CN105678260B - Face recognition method based on sparse hold distance measurement - Google Patents

Face recognition method based on sparse hold distance measurement Download PDF

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CN105678260B
CN105678260B CN201610008056.0A CN201610008056A CN105678260B CN 105678260 B CN105678260 B CN 105678260B CN 201610008056 A CN201610008056 A CN 201610008056A CN 105678260 B CN105678260 B CN 105678260B
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钱冬云
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Zhejiang Industry and Trade Vocational College
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Abstract

The invention provides a face recognition method based on sparse hold distance measurement, which comprises the following steps: step 1, extracting face data with label information from all stored face data, and constructing a frame of a distance measurement algorithm by using a maximum boundary theory based on the face data; step 2, excavating sparse structural information among samples by using a sparse representation theory, and constructing a sparse weight matrix; step 3, constructing a sparse maintenance optimization function, so that sparse structural information of the sample is maximally stored in a newly constructed distance measurement space; step 4, combining the maximum boundary theory and a sparse keeping optimization function by utilizing a regularization frame to obtain sparse keeping distance measurement; and 5, extracting the image characteristics of the face to be recognized by using the characteristic descriptor, performing a face recognition experiment under the sparse distance measurement, and classifying the tested face data. The invention has the advantages of high identification precision, few parameters, full utilization of label samples and label-free samples and the like.

Description

Face recognition method based on sparse hold distance measurement
Technical Field
The invention belongs to the technical field of data mining and artificial intelligence, and particularly relates to a face recognition method based on sparse keeping distance measurement.
Background
The traditional authentication modes, such as keys and passwords, have the defects of complexity, easiness in stealing and the like. With the development of the multimedia age, these traditional authentication methods have been gradually replaced. Face recognition technology is one of the most widely used authentication methods at present. In brief, the face recognition technology is to process the data of the face to be classified, compare the processed data with the data of the face in the database, and recognize the captured face. In recent years, researchers have proposed a plurality of face recognition methods, and good face recognition effects are obtained to a certain extent based on face template matching, dimensionality reduction, neural networks, SVM classifiers and other methods.
However, in order to obtain a better face recognition system, it is important to measure the similarity between face images by using an appropriate distance metric. In the prior art, many distance measurement algorithms (ITML, LMNN and the like) do not fully utilize all unlabeled sample data, and most algorithms consider class labels of samples and ignore spatial position information among the samples, so that the distance measurement algorithms are difficult to further improve the identification accuracy in many applications. Therefore, using an appropriate distance metric algorithm has a crucial impact for many applications, such as face recognition.
Disclosure of Invention
The invention aims to provide a face recognition method based on sparse preserving distance measurement aiming at the defects in the prior art, which fully utilizes all sample data (labeled samples and unlabeled samples) and fully preserves sparse structural information of the sample data so as to improve the accuracy of face recognition.
The purpose of the invention is realized by the following technical scheme: a face recognition method based on sparse hold distance measurement is specifically realized by the following steps:
step 1, extracting face data with label information from all stored face data, and constructing a frame of a distance measurement algorithm by using a maximum boundary theory based on the face data;
step 2, excavating sparse structural information among samples by using a sparse representation theory, and constructing a sparse weight matrix;
step 3, constructing a sparse maintenance optimization function, so that sparse structural information of the sample is maximally stored in a newly constructed distance measurement space;
step 4, combining the maximum boundary theory and a sparse keeping optimization function by utilizing a regularization frame to obtain sparse keeping distance measurement;
and 5, extracting the image characteristics of the face to be recognized by using the characteristic descriptor, performing a face recognition experiment under the sparse distance measurement, and classifying the tested face data.
Further, step 1 specifically includes:
according to the label information of the samples, calculating the sum of squares of distances between samples of different types under the condition of using a distance measurement matrix A, wherein the calculation formula is as follows:
Figure DEST_PATH_GDA0000942136000000021
wherein (x)i,xj) E D denotes the sample xiAnd xjFrom different classes, dA(xi,xj) Denotes sample x in case of using the distance metric matrix AiAnd xjT represents the transpose of the matrix;
according to the label information of the samples, calculating the distance square sum among the same class samples under the condition of using the distance measurement matrix A, wherein the calculation formula is as follows:
Figure DEST_PATH_GDA0000942136000000022
wherein (x)k,xl) E S denotes the sample xkAnd xlFrom the same class, dA(xk,xl) Denotes sample x in case of using the distance metric matrix AkAnd xlT represents the transpose of the matrix; using a maximum boundary theory to construct a distance measurement frame, so that the sum of distances among different samples is maximum and the sum of distances among similar samples is minimum under a distance measurement matrix A, and the distance measurement frame is as follows:
Figure DEST_PATH_GDA0000942136000000031
wherein the content of the first and second substances,
Figure DEST_PATH_GDA0000942136000000032
(xi,xj) E D denotes the sample xiAnd xjFrom different classes, (x)k,xl) E S denotes the sample xkAnd xlFrom the same class, NDIs the number of constraint pairs in set D, NSFor the number of constraint pairs in the set S, α is a regularization parameter, and the proportion of the sum of distances between different types of samples to the sum of distances between similar types of samples is weighed;
changing A to WWTSubstituting the formula (3) for solving, and solving an optimal projection matrix W through characteristic decomposition of the matrix so as to obtain a distance measurement matrix A; wherein WTIs a transposed matrix of W.
Further, step 3 specifically includes:
constructing a sparse weight relationship among samples by keeping sparse representation, and constructing a sparse keeping optimization function as follows:
Figure DEST_PATH_GDA0000942136000000033
in the formula, siIs except for xiLinear composition x of all but samplesiIs expressed as xiSparse correlations with all other samples; x ═ X1,x2,…,xn]Is a dictionary matrix composed of all samples; n is a positive integer;
the equivalence of equation (10) is transformed as follows:
Figure DEST_PATH_GDA0000942136000000034
wherein S ═ S1,s2,…,sn]Is a sparse weight matrix;
equation (11) is transformed into the maximization problem and constraints are added as follows:
Figure DEST_PATH_GDA0000942136000000035
in the formula, S is a sparse weight matrix, X is a dictionary matrix, and W is a projection matrix.
Further, step 4 specifically includes:
adding the sparsity preserving optimization function in step 3 of claim 1 into a distance measurement frame through a regularization structure to obtain an objective function of sparsity preserving distance measurement as follows:
Figure DEST_PATH_GDA0000942136000000041
wherein the content of the first and second substances,
Figure DEST_PATH_GDA0000942136000000042
and P ═ X (S + S)T-STS)XTα and β are both regularization parameters that are used to equalize the specific gravity of the parts to obtain the optimal metric subspace.
Compared with the prior art, the invention has the beneficial effects that: the method properly keeps sparse structural information among face data samples, and fully uses a large amount of label-free face data, so that a distance measurement algorithm can deeply understand the manifold structure of the samples, and finally the recognition accuracy of a face recognition system is further improved.
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FIG. 1 is a flow chart of the present invention.
FIG. 2 is a schematic diagram of the present invention showing different types of samples dispersed and similar types of samples gathered;
FIG. 3 is a comparison graph of recognition accuracy of different distance measurement methods on ORL face data;
fig. 4 is a comparison diagram of recognition accuracy of different distance measurement methods on AR face data.
Detailed Description
The present invention is described in detail with reference to the embodiments shown in the drawings, but it should be understood that these embodiments are not intended to limit the present invention, and those skilled in the art should understand that functional, methodological, or structural equivalents or substitutions made by these embodiments are within the scope of the present invention.
Referring to fig. 1, the embodiment provides a face recognition method based on sparse preserving distance measurement, and the specific implementation method is as follows:
step S1, extracting the face data with label information from all the stored face data (label data and non-label data), and constructing a frame of the distance metric algorithm based on the face data by using the maximum boundary theory.
The method specifically comprises the following steps:
step ①, the maximum boundary theory utilizes all the label data, so that the sum of the distances between the samples of the same type is minimum while the sum of the distances between the samples of different types is maximum under the new distance measurement.
Figure DEST_PATH_GDA0000942136000000051
Wherein (x)i,xj) E D denotes the sample xiAnd xjFrom the different classes, the set D contains all pairs of samples from the different classes, and the maximization formula (1) maximizes the sum of the distances between the samples of the different classes.
And ②, defining the sum of the distances among the samples of the same type under the distance measurement matrix A according to the label information of the samples as follows:
Figure DEST_PATH_GDA0000942136000000052
wherein (x)k,xl) E S denotes the sample xkAnd xlFrom the same class, the set S contains all pairs of samples from the same class, and the maximization formula (2) minimizes the sum of distances between samples of the same class.
Step ③, using the maximum boundary theory, that is, obtaining the optimal distance metric matrix a, so that the samples of the same type are gathered as much as possible while the samples of different types are dispersed as much as possible (as shown in fig. 2), thereby constructing a distance metric framework as follows:
Figure DEST_PATH_GDA0000942136000000053
wherein, therein
Figure DEST_PATH_GDA0000942136000000054
And (x)i,xj) E D denotes the sample xiAnd xjFrom different classes, (x)k,xl) E S denotes the sample xkAnd xlFrom the same class, NDNumber of constraint pairs in set D, NSFor the number of constraint pairs in set S, α weighs the ratio of the two terms to obtain the optimal distance metric matrix A.
Step ④. to obtain the measurement matrix a conveniently, a is WWTSubstituting equation (3) yields:
Figure DEST_PATH_GDA0000942136000000061
where tr (-) represents the trace of the matrix, to represent equation (4) in a more compact form, we define the following two equations:
Figure DEST_PATH_GDA0000942136000000062
Figure DEST_PATH_GDA0000942136000000063
thus, maximum boundary theory can construct a distance metric framework as follows:
W＝arg max2tr(WT(MD-αMS)W)
s.t.WTW＝I (7)
wherein the constraint in equation (7) is to prevent a degenerate solution. W ═ W1,w2,…,wd]Wherein w is1,w2,…,wdIs MD-αMSD eigenvalues greater than 0 correspond to eigenvectors.
The distance measurement matrix obtained preliminarily by the maximum boundary theory is A-WWT. The maximum boundary theory makes full use of the label information of the samples, and in the constructed measurement space, the sum of the distances between different samples is as large as possible, and the distances between similar samples are as small as possible. Therefore, the maximum boundary theory can further improve the accuracy of the face recognition system.
And step S2, fully mining sparse structural information among samples by using a sparse representation theory, and constructing a sparse weight matrix.
Because the maximum boundary theory only utilizes the label samples, a large amount of label-free samples are wasted, and the space structure among the samples in the data set is ignored. The sparse structural information of the data set is fully mined and maintained by utilizing the sparse representation theory. The method specifically comprises the following steps:
①, using sparse representation, using data setDivided by sample xiConstructing the sparsest representation of xi for all but the samples as follows:
Figure DEST_PATH_GDA0000942136000000071
here si＝[si,1,si,2,…,si,i-1,…,si,i+1,…,si,m]Is a vector of m dimensions, where siIs 0 (representing x)iHas been removed from dictionary X).
Step ②. therefore, the sparse weight matrix can be represented as follows:
s＝[s1,s2,…,sn](9)
sparse distance measurement needs to fully maintain sparse weight matrix among original samples, so that sparse structural information of the samples is still fully maintained in a new measurement space.
And step S3, constructing a sparse keeping optimization function, so that sparse structural information of the sample is maximally stored in the newly constructed distance measurement space.
The method specifically comprises the following steps:
① to fully preserve the sparse structured information between the original samples, the present invention assumes that in the new distance metric space, WTxiAs much as possible by WTXsiShown in the table. Thus sparsely structured information is sufficiently preserved in the new metric space, the invention minimizes the following objective function:
Figure DEST_PATH_GDA0000942136000000072
equation (10) aims to find a projection matrix W such that in the new metric space, the sparse weight vector s between samplesiAs consistent as possible. The sparse weight matrix contains sparse structural information among all sample data, wherein the sparse coefficient measures the similarity degree between two samples. Sparsity preserving optimization function preserves as much as possible between samplesAnd sparsifying the structured information so that the constructed metric space fully considers the position structure of the samples in the space. Therefore, the new metric space maximizes and keeps sparse structured information between samples.
Step ② to obtain a simpler mathematical representation of equation (10), the present invention transforms equation (10) as follows:
Figure DEST_PATH_GDA0000942136000000081
wherein eiIs a vector with the ith element being 1 and the rest being 0. Equation (11) can be translated into the following maximization problem:
Figure DEST_PATH_GDA0000942136000000082
maximizing equation (12) allows the metric space to preserve as much sparse structured information as possible between samples.
And step S4, combining the maximum boundary theory and the sparse preservation optimization function by utilizing a regularization frame to obtain sparse preservation distance measurement.
The method specifically comprises the following steps:
step ① to obtain the sparsity preserving distance metric, the present invention aims to preserve the sparsity structuring information between samples while using the maximum boundary theory.
Figure DEST_PATH_GDA0000942136000000083
Wherein M isDAnd MSAre defined in equation (5) and equation (6), respectively. And P ═ X (S + S)T-STS)XTThe sparse structural information containing the samples α and β are regularization parameters used for balancing the proportion of each part to obtain an optimal metric space, and in order to prevent the formula (13) from obtaining a degraded solution, the invention adds a constraint condition WTW＝I。
Step ②, find the best of equation (13)Best solution is W ═ W1,w2,…,wd]Wherein w is1,w2,…,wdIs MD-αMS+ β P is greater than 0, and the distance metric matrix is a — WWT. A metric matrix of sparse hold distance metrics is thus obtained.
The sparse hold distance measurement method uses the maximum boundary theory, so that the distance between samples of the same type is minimized while the sum of the distances between samples of different types is maximized. And by keeping sparse structural information among samples, the obtained measurement space fully considers the sparse correlation of all samples.
Step S5, using proper feature descriptor to extract the image feature of the face to be recognized (image feature of the face with stronger discriminability), and under the sparse distance keeping measurement (similarity measurement calculation is carried out on the extracted face image feature under the sparse distance keeping measurement), carrying out face recognition experiment, and classifying the tested face data.
To further illustrate the effectiveness of the method of the present invention, we have utilized the published ORL and AR face datasets. The ORL face data set contains a total of 400 face data sets for 40 persons, each of which corresponds to 10 of them. All faces of each person are shot and collected at different angles, expressions and the like. The AR face data set contains 4000 pieces of face data corresponding to 126 persons in total, whereas 1680 pieces of face image data corresponding to 120 persons are total, except for occluded face data. Each person contained 14 facial images of different expressions.
The Xing.P, ITML, LMNN and Euclidean distance measurement are used as comparison, the method is called SPML for short, and all face data are normalized and then preprocessed by using a PCA algorithm. In the experiment, different numbers of samples are randomly selected as training samples, and paired constraints are generated as much as possible according to the training samples. After different distance measurement algorithms are used for solving new distance measurement, 1NN is used for classifying the face data, and therefore face recognition is achieved.
Fig. 3 and 4 show the recognition accuracy of the ORL and AR face data by different distance measurement methods, respectively, each accuracy in the experiment is the average value of 10 face recognition experiments, and it can be seen from fig. 2 and 3 that the method of the present invention has high recognition accuracy.
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (1)

1. A face recognition method based on sparse hold distance measurement is characterized by comprising the following steps:
step 1, extracting face data with label information from all stored face data, and constructing a frame of a distance measurement algorithm by using a maximum boundary theory based on the face data;
step 2, excavating sparse structural information among samples by using a sparse representation theory, and constructing a sparse weight matrix;
step 3, constructing a sparse maintenance optimization function, so that sparse structural information of the sample is maximally stored in a newly constructed distance measurement space;
step 4, combining the maximum boundary theory and a sparse keeping optimization function by utilizing a regularization frame to obtain sparse keeping distance measurement;
step 5, extracting image characteristics of the face to be recognized by using a characteristic descriptor, performing a face recognition experiment under the sparse distance measurement, and classifying the tested face data;
the step 1 specifically comprises:
according to the label information of the samples, calculating the sum of squares of distances between samples of different types under the condition of using a distance measurement matrix A, wherein the calculation formula is as follows:
Figure FDA0002292693290000011
wherein (x)i,xj) E D denotes the sample xiAnd xjFrom different classes, where D is a set containing all pairs of samples from different classes; dA(xi,xj) Denotes sample x in case of using the distance metric matrix AiAnd xjT represents the transpose of the matrix;
according to the label information of the samples, calculating the distance square sum among the same class samples under the condition of using the distance measurement matrix A, wherein the calculation formula is as follows:
Figure FDA0002292693290000012
wherein (x)k,xl) E S denotes the sample xkAnd xlFrom the same class, where S is a set containing all pairs of samples from the same class; dA(xk,xl) Denotes sample x in case of using the distance metric matrix AkAnd xlT represents the transpose of the matrix;
using a maximum boundary theory to construct a distance measurement frame, so that under a distance measurement matrix A, the sum of distances among different types of samples is maximum, and the sum of distances among the same type of samples is minimum, wherein the distance measurement frame is as follows:
Figure FDA0002292693290000021
wherein the content of the first and second substances,
Figure FDA0002292693290000022
(xi,xj) E D denotes the sample xiAnd xjFrom different classes, (x)k,xl) E S denotes the sample xkAnd xlFrom the same class, NDIs the number of constraint pairs in set D, NSFor the number of constraint pairs in the set S, α is a regularization parameter, and the proportion of the sum of distances between different types of samples to the sum of distances between similar types of samples is weighed;
changing A to WWTSubstituting the formula (3) for solving, and solving a projection matrix W through characteristic decomposition of the matrix so as to obtain a distance measurement matrix A; wherein WTA transposed matrix that is W;
the step 3 specifically includes:
constructing a sparse weight relationship among samples by keeping sparse representation, and constructing a sparse keeping optimization function as follows:
Figure FDA0002292693290000023
in the formula, siIs except for xiLinear composition x of all but samplesiIs expressed as xiSparse correlations with all other samples; x ═ X1,x2,…,xn]Is a dictionary matrix composed of all samples; n is a positive integer;
the equivalence of equation (10) is transformed as follows:
Figure FDA0002292693290000024
wherein S ═ S1,s2,…,sn]Is a sparse weight matrix, I is a unit matrix, the diagonal element of the unit matrix is 1, and other elements are 0;
equation (11) is transformed into the maximization problem and constraints are added as follows:
Figure FDA0002292693290000031
s.t.WTW＝I (12)
in the formula, S is a sparse weight matrix, X is a dictionary matrix, and W is a projection matrix;
the step 4 specifically includes:
adding the sparse keeping optimization function in the step 3 into a distance measurement frame through a regularization structure to obtain a target function of sparse keeping distance measurement as follows:
Figure FDA0002292693290000032
s.t.WTW＝I (13)
wherein the content of the first and second substances,
Figure FDA0002292693290000033
is a discrete matrix among samples of different types, which measures the discrete degree among all samples of different types,
Figure FDA0002292693290000034
is a discrete matrix among samples of the same type, which measures the discrete degree among all samples from the same type, and P ═ X (S + S)T-STS)XTThe sparse correlation among samples is included, I is a unit matrix, the diagonal element of the unit matrix is 1, other elements are 0, α and β are regularization parameters, and the regularization parameters are used for balancing the proportion of each part to obtain an optimal measurement subspace.
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