CN115131863A - Novel face image clustering method and system based on feature selection strategy - Google Patents

Novel face image clustering method and system based on feature selection strategy Download PDF

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CN115131863A
CN115131863A CN202210789169.4A CN202210789169A CN115131863A CN 115131863 A CN115131863 A CN 115131863A CN 202210789169 A CN202210789169 A CN 202210789169A CN 115131863 A CN115131863 A CN 115131863A
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赵鹏
李博文
张永新
郭培杰
常志玲
赵朝锋
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Abstract

The invention discloses a new face image clustering method and system based on a feature selection strategy, which are applied to the technical field of computer artificial intelligence and comprise the following steps: applying a structured sparse induction norm on a projection matrix, constructing a feature selection matrix, and constructing a face image clustering model based on a feature selection strategy by combining a membership matrix and a cluster center matrix; and solving the face image clustering model based on the feature selection strategy through an iterative optimization algorithm until the model converges to obtain an optimal solution. According to the method, a feature selection matrix is constructed by applying a structured sparse induction norm on a projection matrix, a face image clustering model based on a feature selection strategy is constructed by combining a membership matrix and a cluster center matrix, so that a clustering task and a feature selection process are mutually promoted, and an optimal solution is obtained through an iterative optimization algorithm; the following results are obtained through a face image clustering comparison test: the FKFS method provided by the invention is superior to other methods on most face image data sets.

Description

Novel face image clustering method and system based on feature selection strategy
Technical Field
The invention relates to the technical field of computer artificial intelligence, in particular to a novel face image clustering method and system based on a feature selection strategy.
Background
Clustering is a research hotspot in the fields of data mining, computer vision and the like. When the label information is unavailable, different face images are difficult to be segmented according to the categories, so that the images of the same individual are all divided into one cluster. In the past decades, many human face image clustering algorithms, such as k-means clustering, fuzzy k-means clustering, spectral clustering, etc., have been proposed. Among them, k-means and fuzzy k-means clustering are of great concern because of the simple algorithm theory. k-means is also called hard clustering, and if each face image is treated as a sample, each sample is assigned to the nearest cluster center with a percentage probability. However, due to the influence of factors such as illumination, occlusion, and noise, there is a large difference between different images of the same individual, so that the K-Means (K-Means) clustering performance is affected. To solve this problem, fuzzy k-means (FKM) clustering is proposed. For FKM clustering, a sample is associated with each cluster with a certain membership degree, and the sparsity of the membership degree is controlled by a fuzzy index. FKM clustering can produce certain effect on improving the clustering accuracy of the face images, but the requirement on the high accuracy of face image clustering is far from sufficient.
Therefore, how to provide a new facial image clustering method based on a feature selection strategy, which can reduce the influence of noise and redundant features on the accuracy of facial image clustering and meet the high-accuracy requirement of facial image clustering, is a problem that needs to be solved by technical personnel in the field.
Disclosure of Invention
In view of this, the present invention provides a new face image clustering method (FKFS) and system based on a feature selection policy. The method constructs a feature selection matrix by applying a structured sparse induction norm on a projection matrixThe face image clustering model based on the feature selection strategy is constructed by combining the membership matrix and the cluster center matrix, so that the face image clustering task and the face image feature selection process are mutually promoted, on one hand, the performance of face image clustering can be improved based on the selected discriminative face features, and on the other hand, the quality of feature selection can be further improved by clustering results; and solving the optimal solution of the model through an iterative algorithm, comprising: when W and S are fixed, m is derived k Equal to zero, update M; when M and S are fixed, updating W through an iterative reweighing optimization strategy; and when W and M are fixed, updating S by a Lagrange multiplier method until the model converges to obtain an optimal solution. Finally, by comparing the optimal solution (FKFS) of the face image clustering model based on the feature selection strategy with face image clustering test results of subsets of FKM, AFKM, FNC, RSFKM, SFKM and the like on data sets AR, Yaleb, Umist, Orlraws10P, WarpPIE10P, ORL32 and LFW respectively by using ACC (ACCURACY), NMI (normalized Multi information) and Purity (Purity) as face image clustering evaluation criteria, the new face image clustering method (FKFS) based on the feature selection strategy and the system provided by the invention are superior to other methods on most data sets.
In order to achieve the purpose, the invention adopts the following technical scheme:
a new facial image clustering method based on a feature selection strategy comprises the following steps:
step (1): and applying a structured sparse induction norm on the projection matrix, constructing a feature selection matrix, and constructing a face image clustering model based on a feature selection strategy by combining the membership matrix and the cluster center matrix.
Step (2): and solving the face image clustering model based on the feature selection strategy through an iterative optimization algorithm until the model converges to obtain an optimal solution.
Optionally, in step (1), the face image clustering model based on the feature selection policy is as follows:
Figure BDA0003733111860000021
wherein W ∈ R d×p Selecting a matrix for the feature; p is the dimensionality after dimensionality reduction; beta is a regularization parameter used for adjusting the sparsity of W, and the larger beta is, the more sparse rows of W are; m ═ M 1 ，m 2 ，…，m c ]∈R p×c Is a cluster-centered matrix in a low-dimensional space, m k Is the kth cluster center; s is a membership matrix, where S ik Representing the degree of membership of the ith sample to the kth class or the probability of belonging to the kth class; t represents a transpose of a matrix or vector; r is the blur index.
Optionally, in step (2), the iterative optimization algorithm is as follows:
when W and S are fixed, M is updated by:
Figure BDA0003733111860000031
wherein the content of the first and second substances,
Figure BDA0003733111860000032
is the kth cluster center in original space;
optionally, in step (2), the iterative optimization algorithm further includes:
when M and S are fixed, W is updated by:
Figure BDA0003733111860000033
wherein W is represented by S w The characteristic vectors corresponding to the first p minimum characteristic values of the + beta D are formed; d is a diagonal matrix with the jth diagonal element being 1/2| | | w j || 2 (ii) a Tr () represents a trace of the matrix.
Optionally, in step (2), the iterative optimization algorithm further includes:
when W and M are fixed, S is updated by:
Figure BDA0003733111860000034
optionally, after the step (2), further comprising: and performing face image clustering test and comparison by using the optimal solution of the face image clustering model based on the feature selection strategy.
The invention also provides a new face image clustering system based on the characteristic selection strategy, which comprises the following steps:
a first building block: and the method is used for applying a structured sparse induction norm on the projection matrix to construct a feature selection matrix.
A second building block: the face image clustering method is used for constructing a face image clustering model based on a feature selection strategy by combining the feature selection matrix, the membership degree matrix and the cluster center matrix.
An iterative optimization module: and the face image clustering model is used for solving the face image clustering model based on the feature selection strategy according to an iterative optimization algorithm until the model converges to obtain an optimal solution.
Test comparison module: the method is used for carrying out face image clustering test and comparison by applying the optimal solution of the face image clustering model based on the characteristic selection strategy.
Compared with the prior art, the technical scheme provides a new face image clustering method (FKFS) and system based on the feature selection strategy. The method constructs a feature selection matrix by applying a structured sparse induction norm on a projection matrix, constructs a face image clustering model based on a feature selection strategy by combining a membership matrix and a cluster center matrix, and mutually promotes a face image clustering task and a face image feature selection process; and solving the optimal solution of the model through an iterative algorithm, comprising: when W and S are fixed, m is derived k Equal to zero, update M; when M and S are fixed, updating W through an iterative reweighting optimization strategy; and when W and M are fixed, updating S by a Lagrange multiplier method until the model converges to obtain an optimal solution. Finally, by using ACC (ACCuracy), NMI (Normalized Mu)tual Information) and purity (purity) are used as face image clustering evaluation criteria, the optimal solution (FKFS) of a face image clustering model based on a feature selection strategy is compared with face image clustering test results of subsets of data sets AR, Yaleb, Umist, Orlraws10P, WarpPIE10P, ORL32 and LFW through face image clustering methods such as FKM, AFKM, FNC, RSFKM and SFKM respectively, and the new face image clustering method (FKFS) based on the feature selection strategy and the system are superior to other methods on most data sets.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 is a schematic diagram illustrating an introduction of a data set for verifying superiority of clustering analysis of face images according to the present invention.
FIG. 3 is a schematic diagram showing the relationship between the face image clustering results and the feature numbers in 5 data sets according to the present invention.
Fig. 4 is a schematic diagram of experimental results of the method for clustering face images on 7 data sets according to the present invention.
FIG. 5 is a schematic diagram of the clustering analysis of facial images for parameters r and β on 4 data sets according to the present invention.
FIG. 6 is a graph illustrating the convergence curves of the iterative optimization algorithm of the present invention over 7 data sets.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The embodiment 1 of the invention discloses a new face image clustering method based on a feature selection strategy, and as shown in fig. 1, the method comprises the following steps:
step (1): applying a structured sparse induction norm on a projection matrix, constructing a feature selection matrix, and constructing a face image clustering model based on a feature selection strategy by combining a membership matrix and a cluster center matrix, wherein the face image clustering model is as follows:
Figure BDA0003733111860000051
wherein W ∈ R d×p Selecting a matrix for the feature; p is the dimensionality after dimensionality reduction; beta is a regularization parameter used for adjusting the sparsity of W, and the larger beta is, the more sparse rows of W are; m ═ M 1 ，m 2 ，…，m c ]∈R p×c Is a cluster-centered matrix in a low-dimensional space, m k Is the kth cluster center; s is a membership matrix, where S ik Representing the degree of membership of the ith sample to the kth class, or the probability of belonging to the kth class. T represents a transpose of a matrix or vector. r is a fuzzy index used to adjust the sparsity of the membership matrix and to avoid trivial solutions.
Step (2): solving the face image clustering model based on the feature selection strategy through an iterative optimization algorithm until the model converges to obtain an optimal solution, wherein the iterative optimization algorithm is as follows:
when W and S are fixed, β | | W | | calucity in formula (1) 2，1 As a constant, update M by solving equation (2) as follows:
Figure BDA0003733111860000061
it is divided into c sub-problems, each m is obtained by solving k The optimal solution of (a) is as follows:
Figure BDA0003733111860000062
by taking advantage of m in the problem (3) k And (5) obtaining a derivative, setting the derivative as zero, and finally obtaining:
Figure BDA0003733111860000063
wherein the content of the first and second substances,
Figure BDA0003733111860000064
the kth cluster center in original space.
When M and S are fixed, formula (1) is converted to according to formula (4):
Figure BDA0003733111860000065
through an iterative reweighted optimization strategy, equation (5) is equivalent to equation (6) as follows:
Figure BDA0003733111860000066
finally, the following is obtained:
Figure BDA0003733111860000067
wherein W is represented by S w The characteristic vectors corresponding to the first p minimum characteristic values of the + beta D are formed; d is a diagonal matrix with the jth diagonal element being 1/2| | | w j || 2 (ii) a To avoid the case where the denominator is zero, the jth diagonal element is restated as 1/2| | w j +δ|| 2 (ii) a Tr () represents a trace of the matrix.
The solution of equation (6) is based on the following two lemmas:
introduction 1: for nonnegative real number set { a 1 ，a 2 ，…a n There are n elements of the sequence,
Figure BDA0003733111860000071
satisfies the equation:
Figure BDA0003733111860000072
wherein x is i Is the ith sample, X is the matrix containing all samples;
Figure BDA0003733111860000073
and A ∈ R n×n Is a diagonal matrix; 1 is a column vector with all element values of 1; wherein a is i Is the ith diagonal element; () T Representing a transpose of a matrix or vector, the process of attestation is as follows:
Figure BDA0003733111860000074
2, leading: if the objective function of the problem (9) is W * Time-minimized, objective function of the available problem (6) is at W * The time is minimal.
Figure BDA0003733111860000075
Let the objective function of the problem (6) be represented by J (W). In the introduction 1, it was shown that,
Figure BDA0003733111860000076
Figure BDA0003733111860000081
wherein A is (k) ∈R n×n Is the diagonal matrix associated with the kth cluster; a. the (k) Is the ith diagonal element of
Figure BDA0003733111860000082
And
Figure BDA0003733111860000083
B∈R n×n is a diagonal matrix with the ith diagonal element of
Figure BDA0003733111860000084
C∈R c×c Is a diagonal matrix with the kth diagonal element being
Figure BDA0003733111860000085
P∈R n×c And is and
Figure BDA0003733111860000086
has S w ＝X(B-PCP T )X T 。
Therefore, the problem (6) can be rewritten as:
Figure BDA0003733111860000087
the column of W is composed of p feature vectors corresponding to S w The first p minimum eigenvalues of + β D.
When W and M are fixed, β | | W | | calving in formula (1) 2，1 Is constant, formula (1) is converted to according to formula (4):
Figure BDA0003733111860000088
by using the lagrange multiplier method, the following is finally obtained:
Figure BDA0003733111860000089
the practical application of the iterative optimization algorithm is as follows:
Figure BDA0003733111860000091
further comprising comparing the best solution (FKFS) of the face image cluster model based on the feature selection policy with the face image cluster test results of FKM, AFKM, FNC, RSFKM, SFKM and the like on subsets of data sets AR, YaleB, umit, orlrows 10P, WarpPIE10P, ORL32 and LFW shown in fig. 2 by using acc (accuracy), nmi (normalized Mutual information) and purity (purity) as face image cluster evaluation criteria as follows:
FKM: the fuzzy membership instead of the hard membership is an extension of K-Means, with each cluster center formed by a weighted average of all samples.
AFKM: different from fuzzy K-Means, the method adopts regularization parameters to complete the adjustment of fuzzy membership degree, and in addition, introduces maximum entropy information to optimize the clustering division of the face images.
RSFKM: the influence of the abnormal value on the target function is reduced by adopting the norm of the sparse structure, a weighting algorithm is provided, and the problem is effectively solved.
FNC: the fast normalized cut method, by using an anchoring strategy, can construct a representative similarity matrix with linear time.
SFKM: the shrinkage mode is adopted to approximate an ideal manifold data structure, and the fuzzy clustering of the face images is carried out on the learned shrinkage mode, so that the samples have better distribution under the condition of no dimension reduction.
The face image clustering evaluation criteria acc (accuracy), nmi (normalized Mutual information) and purity (purity) were used to demonstrate the superiority of FKFS. In order to accelerate the convergence rate of the face image clustering method, principal component analysis is performed on each data set to maintain 95% of energy. And embedding the value function range (0,1) into the MatlabR2017b software specification by using a mapminmax function. For the face image clustering method, the sparsity of a membership matrix is optimized by depending on a fuzzy index r, and the value of r is an adjustment range [1.1,2 ]. For other methods such as FKM, AFKM, FNC, RSFKM, SFKM and the like, the value of the regularization parameter is determined according to the setting of a corresponding article. For the FKFS proposed by the invention, the number of selected features is chosen from [4,8, …, d '], where d' is the dimension after PCA and the value of the parameter β is chosen from [0.05,0.1,0.5,1,5,10,5,10,50,100,500,100 ]. Since the comparison method is sensitive to the initialization of the membership matrix, the invention repeats all face image clustering methods 10 times in a random initialization manner and records the average result under the above setting.
Experimental results of FKFS on 5 public data sets are shown in fig. 3, fig. 3 depicts facial image clustering results of the method proposed by the present invention under different numbers of features, which can be obtained from fig. 3, generally, the more features selected by the method proposed by the present invention, the better the facial image clustering results.
The results of comparing the optimal solution (FKFS) of the face image clustering model based on the feature selection strategy with the face image clustering test results of FKM, AFKM, FNC, RSFKM, SFKM and the like on subsets of data sets AR, YaleB, Umist, orlrows 10P, WarpPIE10P, ORL32 and LFW shown in fig. 2 with acc (accuracy), nmi (normalized Mutual information) and purity (purity) as the face image clustering evaluation criteria are shown in fig. 4.
As can be seen from fig. 4: on most data sets, AFKM, RSFKM and SFKM clustered results for face images in ACC, NMI and Purity were superior to FKM, indicating that an improved strategy is useful. For AR, orlrows 10P and ORL32 data sets, SFKM results are better than FKM, AFKM and RSFKM, meaning that new data distributions without noise effects are favorable for face image clustering. However, SFKM is inferior to FKFS in performance on these data sets, probably because all features in the SFKM method are used to partition clusters, and some features may have negative impact on the face image clustering process, and conversely, FKFS proposed by the present invention only selects distinctive features to accomplish this task. The FKFS method proposed by the present invention is superior to other methods over most face image datasets, which may be relevant to adaptive feature selection strategies. The results indicate that the method proposed herein is most effective.
In order to study the sensitivity of the proposed method to r and β, their values were varied while keeping the number of selected features at an optimal value. Then, the face image clustering accuracy of these two parameters is shown in fig. 5. It is clear that the method proposed by the present invention gives better results when the value of β is 0.05 or 0.1.
On the other hand, the convergence curve of the iterative optimization algorithm provided by the invention on 7 data sets is shown in fig. 6, and it can be found that objective values on most data sets converge within 30 iterations, which proves that the iterative optimization algorithm provided by the invention has a high convergence rate.
The embodiment 2 of the invention provides a new face image clustering system based on a feature selection strategy, which comprises the following steps:
a first building block: and the method is used for applying a structured sparse induction norm on the projection matrix to construct a feature selection matrix.
A second building block: the face image clustering method is used for constructing a face image clustering model based on a feature selection strategy by combining the feature selection matrix, the membership degree matrix and the cluster center matrix.
An iterative optimization module: and the face image clustering model is used for solving the face image clustering model based on the feature selection strategy according to an iterative optimization algorithm until the model converges to obtain an optimal solution.
Test comparison module: the method is used for carrying out face image clustering test and comparison by applying the optimal solution of the face image clustering model based on the characteristic selection strategy.
The embodiment of the invention discloses a novel face image clustering method (FKFS) and a system based on a feature selection strategy. The method constructs a feature selection matrix by applying a structured sparse induction norm on a projection matrix, constructs a face image clustering model based on a feature selection strategy by combining a membership matrix and a cluster center matrix, and mutually promotes a face image clustering task and a face image feature selection process; and solving the optimal solution of the model through an iterative algorithm, comprising: when W and S are fixed, m is derived k Equal to zero, update M; when M and S are fixed, updating W through an iterative reweighting optimization strategy; and when W and M are fixed, updating S by a Lagrange multiplier method until the model converges to obtain an optimal solution. Finally, clustering the facial image clustering model based on the characteristic selection strategy by using ACC (accuracy), NMI (normalized Mutual information) and Purity (Purity) as the clustering evaluation criteria of the facial imageThe optimal solution (FKFS) and clustering methods such as FKM, AFKM, FNC, RSFKM and SFKM are respectively compared with the clustering test results of the face images on subsets of data sets AR, Yaleb, Umist, Orlraws10P, WarpPIE10P, ORL32 and LFW, and the new face image clustering method (FKFS) based on the feature selection strategy and the system provided by the invention are superior to other methods on most data sets.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed in the embodiment corresponds to the method disclosed in the embodiment, so that the description is simple, and the relevant points can be referred to the description of the method part.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (7)

1. A new face image clustering method based on a feature selection strategy is characterized by comprising the following steps:
step (1): applying a structured sparse induction norm on a projection matrix, constructing a feature selection matrix, and constructing a face image clustering model based on a feature selection strategy by combining a membership matrix and a cluster center matrix;
step (2): and solving the face image clustering model based on the feature selection strategy through an iterative optimization algorithm until the model converges to obtain an optimal solution.
2. The method for clustering facial images based on a feature selection strategy according to claim 1, wherein in step (1), the facial image clustering model based on the feature selection strategy has the following formula:
Figure FDA0003733111850000011
s.t.，W T W＝I，S ik
≥0，
Figure FDA0003733111850000012
wherein W ∈ R d×p Selecting a matrix for the feature; p is the dimensionality after dimensionality reduction; beta is a regularization parameter used for adjusting the sparsity of W, and the larger beta is, the more sparse rows of W are; m ═ M 1 ，m 2 ，…，m c ]∈R p×c Is a cluster-centered matrix in a low-dimensional space, m k Is the kth cluster center; s is a membership matrix, where S ik Representing the degree of membership of the ith sample to the kth class or the probability of belonging to the kth class; t represents a transpose of a matrix or vector; r is the blur index.
3. The new facial image clustering method based on the feature selection strategy according to claim 2, wherein in step (2), the iterative optimization algorithm is as follows:
when W and S are fixed, M is updated by:
Figure FDA0003733111850000013
wherein the content of the first and second substances,
Figure FDA0003733111850000014
the kth cluster center in original space.
4. The new facial image clustering method based on the feature selection strategy according to claim 3, wherein in step (2), the iterative optimization algorithm further comprises:
when M and S are fixed, W is updated by:
Figure FDA0003733111850000021
wherein W is represented by S w The characteristic vectors corresponding to the first p minimum characteristic values of the + beta D are formed; d is a diagonal matrix with the jth diagonal element being 1/2| | | w j || 2 (ii) a Tr () represents a trace of the matrix.
5. The new facial image clustering method based on the feature selection strategy according to claim 4, wherein in step (2), the iterative optimization algorithm further comprises:
when W and M are fixed, S is updated by:
Figure FDA0003733111850000022
6. the new facial image clustering method based on the feature selection strategy according to claim 1, characterized in that after the step (2), the method further comprises: and carrying out face image clustering test and comparison by applying the optimal solution of the face image clustering model based on the characteristic selection strategy.
7. A new facial image clustering system based on a feature selection strategy is characterized by comprising:
a first building block: the method comprises the steps of applying a structured sparse induction norm on a projection matrix to construct a feature selection matrix;
a second building block: the face image clustering model is used for constructing a face image clustering model based on a feature selection strategy by combining the feature selection matrix, the membership degree matrix and the cluster center matrix;
an iterative optimization module: the face image clustering model based on the feature selection strategy is solved according to an iterative optimization algorithm until the model converges to obtain an optimal solution;
a test comparison module: and the optimal solution of the facial image clustering model based on the characteristic selection strategy is used for carrying out facial image clustering test and comparison.
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CN117076962A (en) * 2023-10-13 2023-11-17 腾讯科技（深圳）有限公司 Data analysis method, device and equipment applied to artificial intelligence field

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CN117076962A (en) * 2023-10-13 2023-11-17 腾讯科技（深圳）有限公司 Data analysis method, device and equipment applied to artificial intelligence field
CN117076962B (en) * 2023-10-13 2024-01-26 腾讯科技（深圳）有限公司 Data analysis method, device and equipment applied to artificial intelligence field

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