix; n represents the total number of samples; x is X i Representing an ith training sample matrix;
3) And classifying the images by using a nearest neighbor classifier, and outputting the classification result of the images.
Preferably, 21) specifically comprises the following steps:
211 Building an intra-class compactgram, building an intra-class compactgram by embedding the following formulas:
Figure GDA0004117608160000041
wherein ,
Figure GDA0004117608160000042
Figure GDA0004117608160000043
representing sample X i In the same class K c Nearest neighbor number of samples, pi c Representing the number of samples belonging to class c; I.I 2 Represents an L2 norm; d (D) C and WC Respectively representing a diagonal matrix and a weight matrix, +.>
Figure GDA0004117608160000044
Kronecker product, I, representing a matrix n Representing an identity matrix of order n, L c =D c -W c
212 Constructing an edge separation graph by embedding the following graph-embedding formula:
Figure GDA0004117608160000045
Figure GDA0004117608160000051
wherein ,
Figure GDA0004117608160000052
Figure GDA0004117608160000053
denoted by K p Recently at
Figure GDA00041176081600000510
Data pair, K in (a) p Representation and sample X i The number of nearest neighbor samples of different classes, pi t Representing the number of samples belonging to the t-th class, D p Representing a diagonal matrix, W p Representing a weight matrix, L p =D p -W p
213 Calculating an optimal J (P):
J(P)=mintr[S w -γS b ]
where tr [. Cndot. ] represents the trace of the matrix.
Preferably, 23) specifically comprises the following steps:
231 Constructing a final objective function of a low-rank two-dimensional local discrimination map embedding algorithm:
Figure GDA0004117608160000054
s.t.X=A+E,A=B,Y i =P T A i
wherein ,
Figure GDA0004117608160000055
representing low rank matrix a, sparseness when the loss function is minimalValues of matrix E and projection matrix P, +.>
Figure GDA0004117608160000056
Representing weight matrix in class,/->
Figure GDA0004117608160000057
Representing an inter-class weight matrix, B representing a noise-free matrix, A i Representing an ith noise-free sample matrix;
232 Construction of an augmented Lagrange multiplier function L (P, B, E, A, M) 1 ,M 2 ,μ):
Figure GDA0004117608160000058
Wherein μ > 0 is a penalty parameter, M 1 and M2 Is the lagrangian multiple multiplier and,
Figure GDA0004117608160000059
represents F norm, L w Representing an intra-class Laplace matrix, L b Representing an inter-class Laplace matrix;
233 Solving for variables B, E, P and a.
Preferably, 3) specifically comprises the following steps:
31 Definition d (Y) 1 ,Y 2 ) The method comprises the following steps:
Figure GDA0004117608160000061
wherein ,
Figure GDA0004117608160000062
Y 1 is a feature matrix;
Figure GDA0004117608160000063
Y 2 Is a feature matrix; y is Y 1 k Is Y 1 Is the kth column feature matrix of (a);
Figure GDA0004117608160000064
Is Y 2 Is the kth column feature matrix of (a); d is a characteristic value, i.i. | 2 Is the L2 norm;
32 If the total characteristic distance is Y 1 ,Y 2 ,…,Y N Each image has a class label c i Corresponds to a new test sample Y, if
Figure GDA0004117608160000065
And Y is j ∈c l Then the classification result is Y ε c l, wherein ,
Figure GDA0004117608160000066
To the value of variable j, c when the loss function is minimal l Is of class I;
33 Solving the final category of all the images and outputting the classification result of the images.
The device comprises:
constructing an image library unit: the method comprises the steps of obtaining a standard image library and constructing a new standard image library to be classified;
a first calculation unit: in-class divergence matrix S for calculating new standard images to be classified w And an inter-class divergence matrix S b A difference J (P);
a first image processing unit: the method comprises the steps of performing low-rank matrix decomposition on an acquired image X to obtain a low-rank matrix A and a sparse matrix E;
a second calculation unit: combining the results of the first computing unit and the first image processing unit to obtain a final objective function:
Figure GDA0004117608160000067
s.t.X=A+E
a feature matrix calculation unit: for according to Y i =P T X i Obtaining a feature matrix Y= (Y) 1 ,…,Y i ,…,Y N ) T
Nearest neighbor classifier unit: the method is used for classifying the images by utilizing the nearest neighbor classifier and outputting the classification result of the images.
Preferably, the first calculation unit includes:
constructing an intra-class compactgram unit: for building a compactgram within a class by a graph embedding formula;
constructing an edge separation graph unit: for constructing an edge separation graph by graph embedding formulas;
a calculation unit: for computing an optimal J (P) from the intra-class compactors and edge separator graphs.
Preferably, the second calculation unit includes:
constructing a final objective function unit: the final objective function is used for constructing a low-rank two-dimensional local identification map embedding algorithm;
constructing an augmented Lagrange multiplier function unit: for constructing an augmented Lagrange multiplier function L (P, B, E, A, M 1 ,M 2 ,μ);
And a solving unit: for solving variables B, E, P and a.
A computer readable storage medium storing a computer program which, when run on a computer, causes the computer to perform the method of any one of the preceding claims.
The beneficial effects of the invention are as follows:
first, in order to overcome the sensitivity of the 2DLPP method, the invention combines low-rank learning with robust learning, introduces low rank into the 2DLPP, and provides a novel dimension reduction method called low-rank two-dimensional local identification map embedding (LR-2 DLDGE), which comprehensively considers the discrimination information in map embedding and the low rank property of data in image classification. First, intra-class graphs and inter-class graphs are constructed, which can retain local neighborhood discrimination information. Second, the given data is divided into a low-order feature encoding section and an error section that ensures noise sparseness. A number of experiments were performed on a number of standard image databases using the present method to verify the performance of the proposed method. Experimental results show that the method has strong robustness to noise points of the image.
Secondly, the invention extracts image recognition features by using a robust image classification method model based on low-rank two-dimensional local discrimination map embedding and a design optimization algorithm, on one hand, the LR-2DLDGE method uses a two-dimensional image matrix, so that the image does not need to be converted into a vector, the method uses a map embedding method to extract features, more image features can be extracted, and the intra-class covariance matrix of the method is reversible, so that the problem of small samples does not exist; on the other hand, the low-rank learning algorithm adopted in the LR-2DLDGE algorithm can well solve the problem that the recognition rate of images is reduced due to changes of illumination, expression, gesture and the like, and can also solve the problem that the recognition rate is reduced when the connection between data sample points which are far away is weak or the overlapping of the data sample points between adjacent domains is insufficient.
Thirdly, the invention uses nearest neighbor classifier to classify, which can effectively improve the image classification precision and promote the further excavation of the sparse characteristic of the image.
Fourth, the existing subspace learning, graph embedding learning and low-rank learning models cannot solve the technical problems of noise points and singular points existing in image classification, the technical problems of low classification precision, noise points and singular points existing in the image classification based on the 2DLPP learning model are solved, the recognition precision is improved, and the method can be used in the fields of national public safety, social safety, information safety, financial safety, man-machine interaction and the like, and has good application prospects.
Drawings
FIG. 1 is a schematic diagram of a robust image classification method based on low-rank two-dimensional local discrimination map embedding of the present invention;
FIG. 2 is a flow chart of a method for classifying robust images based on rain embedding of low rank two-dimensional local discrimination map of the present invention;
FIG. 3 is 10 images of a sub-class in the ORL face image library;
FIG. 4 is a partial image in the USPS handwriting library;
fig. 5 is a partial image in a PolyU palmprint library.
Detailed Description
The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples, so that those skilled in the art can better understand the present invention and implement it, but the examples are not limited thereto.
A robust image classification method based on low-rank two-dimensional local discrimination map embedding comprises the following steps:
1) Acquiring a standard image library and constructing a new standard image library to be classified;
2) The following processing is carried out on the new standard image to be classified:
21 Calculating an intra-class divergence matrix S of a new standard image to be classified w And an inter-class divergence matrix S b Difference J (P):
Figure GDA0004117608160000091
wherein, P is a projection matrix,
Figure GDA0004117608160000092
representing the value of the projection matrix P when the loss function is minimal, gamma being the adjustment parameter and 0 < gamma < 1;
22 Low-rank matrix decomposition is carried out on the acquired image X to obtain a low-rank matrix A and a sparse matrix E):
Figure GDA0004117608160000093
s.t.X=A+E,
wherein s.t. represents a constraint sign,
Figure GDA0004117608160000094
indicating that when the loss function is at a minimum, the values of the low rank matrix a and the sparse matrix E represent, I.I * The number of kernels is represented by a kernel norm, I.I 1 Represents an L1 norm, β represents an adjustable parameter;
23 Combining the results according to 21) and 22) above to obtain the final objective function:
Figure GDA0004117608160000095
s.t.X=A+E
wherein α represents an adjustable parameter; rank (·) represents the rank of matrix a;
24 From Y) i =P T X i Obtaining a feature matrix Y= (Y) 1 ,…,Y i ,…,Y N ) T
wherein ,PT Representing the transposed matrix of P, Y i Representing an ith post-projection sample matrix; n represents the total number of samples; x is X i Representing an ith training sample matrix;
3) And classifying the images by using a nearest neighbor classifier, and outputting the classification result of the images.
According to the method, the image recognition features are extracted by utilizing a robust image classification method model based on low-rank two-dimensional local discrimination map embedding and a design optimization algorithm, on one hand, the LR-2DLDGE method uses a two-dimensional image matrix, so that an image is not required to be converted into a vector, the image features can be extracted more by utilizing a map embedding method to extract features, and the intra-class covariance matrix of the method is reversible, so that the problem of a small sample is avoided; on the other hand, the low-rank learning algorithm adopted in the LR-2DLDGE algorithm can well solve the problem that the recognition rate of images is reduced due to changes of illumination, expression, gesture and the like, and can also solve the problem that the recognition rate is reduced when the connection between data sample points which are far away is weak or the overlapping of the data sample points between adjacent domains is insufficient. The following is a detailed description with reference to fig. 1-5.
First, data acquisition and preprocessing are performed: and acquiring a standard image library (such as an AR face, a USPS handwriting and a PolyU palm print), taking the standard AR face image library as an example, and cutting the standard image library to construct a new standard image library to be classified.
Secondly, feature extraction and feature selection are carried out on the new standard face image to be classified: as shown in fig. 2, a training and testing face image library is obtained, and the optimal image features are obtained by embedding a feature extraction model into a low-rank two-dimensional local identification map, which specifically comprises:
21 Calculating an intra-class divergence matrix S of a new standard image to be classified w And an inter-class divergence matrix S b Difference J (P):
Figure GDA0004117608160000101
wherein, P is a projection matrix,
Figure GDA0004117608160000102
representing the value of the projection matrix P when the loss function is minimal, gamma being the adjustment parameter and 0 < gamma < 1;
preferably, 21) specifically comprises the following steps:
211 First, it is introduced that the intra-class map can be intra-class data compression, and the intra-class map is constructed by the following map embedding formula:
Figure GDA0004117608160000111
wherein ,
Figure GDA0004117608160000112
Figure GDA0004117608160000113
representing sample X i In the same class K c Nearest neighbor number of samples, pi c Representing the number of samples belonging to class c; I.I 2 Represents an L2 norm; d (D) C and WC Respectively representing a diagonal matrix and a weight matrix, +.>
Figure GDA0004117608160000114
Kronecker product, I, representing a matrix n Representing an identity matrix of order n, L c =D c -W c
212 Constructing an edge separation graph by embedding the following graph-embedding formula:
Figure GDA0004117608160000115
wherein ,
Figure GDA0004117608160000116
Figure GDA0004117608160000117
the representation represents K p Recently at
Figure GDA0004117608160000118
Data pair (i.e. two samples not in the same class), K p Representing book X i The number of nearest neighbor samples of different classes, pi t Representing the number of samples belonging to the t-th class, D p Representing a diagonal matrix, W p Representing a weight matrix, L p =D p -W p
213 Embedding: the optimal projection can be obtained by:
J(P)=mintr[S w -γS b ]
where tr [. Cndot. ] represents the trace of the matrix.
In order to improve the precision of sparse representation in the face recognition process, 22) performing low-rank matrix decomposition on the acquired image X to obtain a low-rank matrix A and a sparse matrix E:
assuming that matrix X can be decomposed into two matrices, i.e. (in other words) x=a+e, a being a low rank matrix, E being a sparse (noise) matrix, low rank matrix recovery aims to find a low rank a approximation representing X, low rank matrix recovery can be regarded as the following optimization problem:
Figure GDA0004117608160000121
s.t.X=A+E,
wherein ,
Figure GDA0004117608160000122
representing when the loss function is the mostThe values of the low rank matrix a and the sparse matrix E, for hours, lambda is the variable parameter that is to be adjusted, I.I 0 Representing the L0 norm.
The above is an NP-hard problem that can be equivalent to solving if matrix a is low rank and E is a sparse matrix:
Figure GDA0004117608160000123
s.t.X=A+E,
wherein s.t. represents a constraint sign, I A I * Denoted as the core norm of a, the kernel norm can approximate the rank of a, I E I 1 For L1 norm, it can be approximated to replace E 0
23 Combining the results according to 21) and 22) above to obtain the final objective function:
Figure GDA0004117608160000124
s.t.X=A+E
wherein α represents an adjustable parameter; rank (·) represents the rank of matrix a;
preferably, 23) specifically comprises the following steps:
231 Constructing a final objective function of a low-rank two-dimensional local discrimination map embedding algorithm:
Figure GDA0004117608160000125
s.t.X=A+E,A=B,Y i =P T A i
wherein ,
Figure GDA0004117608160000131
representing the values of the low rank matrix A, the sparse matrix E and the projection matrix P when the loss function is minimal, < >>
Figure GDA0004117608160000132
Representing weight matrix in class,/->
Figure GDA0004117608160000133
Representing an inter-class weight matrix, B representing a noise-free matrix, A i Representing an ith noise-free sample matrix;
232 Construction of an augmented Lagrange multiplier function L (P, B, E, A, M) 1 ,M 2 ,μ):
The augmented Lagrange multiplier function of the LR-2DLDGE algorithm is:
Figure GDA0004117608160000134
wherein μ > 0 is a penalty parameter, M 1 and M2 Is the lagrangian multiple multiplier and,
Figure GDA0004117608160000135
represents F norm, L w Representing an intra-class Laplace matrix, L b Representing an inter-class Laplace matrix;
233 Solving variables B, E, P and a:
(1) Solving the variable B:
fixing all variables except B, the solution equation for B can be expressed as:
Figure GDA0004117608160000136
the solution of the above equation can be found by singular value decomposition SVD:
Figure GDA0004117608160000137
wherein ,
Figure GDA0004117608160000141
Σ=diag(σ 1 ,…,σ r ). U is an m×m unitary matrix; Σ is a half-positive definite m×n order diagonal matrix; v is an n×n unitary matrix, σ j And r is a matrix rank, which is a positive singular value.
(2) Solving the variable E:
fixing all variables except E, the solution equation for E can be expressed as:
Figure GDA0004117608160000142
we can solve the above directly with the contraction operator, we define the soft threshold operator S ε [X]=sign (X). Max (x| -epsilon, 0), there is a solution of the following closed form:
Figure GDA0004117608160000143
where sign is a sign function and ε is a constant.
(3) Solving a variable P:
fixing all variables except P, the solution equation for P can be expressed as:
Figure GDA0004117608160000144
the above equation is rewritten:
Figure GDA0004117608160000145
adding a constraint is as follows:
P T (X-E)(D w -D b )(X-E) T P=1
finally, the final equation can be obtained:
Figure GDA0004117608160000146
the above solution can be obtained by the following generalized eigenvalue problem:
Figure GDA0004117608160000147
where Λ represents a set of eigenvalues, L W Representing intra-class Laplace matrix, I representing identity matrix, D W Representing intra-class diagonal matrix, D B Representing an inter-class diagonal matrix.
(4) Solving the variable A:
fixing all variables except a, the solution equation for a can be expressed as:
Figure GDA0004117608160000151
by setting the derivative
Figure GDA0004117608160000152
The method can obtain:
Figure GDA0004117608160000153
wherein
Figure GDA0004117608160000154
and
Figure GDA0004117608160000155
A is essentially by solving the Sylvester equation.
3) The method and the device can effectively improve the image classification precision and promote the further mining of the sparse characteristics of the images by classifying the images by using the nearest neighbor classifier and outputting the classification result of the images. Preferably, 3) specifically comprises the following steps:
31 Definition d (Y) 1 ,Y 2 ) The method comprises the following steps:
Figure GDA0004117608160000156
wherein ,
Figure GDA0004117608160000157
Y 1 is a feature matrix;
Figure GDA0004117608160000158
Y 2 Is a feature matrix; y is Y 1 k Is Y 1 Is the kth column feature matrix of (a);
Figure GDA0004117608160000159
Is Y 2 Is the kth column feature matrix of (a); d is a characteristic value, i.i. | 2 Is the L2 norm;
32 If the total characteristic distance is Y 1 ,Y 2 ,…,Y N Each image has a class label c i Corresponds to a new test sample Y, if
Figure GDA00041176081600001510
And Y is j ∈c l Then the classification result is Y ε c l, wherein ,
Figure GDA00041176081600001511
To the value of variable j, c when the loss function is minimal l Is of class I;
33 According to 31) and 32) above, solving the final category of all face images, and outputting the classification result of the face images.
The invention solves the technical problems of low classification precision, noise points and singular points in the existing image classification based on a 2DLPP learning model, and improves the recognition precision.
Correspondingly, a robust image classification transpose based on low-rank two-dimensional local identification map embedding, adopting the classification method, the device comprises:
constructing an image library unit: the method comprises the steps of obtaining a standard image library and constructing a new standard image library to be classified;
a first calculation unit: for gaugesCalculating new intra-class divergence matrix S of standard image to be classified w And an inter-class divergence matrix S b A difference J (P);
a first image processing unit: the method comprises the steps of performing low-rank matrix decomposition on an acquired image X to obtain a low-rank matrix A and a sparse matrix E;
a second calculation unit: combining the results of the first computing unit and the first image processing unit to obtain a final objective function:
Figure GDA0004117608160000161
s.t.X=A+E
a feature matrix calculation unit: for according to Y i =P T X i Obtaining a feature matrix Y= (Y) 1 ,…,Y i ,…,Y N ) T
Nearest neighbor classifier unit: the method is used for classifying the images by utilizing the nearest neighbor classifier and outputting the classification result of the images.
Preferably, the first calculation unit includes:
constructing an intra-class compactgram unit: for building a compactgram within a class by a graph embedding formula;
constructing an edge separation graph unit: for constructing an edge separation graph by graph embedding formulas;
a calculation unit: for computing an optimal J (P) from the intra-class compactors and edge separator graphs.
Preferably, the second calculation unit includes:
constructing a final objective function unit: the final objective function is used for constructing a low-rank two-dimensional local identification map embedding algorithm;
constructing an augmented Lagrange multiplier function unit: for constructing an augmented Lagrange multiplier function L (P, B, E, A, M 1 ,M 2 ,μ);
And a solving unit: for solving variables B, E, P and a.
A computer readable storage medium storing a computer program which, when run on a computer, causes the computer to perform the method of any one of the preceding claims.
In order to overcome the sensitivity of the 2DLPP method, the invention combines low-rank learning with robust learning, introduces a low rank into the 2DLPP, and provides a novel dimension reduction method called low-rank two-dimensional local identification map embedding (LR-2 DLDGE), which comprehensively considers the discrimination information in map embedding and the low rank property of data in image classification. First, intra-class graphs and inter-class graphs are constructed, which can retain local neighborhood discrimination information. Second, the given data is divided into a low-order feature encoding section and an error section that ensures noise sparseness. A number of experiments were performed on a number of standard image databases using the present method to verify the performance of the proposed method.
In order to verify the effectiveness of the embedding algorithm in image recognition based on the low-rank two-dimensional partial authentication map, the experiments of recognition are respectively carried out on an AR face database, a USPS handwriting and a PolyU palmprint image database, and the classification recognition performances of the algorithm and 2DPCA,2DPCA-L1, 2DLPP-L1 and LRR are compared, wherein all the algorithms are operated for 10 times and Euclidean distance and nearest neighbor classifiers are adopted. Experimental environment: dell PC, CPU: interAthlon (tm) 64Processor, memory: 1024M,Matlab 7.01.
1. Experiments on ORL face database
The ORL standard face library (http:// www.uk.research.att.com/facedatabase. Html) consists of 40 people, each of which consists of 10 grayscale images of 112 x 92 size, some of which are taken at different times, the facial expression, face details, face pose and face dimensions of the person varying to different extents, e.g. smiling or smiling, eyes or open or close, with or without glasses; depth rotation and plane rotation can reach 20 degrees; there is also a variation in scale of up to 10%. In this experiment, the image was processed in the form of a gray scale of 56×46. Fig. 3 is 10 images of a person in the ORL face library.
In the experiment, l (l=2, 3,4, 5) images of each person are selected for training, and the rest 10-l images are tested, wherein the test results are shown in table 1:
TABLE 1 maximum average recognition rate results for different algorithms on ORL face library
Figure GDA0004117608160000181
2. Experiments on a USPS handwriting database
The USPS hand-written digital image library (http:// www.cs.toronto.edu/-roweis/data.html) has images with numbers 0-9, each number has 1100 samples, and the image size is 16 multiplied by 16. We selected 100 samples per number for the experiment. Fig. 4 shows a portion of an image of the number "2".
In the experiment, l (l=20, 30,40, 50) samples were randomly selected as training samples, and the remaining 100-l were test samples. The maximum recognition rate and the corresponding dimension are listed in table 2 below.
TABLE 2 maximum average recognition rate results for different algorithms on the USPS handwriting library
Figure GDA0004117608160000182
3. Experiments on PolyU palmprint database
In the experiment we selected a sub-library of the PolyU palmprint database of the university of hong Kong's university, which contains 600 images of 100 different palmprints, 6 images per palmprint. The 6 images were taken during two time periods, the first 3 taken during the first time period and the second 3 taken during the second time period, with the two time periods being separated by an average of 2 months. The central region of the image is cropped, scaled to a 128 x 128 pixel size and histogram equalized.
Training is performed by using 3 images obtained in the first time period, and 3 images obtained in the second time period are tested, and table 3 shows the maximum recognition rate and the corresponding dimension.
TABLE 3 maximum average recognition rate results for different algorithms on PolyU palmprint library
Figure GDA0004117608160000191
Through the experimental analysis, the method can effectively improve the image classification precision, has the advantage of high recognition rate, can be used in the fields of national public safety, social safety, information safety, financial safety, man-machine interaction and the like, and has good application prospect.
The foregoing description is only of the preferred embodiments of the present invention, and is not intended to limit the scope of the invention, but rather is intended to cover any equivalents of the structures disclosed herein or modifications in equivalent processes, or any application, directly or indirectly, within the scope of the invention.

Claims (6)

1. The robust image classification method based on the embedding of the low-rank two-dimensional local discrimination map is characterized by comprising the following steps:
1) Acquiring a standard image library and constructing a new standard image library to be classified;
2) The following processing is carried out on the new standard image to be classified:
21 Calculating an intra-class divergence matrix S of a new standard image to be classified w And an inter-class divergence matrix S b Difference J (P):
Figure FDA0004117608150000011
wherein, P is a projection matrix,
Figure FDA0004117608150000012
representing the value of the projection matrix P when the loss function is minimal, gamma being the adjustment parameter and 0 < gamma < 1;
22 Low-rank matrix decomposition is carried out on the acquired image X to obtain a low-rank matrix A and a sparse matrix E):
Figure FDA0004117608150000013
s.t.X=A+E,
wherein s.t. represents a constraint sign,
Figure FDA0004117608150000014
indicating that when the loss function is at a minimum, the values of the low rank matrix a and the sparse matrix E, I.I * The number of kernels is represented by a kernel norm, I.I 1 Represents an L1 norm, β represents an adjustable parameter;
23 Combining the results according to 21) and 22) above to obtain the final objective function:
Figure FDA0004117608150000015
s.t.X=A+E
wherein α represents an adjustable parameter; rank (a) represents the rank of matrix a;
24 From Y) i =P T X i Obtaining a feature matrix Y= (Y) 1 ,…,Y i ,…,Y N ) T
wherein ,PT Representing the transposed matrix of P, Y i Representing an ith post-projection sample matrix; n represents the total number of samples; x is X i Representing an ith training sample matrix;
3) Classifying the images by using a nearest neighbor classifier, and outputting classification results of the images;
21 Specifically comprising the following steps:
211 Building an intra-class compactgram, building an intra-class compactgram by embedding the following formulas:
Figure FDA0004117608150000021
wherein ,
Figure FDA0004117608150000022
Figure FDA0004117608150000023
representing sample X i In the same class K c Nearest neighbor number of samples, pi c Representing the number of samples belonging to class c; I.I 2 Represents an L2 norm; d (D) C and WC Respectively representing a diagonal matrix and a weight matrix, +.>
Figure FDA0004117608150000024
Kronecker product, I, representing a matrix n Representing an identity matrix of order n, L c =D c -W c
212 Constructing an edge separation graph by embedding the following graph-embedding formula:
Figure FDA0004117608150000025
wherein ,
Figure FDA0004117608150000026
Figure FDA0004117608150000027
denoted by K p Recently at
Figure FDA0004117608150000028
Data pair, K in (a) p Representation and sample X i The number of nearest neighbor samples of different classes, pi t Representing the number of samples belonging to the t-th class, D p Representing a diagonal matrix, W p Representing a weight matrix, L p =D p -W p
213 Calculating an optimal J (P):
J(P)=mintr[S w -γS b ]
wherein tr [. Cndot. ] represents the trace of the matrix;
23 Specifically comprising the following steps:
231 Constructing a final objective function of a low-rank two-dimensional local discrimination map embedding algorithm:
Figure FDA0004117608150000031
s.t.X=A+E,A=B,Y i =P T A i
wherein ,
Figure FDA0004117608150000032
representing the values of the low rank matrix A, the sparse matrix E and the projection matrix P when the loss function is minimal, < >>
Figure FDA0004117608150000033
Representing weight matrix in class,/->
Figure FDA0004117608150000034
Representing an inter-class weight matrix, B representing a noise-free matrix, A i Representing an ith noise-free sample matrix;
232 Construction of an augmented Lagrange multiplier function L (P, B, E, A, M) 1 ,M 2 ,μ):
Figure FDA0004117608150000035
Wherein μ > 0 is a penalty parameter, M 1 and M2 Is the lagrangian multiple multiplier and,
Figure FDA0004117608150000036
represents F norm, L w Representing an intra-class Laplace matrix, L b Representing an inter-class Laplace matrix;
233 Solving for variables B, E, P and a.
2. The robust image classification method based on low rank two-dimensional local discrimination map embedding of claim 1, 3) specifically comprising the steps of:
31 Fixed) to a patientMeaning d (Y) 1 ,Y 2 ) The method comprises the following steps:
Figure FDA0004117608150000037
wherein ,
Figure FDA0004117608150000041
Y 1 is a feature matrix;
Figure FDA0004117608150000042
Y 2 Is a feature matrix; y is Y 1 k Is Y 1 Is the kth column feature matrix of (a);
Figure FDA0004117608150000043
Is Y 2 Is the kth column feature matrix of (a); d is a characteristic value, i.i. | 2 Is the L2 norm;
32 If the total characteristic distance is Y 1 ,Y 2 ,…,Y N Each image has a class label c i Corresponds to a new test sample Y, if
Figure FDA0004117608150000044
And Y is j ∈c l Then the classification result is Y ε c l, wherein ,
Figure FDA0004117608150000045
To the value of variable j, c when the loss function is minimal l Is of class I;
33 Solving the final category of all the images and outputting the classification result of the images.
3. A robust image classification transpose based on low rank two-dimensional local authentication graph embedding, characterized in that the apparatus comprises:
constructing an image library unit: the method comprises the steps of obtaining a standard image library and constructing a new standard image library to be classified;
a first calculation unit: in-class divergence matrix S for calculating new standard images to be classified w And an inter-class divergence matrix S b A difference J (P);
a first image processing unit: the method comprises the steps of performing low-rank matrix decomposition on an acquired image X to obtain a low-rank matrix A and a sparse matrix E;
a second calculation unit: combining the results of the first computing unit and the first image processing unit to obtain a final objective function:
Figure FDA0004117608150000046
s.t.X=A+E
a feature matrix calculation unit: for according to Y i =P T X i Obtaining a feature matrix Y= (Y) 1 ,…,Y i ,…,Y N ) T
Nearest neighbor classifier unit: the method is used for classifying the images by utilizing the nearest neighbor classifier and outputting the classification result of the images.
4. A robust image classification transpose based on low rank two-dimensional partial authentication map embedding as defined in claim 3 wherein the first computing unit comprises:
constructing an intra-class compactgram unit: for building a compactgram within a class by a graph embedding formula;
constructing an edge separation graph unit: for constructing an edge separation graph by graph embedding formulas;
a calculation unit: for computing an optimal J (P) from the intra-class compactors and edge separator graphs.
5. The robust image classification transpose based on low rank two-dimensional partial authentication map embedding of claim 4 wherein the second computing unit comprises:
constructing a final objective function unit: the final objective function is used for constructing a low-rank two-dimensional local identification map embedding algorithm;
constructing an augmented Lagrange multiplier function unit: for constructing an augmented Lagrange multiplier function L (P, B, E, A, M 1 ,M 2 ,μ);
And a solving unit: for solving variables B, E, P and a.
6. A computer readable storage medium for storing a computer program which, when run on a computer, causes the computer to perform the method of any of claims 1-2.
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