CN114821145B - Incomplete multi-view image data clustering method based on data restoration - Google Patents
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Abstract
The invention is suitable for the technical field of computer vision image clustering, and provides a data restoration-based incomplete multi-view image data clustering method, which comprises the following steps: s1: inputting a missing multi-view image dataset; s2: repairing the missing multi-view image data set from a data plane based on a Pearson correlation coefficient calculation method to obtain a complete multi-view image data set; according to the method, based on the similarity among the visual angles of the multi-visual-angle image data, an incomplete multi-visual-angle image is accurately repaired from a dimensional layer of a sample through a Pearson correlation coefficient calculation method, the incomplete image data is filled into complete data, the filled data is close to the pixel value of real image data to the greatest extent, and the fact that the image data used for subsequent image clustering model learning contains real and effective information is guaranteed.
Description
Technical Field
The invention relates to the technical field of computer vision image clustering, in particular to a data repairing-based incomplete multi-view image data clustering method.
Background
With the hundreds of flowers of science and technology, the collection modes of image data are gradually increased, and the image data start to appear explosive growth, so that the acquired image data are often in a label-free state, and the quantity of the image data is not enough to train a model. The formation of clustering techniques makes it possible to classify unlabeled image data.
However, due to some objective reasons, the image data collection device often causes the missing phenomenon (i.e. incomplete image data) of the acquired image data, so that the accuracy of the image clustering model is sharply reduced.
Therefore, in view of the above situation, there is an urgent need to provide a non-complete multi-view image data clustering method based on data restoration, so as to overcome the shortcomings in the current practical application.
Disclosure of Invention
The embodiment of the invention aims to provide a data restoration-based incomplete multi-view image data clustering method, and aims to solve the problem of how to restore incomplete multi-view image data.
The embodiment of the invention is realized in such a way that an incomplete multi-view image data clustering method based on data restoration comprises the following steps:
s1: inputting a missing multi-view image dataset;
s2: repairing the missing multi-view image data set from a data plane based on a Pearson correlation coefficient calculation method to obtain a complete multi-view image data set;
s3: constructing a multi-core cooperative representation model, putting a complete multi-view image data set into the multi-core representation model for learning, obtaining an image data robust representation containing multiple effective information, and obtaining different robust representations at different views;
s4: constructing a robust subspace learning model, feeding the robust representation into the robust subspace learning model for learning, obtaining subspace representation of image data, and obtaining different subspace representations from different visual angles;
s5: constructing a low-rank tensor model, putting the subspace representation into the low-rank tensor model, and recombining the subspace representation into a three-dimensional form to explore hidden information of the image data in the three-dimensional space;
s6: defining an effective joint representation model, and putting a multi-core cooperation representation model, a robust subspace learning model and a low-rank tensor model into the joint representation model;
s7: solving the optimal solution of each variable by using a complete multi-view image data set so as to obtain a fusion subspace with high discriminability;
s8: and sending the fusion subspace into a clustering algorithm to obtain a required clustering result.
Preferably, in step S2, the formula for repairing the missing multi-view image data set from the data plane based on the pearson correlation coefficient calculation method is as follows:
whereinpThe dimensions of the current sample are represented by,vthe number of views is represented as,wthe number of missing samples is indicated by the number of samples,
representing the first five samples with the highest similarity to the current missing sample,correpresents the current sample andx b correlation coefficient between samples.
Preferably, in step S3, the multi-core collaborative representation model is:
whereinKRepresenting a kernel matrix acquired from the complete image data,
representing a robust representation of image data;
Preferably, in step S4, the robust subspace learning model is:
wherein,α 1 、α 2 、γ 1 andγ 2 a regularization parameter is represented as a function of,
represents the norm of Frobinus,
the traces representing the matrix are shown as traces of the matrix,H 1 andH 2 robust representation of data representing view 1 and view 2 respectively,K 1 andK 2 respectively representing the kernel matrices acquired from view 1 and view 2,G 1 andG 2 the robust subspace matrices for view 1 and view 2 are represented, respectively.
Preferably, in step S5, the low rank tensor model is:
wherein,
representing a third order tensor composed of robust subspace matrices for view 1 and view 2,δa regularization constant is represented as a function of,
the frobenus norm representing the tensor,
a low rank tensor structure is represented which,
tensor of representationGA low rank tensor structure.
Preferably, in step S6, the joint representation model is:
preferably, in step S7, the step of solving the optimal solution for each variable by using the complete multi-view image data set comprises:
according to the alternating direction multiplier method, the optimal solution is solved for one variable iteration under the condition that other variables are unchanged.
Preferably, the method further comprises the following steps:
calculating the clustering accuracy of the incomplete multi-view image data;
calculating normalized mutual information of incomplete multi-view image data;
and calculating the purity of the incomplete multi-view image data.
Compared with the prior art, the embodiment of the invention has the following beneficial effects:
(1) the embodiment of the invention is based on the similarity among the multi-view image data views, and carries out accurate restoration on the incomplete multi-view image from the dimension layer of the sample through a Pearson correlation coefficient calculation method, so that the filled data is close to the pixel value of the real image data to the greatest extent on the basis of filling the incomplete image data into the complete data, and the image data used for subsequent image clustering model learning is ensured to contain real and effective information;
(2) in order to solve the linear inseparable problem, a multi-core cooperation model is constructed through kernel function learning and used for learning data robust representation of multi-view image data, meanwhile, a robust subspace learning model is constructed, so that each view of the multi-view image data can learn a low-dimensional representation space which is exclusive to the multi-view image data, in addition, in order to better explore potential clues which are contained in the third dimension by the low-dimensional representation of the image data, a low-rank tensor model is introduced to learn a fused subspace representation for a subsequent clustering algorithm;
(3) the embodiment of the invention develops an alternate optimization numerical solving algorithm, solves the optimal solution of each variable coupled in the objective function by using an alternate direction multiplier method, and ensures convergence in iteration.
Drawings
Fig. 1 is a flowchart of a method for clustering incomplete multi-view image data based on data recovery according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
Specific implementations of the present invention are described in detail below with reference to specific embodiments.
Referring to fig. 1, an incomplete multi-view image data clustering method based on data restoration according to an embodiment of the present invention includes the following steps:
s1: inputting a missing multi-view image dataset;
s2: repairing the missing multi-view image data set from a data plane based on a Pearson correlation coefficient calculation method to obtain a complete multi-view image data set;
s3: constructing a multi-core cooperative representation model, putting a complete multi-view image data set into the multi-core cooperative representation model for learning, obtaining an image data robust representation containing multiple effective information, and obtaining different robust representations at different views;
s4: constructing a robust subspace learning model, sending the robust representation into the robust subspace learning model for learning, obtaining subspace representation of image data, and obtaining different subspace representations from different visual angles;
s5: constructing a low-rank tensor model, putting the subspace representation into the low-rank tensor model, and recombining the subspace representation into a three-dimensional form to explore hidden information of the image data in the three-dimensional space;
s6: defining an effective joint representation model, and putting a multi-core cooperation representation model, a robust subspace learning model and a low-rank tensor model into the joint representation model;
s7: solving the optimal solution of each variable by using the complete multi-view image data set so as to obtain a fusion subspace with high discriminability;
s8: and sending the fusion subspace into a clustering algorithm to obtain a required clustering result.
In an embodiment of the present invention, the formula for repairing the missing multi-view image data set from a data plane based on the pearson correlation coefficient calculation method is as follows:
where sigma denotes the sign of the summation, and,pthe dimensions of the current sample are represented by,vthe number of views is represented as,wthe number of missing samples is indicated,
(b=1,2,…,5,mrepresenting the sample dimension) represents the first five samples with the highest similarity to the current missing sample,correpresents the current sample andx b correlation coefficient between samples.
In one embodiment of the present invention, the multi-core collaborative representation model is:
wherein,
the traces representing the matrix are shown as traces of the matrix,
representing constraints, T represents the transpose of the matrix,Ithe matrix of the unit is expressed by,
representing a robust representation of the image data (cThe representation characteristics represent a dimension that is,nrepresenting the number of samples),Krepresenting a kernel matrix obtained from the complete image data, the specific formula being as follows:
wherein,Xrepresenting multi-view image data of a plurality of views,
representing image dataXTo middlevAt a certain angle of viewiThe data of the column is stored in a memory,
representing an index of samples in the image data,srepresenting the kind of mapping of the kernel function in the above formula,
a kernel function set is shown, and in the present embodiment, a total of 5 kinds of kernel functions are employed.
In one embodiment of the present invention, the robust subspace learning model is:
wherein alpha is 1 、α 2 、γ 1 And gamma 2 A regularization parameter is represented as a function of,
represents the norm of Frobinus,
the traces of the matrix are represented by,H 1 andH 2 robust representation of data representing view 1 and view 2 respectively,K 1 andK 2 respectively representing the kernel matrices acquired from view 1 and view 2,G 1 andG 2 the robust subspace matrices for view 1 and view 2 are represented separately.
In one embodiment of the present invention, the low rank tensor model is:
wherein,
representing a third order tensor that is composed of robust subspace matrices for view 1 and view 2,δa regularization constant is represented as a function of,
the frobenus norm representative of the tensor,
a low rank tensor structure is represented which,
tensor of representationGA low rank tensor structure.
In one embodiment of the invention, the joint representation model is:
in an embodiment of the present invention, the step of solving the optimal solution of each variable by using the complete multi-view image data set is:
according to the alternative direction multiplier method, solving an optimal solution aiming at one variable iteration under the condition that other variables are unchanged;
specifically, the method comprises the following steps:
1) fixing other variables, deleting andH 1 independent function terms, available variablesH 1 The minimization function of (c) is as follows:
the above formula can be converted into:
the above formula can be solved using eigen decomposition, wherein,H 1 by a matrixM 1 Corresponding frontcThe characteristic vector of the maximum characteristic value is formed and represents a characteristic vector matrix;
2) fixing other variables, deleting andG 1 independent function terms, obtaining variables as shown belowG 1 Minimization objective function of (1):
setting the derivative of the above equation to 0, a closed-form solution can be obtained as follows:
3) fixing other variables, deleting andH 2 independent function terms, available variablesH 2 The minimization function of (c) is as follows:
the above equation can be converted into:
the above formula can be solved using eigen decomposition, wherein,H 2 by a matrixM 2 Corresponding front partcThe characteristic vector of the maximum characteristic value is formed and represents a characteristic vector matrix;
4) fixing other variables, deleting andG 2 independent function terms, obtaining variables as shown belowG 2 Minimization objective function of (c):
setting the derivative of the above equation to 0, a closed-form solution can be obtained as follows:
in one embodiment of the present invention, the method further comprises the following steps:
calculating the clustering accuracy of the incomplete multi-view image data;
calculating normalized mutual information of incomplete multi-view image data;
and calculating the purity of the incomplete multi-view image data.
In summary, the embodiment of the present invention can restore incomplete multi-view image data into complete multi-view image data that is close to the real data value to the maximum extent, and calculate the robust data representation of the complete image data through the multi-kernel function; solving the low-dimensional representation of the image data by combining a subspace learning method; in order to explore potential clues in image data, a tensor low-rank model is used for exploring high-dimensional similarity among multi-view image data, a fusion subspace with high discriminability is solved, and the subspace is sent to a clustering algorithm to obtain an image clustering result.
Further, suppose that an incomplete multi-view image data is put into the image clustering model of the present embodiment, a result that the image clustering accuracy reaches more than 90% will be obtained;
the specific implementation mode is as follows:
the embodiment adopts three published multi-view image data sets to verify the method of the embodiment, wherein the data sets comprise a handwriting image data set and two face image data sets;
the handwriting image data set adopts a UCI data set, and the UCI data set comprises ten different handwriting images from 0, 1, … and 9, wherein the total number of the handwriting images is 2000 samples; in the embodiment, 500 samples are selected as verification objects, and two view angles are constructed according to the 500 samples, wherein the first view angle is a 216-dimensional profile correlation characteristic, and the second view angle is a 76-dimensional Fourier coefficient;
in addition, one of the face data sets is a YALE data set, the YALE data set comprises 15 face images of people with different sexes and ages under different light rays and angles, and each person takes 11 images and 165 face images in total; in the embodiment, two features extracted from the YALE data set are respectively used as two visual angles to verify the embodiment;
the other facial image dataset is an ORL dataset, which collects facial images of 40 persons under different light and facial expressions, and each person collects 10 images, 400 images in total; the embodiment selects the gray intensity and the local binary pattern of each sample in the image data set as two visual angles to verify the embodiment;
in this embodiment, three common clustering indexes are used as measurement indexes, namely Accuracy (ACC), Normalized Mutual Information (NMI), and Purity (PUR); in this embodiment, incomplete multi-view image data is used as an object, that is, the image data randomly selects a missing sample according to a given loss rate, and sets a pixel value of the selected sample to 0, in this embodiment, an experiment is performed on the image clustering model of this embodiment by adjusting different loss rates, an adjustment range of the loss rate is 0.1-0.5, and an interval of each experiment is 0.1;
as can be seen from the experimental results in the table above, the present embodiment shows good experimental results in all of the three indexes;
on the YALE data set, when the loss rate reaches 0.4, the accuracy shows a certain descending trend, but the obvious descending amplitude is small, and good stability is shown;
the experimental results on the other two data sets show that the embodiment always presents a stable trend with a gentle fluctuation trend along with the increase of the loss rate, and the embodiment is proved to have better robustness and wide practical applicability when facing incomplete multi-view image data.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (6)
1. A method for clustering incomplete multi-view image data based on data restoration is characterized by comprising the following steps:
s1: inputting a missing multi-view image dataset;
s2: repairing the missing multi-view image data set from a data layer based on a Pearson correlation coefficient calculation method to obtain a complete multi-view image data set; the formula for repairing the missing multi-view image data set from the data plane based on the Pearson correlation coefficient calculation method is as follows:
where p represents the dimension of the current sample, v represents the number of views, w represents the number of missing samples, x b ＝[x b1 ,x b2 ,...,x bm ]Represents the first five samples with the highest similarity to the current missing sample;
s3: constructing a multi-core cooperative representation model, putting a complete multi-view image data set into the multi-core cooperative representation model for learning, obtaining an image data robust representation containing multiple effective information, and obtaining different robust representations at different views;
s4: constructing a robust subspace learning model, sending the robust representation into the robust subspace learning model for learning, obtaining a subspace representation of image data, and obtaining different subspaces from different visual angles;
s5: constructing a low-rank tensor model, putting the subspace into the low-rank tensor model, and recombining the subspace into a three-dimensional form to explore hidden information of the image data in the three-dimensional space; the low rank tensor model is:
wherein δ represents a third-order tensor composed of robust subspace matrices of view 1 and view 2, δ represents a regularization constant, | · | | survival F The frobenus norm representative of the tensor,
a low rank tensor structure is represented which,
tensor of representation
A low rank tensor structure;
s6: defining an effective joint representation model, and putting a multi-core representation model, a robust subspace model and a low-rank tensor model into the joint representation model;
s7: solving the optimal solution of each variable by using a complete multi-view image data set so as to obtain a fusion subspace with high discriminability;
s8: and sending the fusion subspace into a clustering algorithm to obtain a required clustering result.
2. The method for clustering incomplete multi-view image data based on data recovery as claimed in claim 1, wherein in step S3, the multi-kernel collaborative representation model is:
s.t.HH T ＝I；
wherein K represents a group consisting ofA kernel matrix obtained from the image data, H ∈ R c×n Representing a robust representation of image data;
H∈R c×n where c represents the feature representation dimension and n represents the number of samples.
3. The method for clustering incomplete multi-view image data based on data recovery as claimed in claim 1, wherein in step S4, the robust subspace learning model is:
s.t.H 1 H 1 T ＝I,H 2 H 2 T ＝I；
wherein alpha is 1 、α 2 、γ 1 And gamma 2 Representing regularization parameters, | · | calculation of the F Denotes the Frobinus norm, G 1 And G 2 The robust subspace matrices for view 1 and view 2 are represented, respectively.
4. The incomplete multi-view image data clustering method based on data recovery as claimed in claim 1, wherein in step S6, the joint representation model is:
s.t.H 1 H 1 T ＝I,H 2 H 2 T ＝I,G＝(G 1 ,G 2 )。
5. the method for clustering incomplete multi-view image data based on data recovery as claimed in claim 1, wherein in step S7, the step of solving the optimal solution for each variable by using the complete multi-view image data set comprises:
according to the alternating direction multiplier method, the optimal solution is solved for one variable iteration under the condition that other variables are unchanged.
6. The method for clustering incomplete multi-view image data based on data recovery according to any one of claims 1-5, further comprising the steps of:
calculating the clustering accuracy of the incomplete multi-view image data;
calculating normalized mutual information of incomplete multi-view image data;
and calculating the purity of the incomplete multi-view image data.
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