CN115131588A - Image robust clustering method based on fuzzy clustering - Google Patents

Image robust clustering method based on fuzzy clustering Download PDF

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CN115131588A
CN115131588A CN202210665911.0A CN202210665911A CN115131588A CN 115131588 A CN115131588 A CN 115131588A CN 202210665911 A CN202210665911 A CN 202210665911A CN 115131588 A CN115131588 A CN 115131588A
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王靖宇
张欣茹
聂飞平
李学龙
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Abstract

The invention relates to an image robust clustering method based on fuzzy clustering, which screens out images polluted by noise while clustering image data, retains pure and pollution-free image data and has higher robustness to noise change. The invention is an unsupervised algorithm, does not need to use the label data, and reduces a large amount of time for acquiring the label data. The algorithm does not need to update the graph matrix in the solving process, so the calculation complexity of the algorithm is reduced, and the calculation speed is accelerated. Therefore, the fast, effective and robust clustering of the noise-polluted images can be realized. According to the method, the corresponding regularization parameter of each sample can be calculated in a self-adaptive manner through the regularization parameter of the iterative optimization objective function, so that the difficulty in adjusting the regularization parameter is greatly reduced in the application process, the labor cost is saved, and the image clustering accuracy is improved while the image data polluted by noise is robustly screened out.

Description

Image robust clustering method based on fuzzy clustering
Technical Field
The invention belongs to the field of image identification and classification and pattern identification, and relates to an image robust clustering method based on fuzzy clustering.
Background
With the development of computer technology and digital imaging systems, it is more and more convenient for people to transmit information through images. However, in a real environment, image information is easily polluted by noise, so that image quality is lost to a certain extent, and effective identification of an image is difficult. Because the processed image information is increasingly complex and the acquisition difficulty of the label is more and more high, the application of the unsupervised image clustering technology in the information era is widely concerned, the image clustering technology can cluster the images in the image database according to the similarity of the images, so that the similarity of the images in the same cluster is as large as possible, and the similarity between different clusters is as small as possible. And the image information is susceptible to noise, and if the images polluted by the noise are still subjected to traditional unsupervised image clustering, the accuracy and reliability of image retrieval are greatly influenced. And screening out the images polluted by noise, and comparing the new images with the clusters with higher similarity in the database one by one to quickly finish the identification and classification. Therefore, the clustering after noise suppression of the image data before the image retrieval can effectively and quickly realize the high-quality image data retrieval.
Likang et al (fuzzy spectral clustering algorithm for hyperspectral image classification) (Chinese scientific and technological paper 2021,16(07): 743-. However, updating the graph matrix also increases the time complexity of the fuzzy clustering algorithm, and affects the operation speed. Although the graph learning and the fuzzy clustering learning are integrated into a combined learning frame, the method is limited by the traditional fuzzy clustering algorithm, the robustness is poor, the noise data cannot be effectively removed, and the subsequent image data retrieval is influenced.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides an image robust clustering method based on fuzzy clustering, which aims at solving the problems that the existing supervised image algorithm needs to consume a large amount of time to obtain a data label, and the influence of noise on image data retrieval and poor robustness cannot be effectively solved.
Technical scheme
An image robust clustering method based on fuzzy clustering is characterized by comprising the following steps:
step 1: for n pictures of u × v resolution, stretching each picture to obtain a 1 × d row vector, where d is u × v; converting image data formed by n pictures into a target data matrix
Figure BDA0003691609690000021
Wherein each row of the matrix
Figure BDA0003691609690000022
Represents an image; each image represents a data sample; giving the real category number c contained in the target data, and randomly initializing the clustering centers of the c clusters, namely obtaining the initial
Figure BDA0003691609690000023
Is the centroid of the jth cluster;
and 2, step: establishing robust fuzzy clustering RFCM framework for noise suppression
Figure BDA0003691609690000024
Wherein
Figure BDA0003691609690000025
Is fuzzy membership degree, and the centroid matrix of the cluster is
Figure BDA0003691609690000026
The matrix Y represents each element Y ij Representing the membership degree of the ith sample belonging to the jth cluster;
Figure BDA0003691609690000027
for screening n-k noise numbersAccording to s i Is the value of the ith element;
and step 3: alternative iteration optimization robust fuzzy clustering RFCM framework
The solving steps are as follows:
step 3.1: randomly initializing the clustering centers of c clusters to obtain initial clusters
Figure BDA0003691609690000028
Initializing all elements in Y to Y ij 1/c; definition e i To a sample x with a certain degree of membership i Weighting and summing the resulting values to all cluster center distances, e i Arranged as e in descending order 1 ≤e 2 ≤...≤e k ≤...≤e n Calculating to obtain its correspondence s i
Figure BDA0003691609690000031
Step 3.2: respectively carrying out different optimization on real samples and noise data to obtain Y
S corresponding to the first k samples nearest to all the cluster centers i 1, s for the remaining samples i 0; will be compared with the sequence e i Corresponding sample x i Sorting to obtain sorted data matrix
Figure BDA0003691609690000032
Its corresponding sorted membership degree matrix
Figure BDA0003691609690000033
Step 3.2.1: when the sample corresponds to s i When the number of the clusters is 1, q clusters nearest to the real sample are thinned out, and y is limited i L of 0 Norm q, defined
Figure BDA0003691609690000034
Ith real sample point
Figure BDA0003691609690000035
Quadratic distance to jth cluster center, RFCM framework equivalent transformation
Figure BDA0003691609690000036
Calculating an optimal parameter gamma by the parameter gamma in the target function in a self-adaptive mode;
Figure BDA0003691609690000037
optimizing to obtain the optimal membership degree corresponding to the selected real sample
Figure BDA0003691609690000038
i∈{1,2,...,k}
Figure BDA0003691609690000039
Step 3.2.2: for the noise data in the optimization process, s is corresponding to the sample i When the value is equal to 0, the optimal membership value corresponding to the noise data in the optimization process is obtained by solving the Cauchy inequality as
Figure BDA00036916096900000310
Obtaining the optimal solution of all sample point membership degrees
Figure BDA00036916096900000311
Is composed of
Figure BDA00036916096900000312
Step 3.3: fixing s and Y to get a sub-problem of the RFCM framework
Figure BDA0003691609690000041
Solving the partial derivative of m to be equal to 0 to obtain:
Figure BDA0003691609690000042
in each optimization process, m, Y and s are continuously updated, and the next iterative operation is carried out again until m is not changed; one row of sample data corresponds to one picture, and according to the obtained membership matrix Y, the label of the cluster corresponding to the maximum value of each row of the sample data is selected as the class of the picture to be divided, so that a predicted label vector is obtained, and image clustering cluster division is realized; the obtained s vector contains k 1, n-k 0 s, and s corresponding to the ith image i If 0, then the picture is screened as a noise contaminated image.
Advantageous effects
According to the image robust clustering method based on fuzzy clustering provided by the invention, the image data is clustered, and simultaneously, the image polluted by noise is screened out, so that pure and pollution-free image data is reserved, and the image robust clustering method based on fuzzy clustering has higher robustness to noise change. The invention is an unsupervised algorithm, does not need to use the label data, and reduces a large amount of time for acquiring the label data. The algorithm does not need to update the graph matrix in the solving process, so the calculation complexity of the algorithm is reduced, and the calculation speed is accelerated. Therefore, the fast, effective and robust clustering of the noise-polluted images can be realized.
The invention provides a noise suppression image clustering method based on an improved robust fuzzy clustering framework of FCM (fuzzy C-means), which can robustly screen out image data polluted by noise in the application process, can also be used for image clustering, simultaneously improves the robustness and precision of an algorithm, and improves the data processing speed by sparsifying a membership matrix. In the algorithm, an objective function is composed of a robust noise suppression term and a regularization term, and self-adaptive weight is added to each sample point through iterative optimization of the objective function, so that pure samples and noise pollution samples are screened, and the robustness of the algorithm is enhanced. And the data samples polluted by noise can be screened by optimizing the objective function, and then the image clustering of noise suppression is carried out.
The method of the invention has the following beneficial effects:
(1) a robust fuzzy clustering algorithm is provided, in the algorithm, a robust noise suppression term of an objective function enables the algorithm to iteratively optimize the objective function, self-adaptive weight is added to each sample point, pure samples and noise pollution samples are screened according to the self-adaptive weight, and the robustness of the algorithm is enhanced.
(2) According to the noise suppression image clustering method based on robust fuzzy clustering provided by the invention, the membership degree matrix is thinned while the robust noise suppression is carried out, so that a more effective sample and characteristic distribution structure is obtained, the influence of noise pollution on image data clustering is avoided, the storage capacity of data is reduced, the calculation amount of the data is reduced, and the calculation efficiency is improved.
(3) The method can adaptively calculate the corresponding regularization parameter of each sample by iteratively optimizing the regularization parameter of the target function, greatly reduce the difficulty of adjusting the regularization parameter in the application process, save the labor cost, and improve the image clustering accuracy while robustly screening the image data polluted by noise.
Drawings
FIG. 1: is a flow chart of the method
FIG. 2 is a schematic diagram: is an example of a partially noisy contaminated image
FIG. 3: is a graph of the results of the detection of the method on a particular data set
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the invention is realized by the following technical scheme, and the noise suppression image clustering method based on robust fuzzy clustering comprises the following specific steps:
step 1: obtaining image data information to construct a data matrix
For n picture data of u × v resolution, each picture is elongated to obtain a 1 × d pictureA row vector, where d ═ u × v; converting image data formed by n pictures into a target data matrix
Figure BDA0003691609690000051
Wherein each row of the matrix
Figure BDA0003691609690000061
Represents an image; each image represents a data sample; giving the real category number c contained in the target data, and randomly initializing the clustering centers of c clusters to obtain the initial
Figure BDA0003691609690000062
Is the centroid of the jth cluster.
Step 2: establishing a Robust Fuzzy Clustering (RFCM) framework that can perform noise suppression
A Fuzzy C-means (Fuzzy C-means) algorithm is called FCM algorithm for short, and in order to improve the noise suppression robustness of the Fuzzy C-means algorithm, a noise suppression term and a regularization term are introduced into a framework.
Figure BDA0003691609690000063
Wherein
Figure BDA0003691609690000064
Is fuzzy membership degree, and the centroid matrix of the cluster is
Figure BDA0003691609690000065
The matrix Y represents each element Y ij Representing the degree of membership that the ith sample belongs to the jth cluster.
Figure BDA0003691609690000066
For screening n-k noisy data, s i Is the value of the ith element of s.
And step 3: alternately iteratively optimizing an objective function:
solving three variables of m, Y and s in the objective function by adopting an alternating iterative optimization method, firstly initializing m and Y, and calculating according to a formula to obtain s; fixing s and m, and respectively carrying out different optimizations on the real sample and the noise data to obtain Y; then fixing s and Y, solving m according to a formula, and sequentially circulating until convergence;
the solving steps are as follows:
step 3.1: according to the cluster centers of c clusters which are randomly initialized, obtaining the initial
Figure BDA0003691609690000067
Initializing all elements in Y to Y ij 1/c. The initial probability of distributing samples to each class is considered to be equal. Definition e i To the sample x with a certain degree of membership i The distances to all cluster centers are weighted and the resulting values are summed. E is to be i Arranged as e in descending order 1 ≤e 2 ≤...≤e k ≤…≤e n The corresponding s can be calculated i
Figure BDA0003691609690000068
Step 3.2: and respectively carrying out different optimizations on the real sample and the noise data to obtain Y.
In step 3.1 we obtain s corresponding to the first k samples nearest to all cluster centers i 1, s for the remaining samples i 0. E is to be i Sorting according to the sequence from small to large, and sorting the corresponding samples x i Sorting is carried out, and a sorted data matrix can be obtained
Figure BDA0003691609690000071
Its corresponding sorted membership degree matrix
Figure BDA0003691609690000072
Step 3.2.1: for real samples. When the sample corresponds to s i When the number of the clusters is 1, only q clusters nearest to the real sample are considered, the membership matrix is thinned, and y is limited i L of 0 The norm is q. Definition of
Figure BDA0003691609690000073
For the selected ith real sample point
Figure BDA0003691609690000074
The square of the distance to the jth cluster center, the problem translates equivalently to
Figure BDA0003691609690000075
The parameter γ in the objective function usually needs to be adjusted appropriately to avoid the occurrence of trivial solution, and the present invention can adaptively calculate the optimal parameter γ.
Figure BDA0003691609690000076
Optimizing to obtain the optimal membership degree corresponding to the selected real sample
Figure BDA0003691609690000077
i∈{1,2,...,k}
Figure BDA0003691609690000078
Step 3.2.2: for noisy data in the optimization process. When the sample corresponds to s i When the value is equal to 0, solving the Cauchy inequality to obtain the optimal membership value corresponding to the noise data in the optimization process
Figure BDA0003691609690000079
The optimal solution of all sample point membership degrees can be obtained
Figure BDA00036916096900000710
Is composed of
Figure BDA00036916096900000711
Step 3.3:
solving the partial derivative of m to be equal to 0 by the subproblem of the objective function to obtain
Figure BDA0003691609690000081
And finally, after the m, the Y and the s are updated, next iteration operation is carried out again until the m is not changed any more. And one row of sample data corresponds to one picture, and according to the obtained membership matrix Y, the label of the cluster corresponding to the maximum value of each row of the sample data is selected as the class of the picture to be divided, so that a predicted label vector is obtained, and the image clustering cluster division is realized. The obtained s vector contains k 1, n-k 0 s, and s corresponding to the ith image i If 0, then the picture is screened as a noise contaminated image.
The specific embodiment is as follows:
the comprehensive model solving process of the noise suppression image clustering method based on robust fuzzy clustering is shown in figure 1, an ORL face image data set is selected for clustering, the ORL face image data set comprises 400 face images in total, the resolution ratio is 92 multiplied by 112, each face image corresponds to one sample, and the real label corresponding to 400 images is
Figure BDA0003691609690000082
The predicted labels of 400 images obtained by the clustering algorithm are
Figure BDA0003691609690000083
Wherein the real label z t And the method is only used for final clustering effect verification and is not included in the clustering algorithm. To test the algorithm, the number of noise contaminated image samples p is 160, for example, with a 40% proportion of noise added. The specific implementation mode comprises the following steps:
step one, inputting an ORL data matrix
Figure BDA0003691609690000084
The true class number c, the number p of the noise-contaminated image samples is 160 and the membership degree thinning parameter q, wherein each row of the matrix
Figure BDA0003691609690000085
For one sample, n-400 is the number of samples, d-92 × 112-10304 is the dimension of the data matrix, and c-40 is the number of true categories included in the face data.
And randomly initializing the clustering centers of the c clusters, namely obtaining the initial m. Initializing all elements in Y to Y ij 1/40, and 240, n-p. The initial probability of distributing samples to each class is considered to be equal. I.e., m and Y can be fixed and s can be calculated. Fixing m and Y, converting the objective function into
Figure BDA0003691609690000086
Definition e i To the sample x with a certain degree of membership i The distances to all cluster centers are weighted and the resulting values are summed.
Figure BDA0003691609690000091
E is to be i Arranged as e in descending order 1 ≤e 2 ≤...≤e k ≤…≤e n The optimal solution of the objective function can be calculated and obtained in a constraint s T S corresponding to 1-k i
Figure BDA0003691609690000092
Therefore, the sample data which is not polluted by the noise and the sample which is polluted by the noise can be obtained by screening, and the optimization is continuously carried out in the subsequent iteration process.
Step two: and respectively carrying out different optimizations on the real sample and the noise data to obtain Y.
Obtaining s corresponding to the first k samples nearest to all cluster centers in the first step i 1, s for the remaining samples i 0. E is to be i Sorting according to the sequence from small to large, and sorting the corresponding samples x i Sorting is carried out to obtain a sorted data matrix
Figure BDA0003691609690000093
Its corresponding sorted membership degree matrix
Figure BDA0003691609690000094
Step 2.1: for real samples. Definition of
Figure BDA0003691609690000095
Is a sorted data matrix
Figure BDA0003691609690000096
The vector composed of the ith row elements.
Figure BDA0003691609690000097
Is a matrix of degree of membership after sorting
Figure BDA0003691609690000098
The jth element of row i. When the sample corresponds to s i When 1, a sub-problem of the objective function is
Figure BDA0003691609690000099
Only q clusters nearest to the real sample are considered, the membership matrix is thinned, and y is limited i L of 0 The norm is q. Definition of
Figure BDA00036916096900000910
For the selected ith real sample point
Figure BDA00036916096900000911
Average distance to jth cluster centerThe problem can be equivalently transformed into
Figure BDA00036916096900000912
The second term of the original objective function is the regularization term to avoid the trivial solution of two extreme cases: the similarity of all samples is 1/n with the similarity of only the nearest neighbor sample being 1. By lagrange multiplier method, KKT conditions and constraints
Figure BDA0003691609690000101
Figure BDA0003691609690000102
Since each term of the problem is independent for i, we can be directed to each
Figure BDA0003691609690000103
Independently solving, solving the objective function equivalence sub-problem by adopting a Lagrange multiplier method, and optimizing to obtain the optimal membership degree corresponding to the selected real sample
Figure BDA0003691609690000104
i∈{1,2,...,k}
Figure BDA0003691609690000105
Step 2.2: for noisy data in the optimization process. When the sample corresponds to s i When the value is equal to 0, the optimal membership value corresponding to the noise data in the optimization process is obtained by solving the Cauchy inequality as
Figure BDA0003691609690000106
The optimal solution of all sample point membership degrees can be obtained
Figure BDA0003691609690000107
Is composed of
Figure BDA0003691609690000108
Step three: fix s and Y, solve for m
The objective function sub-problem is then rewritten as
Figure BDA0003691609690000109
Solving the partial derivative of m to be equal to 0 by the subproblem of the objective function to obtain
Figure BDA00036916096900001010
And when s, Y and m are updated, next iteration operation is carried out again until the clustering center m is not updated, namely the change of the clustering center m is smaller than a certain threshold value. Contaminated sample correspondence s i When the solution is finished, optimizing the obtained s i The ith sample corresponding to 0 is screened as the image sample polluted by noise, and 160 image samples polluted by noise can be screened out in total. Clustering prediction label capable of directly obtaining 400 face images
Figure BDA0003691609690000111
So as to achieve considerable clustering effect. Different from classification, the prediction labels obtained by the clustering method can only achieve the grouping effect under the unsupervised condition, so that the numbers in the prediction labels correspond to the real class labels one by one, but the specific corresponding relation cannot be known, and the unsupervised and grouped face data images can be grouped and classified for the face data images without label information, so as to assist face retrieval and greatly improve retrieval precision and speed. By contrasting the real labels z t And a predictive label z obtained by a clustering algorithm p And calculating the accuracy of image clustering.
Take an ORL face image data set (400 pictures, each picture having 92 × 112 pixels) as an example. When 40% of noise is added, the clustering accuracy of the FCM on the ORL face image data is only 8.61%, and the clustering normalization mutual information is 14.13%. When 40% of noise is added, the clustering accuracy of the robust fuzzy clustering-based noise suppression image cluster (RFCM) on the ORL face image data set is 64.83%, the clustering normalization mutual information is 71.29%, 56.22% and 57.16% are respectively improved, and the clustering accuracy of the face image data is remarkably improved.

Claims (1)

1. An image robust clustering method based on fuzzy clustering is characterized by comprising the following steps:
step 1: for n pictures with u × v resolution, lengthening each picture to obtain a 1 × d row vector, where d is u × v; converting image data formed by n pictures into a target data matrix
Figure FDA0003691609680000011
Wherein each row of the matrix
Figure FDA0003691609680000012
Represents an image; each image represents a data sample; giving the real category number c contained in the target data, and randomly initializing the clustering centers of the c clusters, namely obtaining the initial
Figure FDA0003691609680000013
Is the centroid of the jth cluster;
step 2: establishing robust fuzzy clustering RFCM framework for noise suppression
Figure FDA0003691609680000014
Wherein
Figure FDA0003691609680000015
Is fuzzy membership degree, and the centroid matrix of the cluster is
Figure FDA0003691609680000016
The matrix Y represents each element Y ij Representing the membership degree of the ith sample belonging to the jth cluster;
Figure FDA0003691609680000017
for screening n-k noisy data, s i Is the value of the ith element;
and step 3: alternative iteration optimization robust fuzzy clustering RFCM framework
The solving steps are as follows:
step 3.1: randomly initializing the clustering centers of c clusters to obtain initial clusters
Figure FDA0003691609680000018
Initializing all elements in Y to Y ij 1/c; definition e i To the sample x with a certain degree of membership i Distances to all cluster centers are weighted and the resulting values are summed, e i Arranged as e in descending order 1 ≤e 2 ≤...≤e k ≤...≤e n Calculating to obtain its correspondence s i
Figure FDA0003691609680000019
Step 3.2: respectively carrying out different optimizations on the real sample and the noise data to obtain Y
S corresponding to the first k samples nearest to all the cluster centers i 1, s for the remaining samples i 0; will be compared with the sequence e i Corresponding sample x i Sorting is carried out to obtain a sorted data matrix
Figure FDA00036916096800000110
Its corresponding sorted membership degree matrix
Figure FDA00036916096800000111
Step 3.2.1: when the sample corresponds to s i When the number of the clusters is 1, q clusters nearest to the real sample are thinned out, and y is limited i L of 0 Norm q, defined
Figure FDA0003691609680000021
Ith real sample point
Figure FDA0003691609680000022
RFCM framework equivalence transformation to the square of the distance to the jth cluster center
Figure FDA0003691609680000023
Calculating an optimal parameter gamma by the parameter gamma in the target function in a self-adaptive mode;
Figure FDA0003691609680000024
optimizing to obtain the optimal membership degree corresponding to the selected real sample
Figure FDA0003691609680000025
Figure FDA0003691609680000026
Step 3.2.2: for the noise data in the optimization process, s corresponding to the sample i When the value is equal to 0, the optimal membership value corresponding to the noise data in the optimization process is obtained by solving the Cauchy inequality as
Figure FDA0003691609680000027
Obtaining the optimal solution of all sample point membership degrees
Figure FDA0003691609680000028
Is composed of
Figure FDA0003691609680000029
Step 3.3: fixing s and Y to get a sub-problem of the RFCM framework
Figure FDA00036916096800000210
Solving the partial derivative of m to be equal to 0 to obtain:
Figure FDA00036916096800000211
in each optimization process, m, Y and s are continuously updated, and the next iterative operation is carried out again until m is not changed; one row of sample data corresponds to one picture, and according to the obtained membership degree matrix Y, the label of the cluster corresponding to the maximum value of each row of the sample data is selected as the classified class of the picture, so that a predicted label vector is obtained, and the image clustering cluster division is realized; the obtained s vector contains k 1, n-k 0 s, and s corresponding to the ith image i Then the picture is screened as an image contaminated with noise.
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