CN115131588B - Image robust clustering method based on fuzzy clustering - Google Patents

Abstract

The present invention relates to an image robust clustering method based on fuzzy clustering. While clustering image data, it filters out images contaminated by noise, retains pure and pollution-free image data, and has high robustness to noise changes. Great sex. Moreover, the present invention is an unsupervised algorithm, does not require the use of label data, and reduces a large amount of time spent in obtaining label data. The algorithm does not need to update the graph matrix during the solution process, thus reducing the computational complexity of the algorithm and speeding up the operation. Therefore, fast, effective and robust clustering of noise-contaminated images can be achieved. The present invention can adaptively calculate the corresponding regularization parameters of each sample by iteratively optimizing the regularization parameters of the objective function, which greatly reduces the difficulty of adjusting the regularization parameters during the application process, saves labor costs, and robustly While filtering out image data contaminated by noise, the accuracy of image clustering is improved.

Description

A robust image clustering method based on fuzzy clustering

Technical field

The invention belongs to the field of image recognition and classification and pattern recognition, and relates to a robust image clustering method based on fuzzy clustering.

Background technique

With the development of computer technology and digital imaging systems, it is becoming more and more convenient for people to transmit information through images. However, in real environments, image information is easily contaminated by noise, which causes a certain loss of image quality and makes effective image recognition difficult. As the image information being processed becomes increasingly complex and it becomes increasingly difficult to obtain labels, the application of unsupervised image clustering technology in the information age has received widespread attention. Image clustering technology can cluster pictures in image databases into groups based on their similarities. Clusters, so that the similarity of pictures in the same cluster is as large as possible and the similarity between different clusters is as small as possible. Image information is easily affected by noise. If traditional unsupervised image clustering is still performed on images contaminated by noise, the accuracy and reliability of image retrieval will be greatly affected. Screen out the images contaminated by noise, and then compare the new images one by one with the clusters with higher similarity in the database to quickly complete the identification and classification. Therefore, clustering image data after noise suppression before image retrieval can effectively and quickly achieve high-quality image data retrieval.

Li Kang et al. ("A fuzzy spectral clustering algorithm for hyperspectral image classification" Chinese Science and Technology Papers, 2021,16(07):743-747.) A fuzzy similarity measure spectrum for hyperspectral remote sensing image classification The clustering (FSMSC) algorithm aims to construct an effective fuzzy similarity matrix and improve the performance of the clustering algorithm by introducing fuzzy similarity measurement and robust anchor graph structure. However, updating the graph matrix will also increase the time complexity of the fuzzy clustering algorithm and affect the operation speed. Although it integrates graph learning and fuzzy clustering learning into a joint learning framework, it is limited by the traditional fuzzy clustering algorithm, which has poor robustness and cannot effectively remove noise data, which affects subsequent image data retrieval. .

Contents of the invention

Technical issues to be solved

In order to avoid the shortcomings of the existing technology, the present invention proposes a robust image clustering method based on fuzzy clustering. The existing supervised image algorithms need to spend a lot of time to obtain data labels and cannot effectively solve the problem. The impact of noise on image data retrieval is a problem of poor robustness.

Technical solutions

An image robust clustering method based on fuzzy clustering, characterized by the following steps:

Step 1: For n picture data with u×v resolution, stretch each picture to obtain a 1×d row vector, where d=u×v; convert the image data composed of n pictures into a target data matrix Each row of the matrix/> Represents an image; each image represents a data sample; given the number of real categories c contained in the target data, randomly initialize the cluster centers of c clusters, that is, obtain the initial /> is the centroid of the jth cluster;

Step 2: Establish a robust fuzzy clustering RFCM framework for noise suppression

in is the fuzzy membership degree, and the centroid matrix of clustering is/> The matrix Y represents each element y _ij represents the membership degree of the i-th sample belonging to the j-th cluster;/> Used to filter nk noise data, s _i is the value of the i-th element of s;

Step 3: Alternate iterative optimization of robust fuzzy clustering RFCM framework

The solution steps are as follows:

Step 3.1: Randomly initialize the cluster centers of c clusters to obtain the initial Initialize all elements in Y to y _ij =1/c; define e _i as the value obtained by weighting and summing the distances from sample x _i to all cluster centers with a certain degree of membership, and arrange e _i in order from small to large The arrangement is e ₁ ≤e ₂ ≤...≤e _k ≤...≤e _n , and the corresponding s _i is calculated;

Step 3.2: Perform different optimizations on real samples and noise data to obtain Y

The first k samples closest to all cluster centers correspond to s _i = 1, and the remaining samples correspond to s _i = 0; sort the samples _xi corresponding to the ordered e _i to obtain the sorted data matrix Its corresponding sorted membership matrix/>

Step 3.2.1: When the s _i corresponding to the sample = 1, the q clusters closest to the real sample, sparse the membership matrix, and limit the l ₀ norm of y _i to q, defined The i-th real sample point/> The square of the distance to the jth cluster center, the RFCM framework is equivalent to

The parameter γ in the objective function is adaptively calculated to calculate the optimal parameter γ;

Optimize to obtain the optimal membership degree corresponding to the selected real sample i∈{1,2,...,k}

Step 3.2.2: For the noise data in the optimization process, when the s _i corresponding to the sample = 0, the optimal membership value corresponding to the noise data in the optimization process is solved by Cauchy's inequality:

Obtain the optimal solution for the membership degree of all sample points for

Step 3.3: Fix s and Y to obtain the sub-problems of the RFCM framework

The partial derivative of the sub-problem with respect to m is equal to 0, and the solution is:

During each optimization process, m, Y, s are constantly updated, and the next iteration operation is performed again until m no longer changes; one row of sample data corresponds to one picture, and according to the obtained membership matrix Y, the maximum value of each row is selected The label of the cluster corresponding to the value is used as the category into which this picture is divided, that is, the predicted label vector is obtained to implement image clustering; the obtained s vector contains k 1s, nk 0s, and the i-th image The corresponding s _i =0, then this image is filtered as an image contaminated by noise.

beneficial effects

The invention proposes a robust image clustering method based on fuzzy clustering. While clustering image data, it filters out images contaminated by noise, retains pure and pollution-free image data, and has a high tolerance to noise changes. robustness. Moreover, the present invention is an unsupervised algorithm, does not require the use of label data, and reduces a large amount of time spent in obtaining label data. The algorithm does not need to update the graph matrix during the solution process, thus reducing the computational complexity of the algorithm and speeding up the operation. Therefore, fast, effective and robust clustering of noise-contaminated images can be achieved.

The present invention provides a noise suppression image clustering method based on an improved robust fuzzy clustering framework based on FCM. During the application process, it can not only robustly filter out noise-contaminated image data, but also be used for image clustering. At the same time, the robustness and accuracy of the algorithm are improved, and the sparse processing of the membership matrix improves the data processing speed. In this algorithm, the objective function consists of a robust noise suppression term and a regularization term. By iteratively optimizing the objective function, an adaptive weight is added to each sample point, and pure samples and noise-contaminated samples are screened accordingly, which enhances the robustness of the algorithm. Great sex. By optimizing the objective function, data samples contaminated by noise can be screened, and then noise-suppressed image clustering can be performed.

The beneficial effects of adopting the method of the present invention mainly include:

(1) A robust fuzzy clustering algorithm is proposed. In this algorithm, the robust noise suppression term of the objective function allows the algorithm to iteratively optimize the objective function, add adaptive weights to each sample point, and filter pure samples accordingly. Contaminated samples with noise enhance the robustness of the algorithm.

(2) The present invention proposes a noise suppression image clustering method based on robust fuzzy clustering. While performing robust noise suppression, the membership matrix is sparsely obtained to obtain a more effective sample and feature distribution structure, which avoids It eliminates the impact of noise pollution on image data clustering, reduces the amount of data storage, reduces the amount of data calculation, and improves calculation efficiency.

(3) The present invention can adaptively calculate the corresponding regularization parameters of each sample by iteratively optimizing the regularization parameters of the objective function, which greatly reduces the difficulty of adjusting the regularization parameters during the application process and saves labor costs. Robustly filter out noise-contaminated image data while improving image clustering accuracy.

Description of drawings

Figure 1: Method flow chart

Figure 2: An example of some noise-contaminated images

Figure 3: Is the detection result of the method on a specific data set

Detailed ways

The present invention will now be further described with reference to the embodiments and drawings:

The present invention is realized through the following technical solutions, a noise suppression image clustering method based on robust fuzzy clustering, the specific steps of which are as follows:

Step 1: Obtain image data information and construct a data matrix

For n picture data with u×v resolution, stretch each picture to obtain a 1×d row vector, where d=u×v; convert the image data composed of n pictures into a target data matrix Each row of the matrix/> Represents an image; each image represents a data sample; given the number of real categories c contained in the target data, randomly initialize the cluster centers of c clusters, that is, obtain the initial /> is the centroid of the jth cluster.

Step 2: Establish a robust fuzzy clustering (RFCM) framework that can perform noise suppression

The Fuzzy C-means algorithm is referred to as the FCM algorithm. In order to improve its noise suppression robustness, the framework introduces noise suppression terms and regularization terms.

in is the fuzzy membership degree, and the centroid matrix of clustering is/> The matrix Y represents that each element y _ij represents the membership degree of the i-th sample belonging to the j-th cluster. /> Used to filter nk noise data, s _i is the value of the i-th element of s.

Step 3: Alternate iteration to optimize the objective function:

The alternating iterative optimization method is used to solve the three variables m, Y, and s in the objective function. First, m and Y are initialized, and s is calculated according to the formula; then s and m are fixed, and different optimizations are performed for real samples and noise data to obtain Y. ; Then fix s and Y, solve m according to the formula, and loop until convergence;

The solution steps are as follows:

Step 3.1: Obtain the initial clustering center according to the random initialization of c clusters. Initialize all elements in Y to y _ij =1/c. Consider distributing samples to each class with equal initial probability. Define e _i as the value obtained by weighting and summing the distances from sample x _i to all cluster centers with a certain degree of membership. Arrange e _i in order from small to large as e ₁ ≤e ₂ ≤...≤e _k ≤...≤e _n , and its corresponding s _i can be calculated

Step 3.2: Perform different optimizations on real samples and noise data to obtain Y.

In step 3.1, we obtained s _i =1 corresponding to the first k samples closest to all cluster centers, and s _i =0 corresponding to the remaining samples. Sort e _i in order from small to large, and sort the corresponding samples x _i to get the sorted data matrix. Its corresponding sorted membership matrix/>

Step 3.2.1: For real samples. When the s _i corresponding to the sample = 1, only the q clusters closest to the real sample are considered, the membership matrix is sparse, and the l ₀ norm of y _i is limited to q. definition is the selected i-th real sample point/> The square of the distance to the jth cluster center, the problem can be equivalently transformed into

The parameter γ in the objective function usually needs to be adjusted appropriately to avoid the occurrence of trivial solutions. The present invention can adaptively calculate the optimal parameter γ.

Optimize to obtain the optimal membership degree corresponding to the selected real sample i∈{1,2,...,k}

Step 3.2.2: For noisy data during optimization. When the s _i corresponding to the sample = 0, the optimal membership value corresponding to the noise data in the optimization process is obtained by solving Cauchy's inequality:

The optimal solution of the membership degree of all sample points can be obtained for

Step 3.3:

The partial derivative of the sub-problem of the objective function with respect to m is equal to 0, which can be solved

At this point, m, Y, s have been updated, and then the next iteration operation is performed again until m no longer changes. One row of sample data corresponds to one picture. According to the obtained membership matrix Y, select the label of the cluster corresponding to the maximum value of each row as the category into which this picture is divided. That is, the predicted label vector is obtained to implement image clustering. Cluster partitioning. The obtained s vector contains k 1s, nk 0s, and _si = 0 corresponding to the i-th image, then this image is screened as an image contaminated by noise.

Specific examples:

The comprehensive model solution process of the noise suppression image clustering method based on robust fuzzy clustering of the present invention is shown in Figure 1. The ORL face image data set is selected for clustering example. The ORL data set contains a total of 400 face images. The rate is 92×112, each face image corresponds to a sample, and the real labels corresponding to 400 images are The predicted labels of 400 images obtained by the clustering algorithm are/> The real label z _t is only used for the final clustering effect verification and is not included in the clustering algorithm itself. In order to test the algorithm, taking the addition of 40% noise as an example, the number of noise-contaminated image samples p=160. The specific implementation includes the following steps:

Step 1. Enter the ORL data matrix The number of real categories c, the number of noise-contaminated image samples p=160 and the membership sparsification parameter q, where each row of the matrix/> is a sample, n=400 is the number of samples, d=92×112=10304 is the data matrix dimension, and c=40 is the number of real categories contained in the face data.

Randomly initialize the cluster centers of c clusters, that is, obtain the initial m. Initialize all elements in Y to y _ij =1/c=1/40, k=np=240. Consider distributing samples to each class with equal initial probability. That is, you can fix m and Y and calculate s. Fixed m and Y, the objective function is transformed into

Define e _i as the value obtained by weighting and summing the distances from sample x _i to all cluster centers with a certain degree of membership.

Arrange e _i in order from small to large as e ₁ ≤ e ₂ ≤...≤e _k ≤...≤e _n , we can calculate the optimal solution of the objective function under the constraint s ^T 1=k and its corresponding _i

Based on this, sample data that are not contaminated by noise and samples that are contaminated by noise can be screened out, and continuously optimized in the subsequent iteration process.

Step 2: Perform different optimizations on real samples and noise data to obtain Y.

In step 1, the s _i =1 corresponding to the first k samples closest to all cluster centers are obtained, and the s _i =0 corresponding to the remaining samples are obtained. Sort e _i in order from small to large, and sort the corresponding samples x _i to get the sorted data matrix. Its corresponding sorted membership matrix/>

Step 2.1: For real samples. definition is the sorted data matrix/> A vector composed of elements in row i. /> is the sorted membership matrix/> The j-th element of the i-th row. When s _i =1 corresponding to the sample, the sub-problem of the objective function is

Only consider the q clusters closest to the real samples, sparse the membership matrix, and limit the l ₀ norm of y _i to q. definition is the selected i-th real sample point/> The square of the distance to the jth cluster center, the problem can be equivalently transformed into

The second term of the original objective function is the regularization term in order to avoid the trivial solutions of two extreme cases: only the nearest neighbor sample has a similarity of 1 and the similarity of all samples is 1/n. Through Lagrange multiplier method, KKT conditions and constraints

Since each term of the problem is independent for i, we can Solve separately, use the Lagrange multiplier method to solve the equivalent sub-problem of the objective function, and optimize to obtain the optimal membership degree corresponding to the selected real sample/> i∈{1,2,...,k}

Step 2.2: For noisy data during optimization. When the s _i corresponding to the sample = 0, the optimal membership value corresponding to the noise data in the optimization process is obtained by solving Cauchy's inequality:

The optimal solution of the membership degree of all sample points can be obtained for

Step 3: Fix s and Y and solve for m

At this time, the objective function sub-problem is rewritten as

The partial derivative of the sub-problem of the objective function with respect to m is equal to 0, which can be solved

At this point, s, Y and m have been updated, and then the next iteration operation is performed again until the cluster center m is no longer updated, that is, its change is less than a certain threshold. The contaminated sample corresponds to s _i =0. After the solution is completed, the i-th sample corresponding to s _i =0 obtained through optimization is screened as an image sample contaminated by noise. A total of 160 image samples contaminated by noise can be screened out. Finally, we can directly obtain the cluster prediction labels of 400 face images. to achieve considerable clustering effects. Different from classification, the predicted labels obtained by the clustering method can only achieve the effect of grouping without supervision. Therefore, although the numbers in the predicted labels correspond to the real category labels one-to-one, the specific correspondence cannot be known, so there is no Supervising the grouped face data images can group and classify the face data images without label information to assist face retrieval and greatly improve the retrieval accuracy and speed. The accuracy of image clustering is calculated by comparing the true label z _t with the predicted label z _p obtained by the clustering algorithm.

Take the ORL face image data set (400 pictures, each picture has 92×112 pixels) as an example. When adding 40% noise, the clustering accuracy of FCM on ORL face image data is only 8.61%, and the clustering normalized mutual information is 14.13%. When adding 40% noise, the clustering accuracy of the noise-suppressed image clustering (RFCM) based on robust fuzzy clustering proposed by the present invention on the ORL face image data set is 64.83%, and the clustering normalized interaction is 64.83%. The information is 71.29%, which is an improvement of 56.22% and 57.16% respectively, which significantly improves the clustering accuracy of face image data.

Claims (1)

1. The image robust clustering method based on fuzzy clustering is characterized by comprising the following steps:

step 1: for n-sheet uXv resolutionDrawing each picture to obtain a row vector of 1×d, wherein d=u×v; converting image data composed of n pictures into target data matrixWherein each row of the matrix is>Representing an image; each image represents a data sample; giving the true class number c contained in the target data, randomly initializing the clustering centers of c clusters to obtain initial +.>Is the centroid of the j-th cluster;

step 2: establishing robust fuzzy clustering RFCM framework for noise suppression

Wherein the method comprises the steps ofIs fuzzy membership, and the centroid matrix of the cluster is +.>The matrix Y represents each element Y _ij Representing the membership degree of the ith sample belonging to the jth cluster; />For screening n-k noise data s _i Values for the ith element of s;

step 3: alternating iterative optimization robust fuzzy clustering RFCM framework

The solving steps are as follows:

step 3.1: randomly initializing the cluster centers of c clusters to obtain an initial clusterA kind of electronic deviceInitializing all elements in Y to Y _ij =1/c; definition e _i To a certain membership degree to sample x _i Weighting and summing the obtained values to all cluster center distances, and adding e _i Arranged in order from small to large as e ₁ ≤e ₂ ≤...≤e _k ≤...≤e _n Calculating to obtain the corresponding s _i ；

Step 3.2: different optimizations are respectively carried out on the real sample and the noise data to obtain Y

The first k samples nearest to all cluster centers correspond to s _i =1, s corresponding to the remaining samples _i =0; e after the sequence of the two steps _i Corresponding sample x _i Sequencing to obtain a sequenced data matrixCorresponding to the ordered membership matrix

Step 3.2.1: when the sample corresponds to s _i When=1, the q clusters nearest to the real sample, the membership matrix is thinned, and y is limited _i L of (2) ₀ The norm is q, defined asThe i-th real sample point->The distance squared to the j-th cluster center, the RFCM frame equivalent translates to

The parameter gamma in the objective function is used for adaptively calculating the optimal parameter gamma;

optimizing to obtain the optimal membership degree corresponding to the selected real sample

Step 3.2.2: for noise data in the optimization process, when the sample corresponds to s _i When=0, the optimal membership value corresponding to the noise data in the optimization process is obtained by solving the cauchy inequality

Obtaining the optimal solution of all sample point membership degreesIs that

Step 3.3: fixing s and Y, obtaining the sub-problem of the RFCM framework

The sub-problem is solved by solving the m bias guide equal to 0:

in each optimization process, m, Y and s are continuously updated, and the next iteration 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 is selected as the classified type of the picture, namely a predicted label vector is obtained, and image clustering cluster division is realized; the obtained s vector contains k 1, n-k 0 s corresponding to the ith image _i =0, then this picture is screened as an image contaminated with noise.