A fuzzy mean clustering method and system based on de-redundancy and density constraint

Abstract

The application provides a fuzzy mean clustering method and system based on de-redundancy and density constraint, and relates to the technical field of machine learning, and comprises the following steps: based on the traditional PCA dimension reduction principle, a de-redundancy algorithm PCAW algorithm is constructed; redundancy is removed through the PCAW algorithm; the density of each data point is calculated after the data is de-redundant; the sum of the membership degrees of each data point with respect to all clusters is changed from 1 to the density value function of the data point, and the membership degree is updated according to the initialized clustering center; based on the updated membership degree, the clustering center is updated, and it is judged whether the updated clustering center function satisfies the convergence condition; if not, the membership degree and the clustering center are updated in turn. If it is satisfied, the clustering is completed. In view of the problem that redundant features, noise points and outliers cause the performance of the fuzzy clustering algorithm to decline, the PCAW de-redundancy method and the density constraint are proposed, the redundant features are removed, and the effects of the noise points and outliers on the updating of the clustering center are inhibited, so that the clustering precision is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of machine learning, and particularly relates to a fuzzy mean clustering method and system based on de-redundancy and density constraint. BACKGROUND

[0002] Fuzzy clustering belongs to unsupervised learning algorithm, which can effectively deal with data with fuzziness and uncertainty. It is widely used in image segmentation, medical imaging, resource optimization and other fields. Fuzzy clustering groups the data in the data set according to the distance between the data (divided into multiple clusters), each data point in the data set has a membership degree relative to each cluster (the membership degree is calculated by the distance between the data point and the cluster center of each cluster, the membership degree can be regarded as the similarity between the data point and the cluster). In fuzzy clustering, cluster center and membership degree play a very important role, membership degree can be calculated by cluster center, and cluster center can be calculated by membership degree, they are calculated alternately until convergence. Data from the real world inevitably produces noise and outliers (noise and outliers are usually far away from other points and relatively sparse) in the process of data collection, storage and processing. The existence of noise and outliers inevitably leads to the decrease of clustering quality, causing the inaccuracy of cluster center and the deviation of cluster center to noise and outliers. FCM algorithm is limited by the constraint that the sum of the membership degree of any data point to all clusters is 1, so it is sensitive to noise data and outliers. Noise data and outliers far away from the cluster center of each cluster can obtain a higher membership degree in the clustering process, so when updating the cluster center, the cluster center will deviate to the noise point or the outlier. And the Euclidean distance will lead to the performance decline of fuzzy clustering algorithm when calculating high-dimensional data due to the influence of redundant features [Xia S, Xiong Z, Luo Y, et al. Effectiveness of the Euclidean distance in high dimensional spaces [J]. Optik, 2015, 126(24): 5614-5619.].To solve the influence of noise and outliers on clustering centers, R. Krishnapuram et al. proposed PCM [Krishnapuram R, Keller J M. A possibilistic approach to clustering [J]. IEEE transactions on fuzzy systems, 1993, 1(2): 98-110.], abandoned the constraint that the sum of the membership degrees of any data point to all clusters is 1 in FCM, but the membership degree of the data point to a certain cluster is only related to the clustering center of the cluster, which is very easy to cause the phenomenon of clustering center consistency of all clusters (that is, all clustering centers become the same one); Pal et al. proposed PFCM [Pal N R, Pal K, Keller J M, et al. A possibilistic fuzzy c-means clustering algorithm [J]. IEEE transactions on fuzzy systems, 2005, 13(4): 517-530.], combined FCM and PCM, solved the noise sensitivity defect of FCM, and overcame the problem of overlapping clusters of PCM; Xu, Jinglin, et al. proposed RSFKM [Xu J, Han J, Xiong K, et al. Robust and sparse fuzzy k-means clustering [C] / / IJCAI. 2016: 2224-2230.], introduced a robust distance function to suppress the effect of noise; Chen, Jingwei, et al. proposed P_SFCM [Chen J, Zhu J, Jiang H, et al. Sparsity Fuzzy C-Means Clustering with Principal Component Analysis Embedding [J]. IEEE Transactions on Fuzzy Systems, 2022.], constructed a unified framework of dimension reduction and clustering to improve the performance of fuzzy clustering on high-dimensional data clustering, and added a weighting factor to judge whether the point is noise and outlier, if it is noise, set its membership degree to 0 to suppress the effect of noise and outliers.

[0003] The PCM abandons the constraint that the sum of the membership degrees of any data point in the FCM to all clusters is 1, but the membership degree of the data point to a certain cluster is only related to the cluster center of the cluster, which can easily lead to the phenomenon that the cluster centers of all clusters are consistent (that is, all cluster centers become the same one); the PFCM combines the FCM and the PCM to solve the noise sensitivity defect of the FCM and overcome the coincidence cluster problem of the PCM; the RSFKM suppresses the effect of noise by introducing a robust distance function, but when the selected parameter is not appropriate, the suppression effect is not obvious. The above algorithms do not consider the high-dimensional data clustering problem. The P_SFCM improves the performance of high-dimensional data clustering by constructing a unified framework of PCA dimension reduction and fuzzy clustering, and adds a weighting factor to judge whether the data point is noise, and if it is noise, the membership degree is set to 0, but PCA is lossy compression, and when the dimension is reduced to a dimension suitable for Euclidean distance calculation, part of the information will be lost, and the noise rate (the percentage of noise data points in all data points) needs to be set manually, and the manually set noise rate is often inaccurate. SUMMARY

[0004] The application provides a fuzzy mean clustering method and system based on de-redundancy and density constraint, which reduces the information loss caused by PCA dimension reduction and solves the problem of inaccurate manually set parameters or noise rate.

[0005] To solve the above-mentioned application purposes, the technical scheme provided by the application is as follows: a fuzzy mean clustering method based on de-redundancy and density constraint, characterized in that the steps include:

[0006] S1, input a preset data set X; obtain system data; the system data includes: a dimension reduction dimension m, a cluster number c, an initial membership degree matrix U, an initial cluster center matrix V, and an initial projection matrix P;

[0007] S2, based on the traditional PCA dimension reduction principle, construct a de-redundancy algorithm PCAW algorithm; remove the redundancy through the PCAW algorithm;

[0008] S3, calculate the density of each data point after removing the redundancy;

[0009] S4, change the sum of the membership degrees of each data point to all clusters from 1 to the density value function of the data point, and update the membership degree;

[0010] S5, based on the updated membership degree, update the cluster center, judge whether the updated cluster center function meets the convergence condition, if not, re-update the membership degree and the cluster center; if yes, complete the fuzzy mean clustering based on de-redundancy and density constraint.

[0011] Preferably, in step S2, a de-redundancy algorithm PCAW algorithm is constructed based on the traditional PCA dimension reduction principle; the de-redundancy is removed through the PCAW algorithm, including:

[0012] Based on the PCA dimension reduction principle, the following formula (1) is obtained:

[0013]

[0014] Wherein, n is the number of data; X is the data set matrix; x i (i∈1,…n) represents the i-th column of X, i.e. the i-th data point; P is the projection matrix; tr(B) represents the trace of matrix B; I represents the unit matrix; 1=[1,1,…1] T , represents a vector with all elements being 1;

[0015] Based on the PCA objective function, the following formula (2) is constructed to remove the de-redundancy algorithm PCAW algorithm:

[0016]

[0017] Wherein, is used to maintain the neighborhood structure property between data; W is the affinity matrix, W ij represents the relationship between data point i and data point j;

[0018] Through the PCAW algorithm, the data is processed to reduce the data redundancy feature.

[0019] Preferably, in step S3, the density of each data point is calculated after removing the de-redundancy data, including:

[0020] Obtain the de-redundancy data;

[0021] Different distances d e are selected for different data sets in the de-redundancy data e The average number of neighbors of each data point needs to be 1% to 2% of the total number of data points;

[0022] The density of data point i is calculated according to the following formula (3):

[0023]

[0024] Wherein, p i represents the density of data point i, Ω k represents the number of neighbors of data point i, d ik represents the Euclidean distance between data point i and data point k.

[0025] Preferably, the neighbors of the data point i are data points with distance less than d e to the data point i.

[0026] Preferably, in step S4, the sum of the membership degrees of each data point to all clusters is changed from 1 to a density value function of the data point, the membership degrees are updated, including:

[0027] the sum of the membership degrees of any data point to all clusters is changed from 1 to a function of the respective density value, wherein the function of the density value is: density value function = (density value of the data point - minimum value of the density of all data points) ÷ (maximum value of the density of all data points - minimum value of the density of all data points);

[0028] The membership degrees are updated according to the following membership degree updating formula (4):

[0029]

[0030] wherein x j is the jth data point, v i is the ith cluster center, u ij is the membership degree of the jth data point x j to the ith cluster, p j is the density of the jth data point, p min is the minimum value of the density of all data points, p max is the maximum value of the density of all data points.

[0031] Preferably, in step S5, based on the updated membership degrees, the cluster centers are updated, it is judged whether the updated cluster center function satisfies a convergence condition, if not, the membership degrees and the cluster centers are updated again; if yes, the fuzzy mean clustering based on de-redundancy and density constraint is completed, including:

[0032] The cluster centers are updated according to the following cluster center updating formula (5):

[0033]

[0034] It is judged whether the updated cluster center function satisfies a convergence condition, if not, the membership degrees and the cluster centers are updated again; if yes, the fuzzy mean clustering based on de-redundancy and density constraint is completed.

[0035] Preferably, the convergence condition includes:

[0036] the l 21 norm of the difference between the (t+1)th updated cluster center and the tth updated cluster center is less than 1e-6, where V is a k-row d-column matrix, k is the number of clusters, and d is the dimension of the data.

[0037] A fuzzy mean clustering system based on de-redundancy and density constraint, the system is used for the fuzzy mean clustering method based on de-redundancy and density constraint, the system comprises:

[0038] An information acquisition module for inputting a preset data set X; acquiring system data; the system data comprises: dimensionality reduction dimension m, cluster number c, initial membership matrix U, initial clustering center matrix V, and initial projection matrix P;

[0039] A redundancy removal module for constructing a de-redundancy algorithm PCAW algorithm based on a traditional PCA dimensionality reduction principle; removing redundancy through the PCAW algorithm; and calculating the density of each data point after removing the redundancy;

[0040] A membership update module for changing the sum of the membership of each data point with respect to all clusters from 1 to the density value function of the data point, and updating the membership;

[0041] A clustering center update module for updating the clustering center based on the updated membership, judging whether the updated clustering center function satisfies the convergence condition, if not, re-updating the membership and the clustering center; if yes, completing the fuzzy mean clustering based on de-redundancy and density constraint.

[0042] Preferably, the redundancy removal module is configured to obtain a PCA objective function as shown in the following formula (1) based on the PCA dimensionality reduction principle:

[0043]

[0044] Wherein, n is the number of data; X is a data set matrix; x i (i∈1,…n) represents the ith column of X, i.e. the ith data point; P is a projection matrix; tr(B) represents the trace of matrix B; I represents an identity matrix; 1=[1,1,…1] T , represents a vector with all elements being 1;

[0045] Based on the PCA objective function, a de-redundancy algorithm PCAW algorithm as shown in the following formula (2) is constructed:

[0046]

[0047] Wherein, For maintaining the neighborhood structure property between data; W is an affinity matrix, W ij represents the relationship between data point i and data point j;

[0048] The data is processed through the PCAW algorithm to reduce the redundant features of the data.

[0049] Preferably, the redundancy removal module is configured to obtain the data after removing the redundancy; and select different distances d for different data sets in the data after removing the redundancy e wherein the selected distance d e The average number of neighbors of each data point needs to be 1% to 2% of the total number of data points;

[0050] The density of the data point i is calculated according to the following formula (3):

[0051]

[0052] wherein p i represents the density of the data point i, Ω k represents the number of neighbors of the data point i, d ik represents the Euclidean distance between the data point i and the data point k.

[0053] In one aspect, an electronic device is provided, which includes a processor and a memory, the memory having stored therein at least one instruction, which is loaded and executed by the processor to implement the above-described fuzzy mean clustering method based on redundancy removal and density constraint.

[0054] In one aspect, a computer-readable storage medium is provided, which has stored therein at least one instruction, which is loaded and executed by a processor to implement the above-described fuzzy mean clustering method based on redundancy removal and density constraint.

[0055] Compared with the prior art, the above technical solution has at least the following beneficial effects:

[0056] The above solution proposes a fuzzy mean clustering method based on redundancy removal and density constraint, and proposes a PCAW redundancy removal method to address the problem of performance degradation of fuzzy clustering algorithm caused by redundant features, which can effectively reduce information loss while reducing the dimension of high-dimensional data, thereby improving clustering accuracy. The constraint condition that the sum of the membership degrees of the data points with respect to each cluster is 1 is replaced by the constraint condition that the sum of the membership degrees is the density normalized value of the data point, which suppresses the influence of noise points and outliers on the update of the cluster center. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0058] Figure 1A flowchart of a fuzzy mean clustering method based on de-redundancy and density constraint provided by an embodiment of the present application is shown in the figure.

[0059] Figure 2 A system block diagram of a fuzzy mean clustering system based on de-redundancy and density constraint provided by an embodiment of the present application is shown in the figure.

[0060] Figure 3 A structural diagram of an electronic device provided by an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0061] To make the objectives, technical solutions and advantages of embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be described below in connection with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the described embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort belong to the scope of the present application.

[0062] The present application aims at the problem of performance degradation of fuzzy clustering algorithm caused by redundant features in the prior art, and the problem of loss of part of information when reducing dimension to a dimension suitable for Euclidean distance calculation, and the problem of inaccurate manual setting of noise rate.

[0063] As shown in the figure, Figure 1 An embodiment of the present application provides a fuzzy mean clustering method based on de-redundancy and density constraint, which can be implemented by an electronic device. As shown in the figure, Figure 1 A flowchart of a fuzzy mean clustering method based on de-redundancy and density constraint, the processing flow of the method can include the following steps:

[0064] S101, input a preset data set X; obtain system data; the system data includes: a dimension reduction dimension m, a cluster number c, an initial membership degree matrix U, an initial clustering center matrix V, and an initial projection matrix P.

[0065] A feasible implementation manner is to add an input data set X, so that the system can automatically generate the dimension reduction dimension m, the cluster number c, the initial membership degree matrix U, the initial clustering center matrix V, and the initial projection matrix P according to the input data set X.

[0066] S102, based on the traditional PCA dimension reduction principle, construct a de-redundancy algorithm PCAW algorithm; remove redundancy through the PCAW algorithm.

[0067] In a feasible implementation, the application designs a fuzzy mean clustering algorithm based on redundancy reduction and density constraints (RDFCM: A Fuzzy Mean Clustering Algorithm Based on Redundancy Reduction and Density Constraints). In image classification, the Yale and ORL data sets are adjusted to 32x32 and 46x46 pixels, respectively. Since the dimensions of the data sets are 1024 and 2116, respectively, the distance function is inevitably affected by redundant features during clustering, thereby affecting the clustering results. Therefore, the PCAW algorithm is used to remove redundant features to generate an image representation vector suitable for clustering. At the same time, noise and outliers are inevitably generated during data collection. Noise and outliers will cause the clustering center to deviate during clustering, thereby affecting the clustering results. Noise and outliers are usually far away from other points and are relatively sparse. The clustering center is usually located in a high-density area. Therefore, the sum of the membership degrees of each data point with respect to all clusters is changed from 1 to the density value function of the data point. Since the distance function is also affected by redundant features when calculating the density, the PCAW is used to remove the redundant features before calculating the density. Then the membership degree and the clustering center are constantly updated until convergence.

[0068] The principle of PCA dimension reduction is to rotate the coordinate axes to generate new coordinate axes. If the projection of data on some new coordinate axes has a large variance, these new coordinate axes can be used as the coordinate system of the projection. Therefore, based on the principle of PCA dimension reduction, the PCA objective function of the following formula (1) is obtained:

[0069]

[0070] Where n is the number of data; X is the data set matrix; x i (i∈1,…n) represents the ith column of X, i.e., the ith data point; P is the projection matrix; tr(B) represents the trace of matrix B; I represents the unit matrix; 1=[1,1,…1] T , represents a vector with all elements being 1.

[0071] Where:

[0072]

[0073] Since PCA inevitably causes information loss during dimension reduction, a redundancy reduction method PCAW is designed to reduce information loss.

[0074] In a feasible implementation, based on the PCA objective function, the following formula (2) is constructed to remove redundancy PCAW algorithm:

[0075]

[0076] wherein, for keeping the neighborhood structure property between data, the neighborhood structure property is the relationship between data point i and its neighbors around; W is the affinity matrix, W ij represents the relationship between data point i and data point j, W can be obtained by LLE (Roweis S T, Saul L K. Nonlinear dimensionality reduction by locally linear embedding[J]. science, 2000, 290 (5500): 2323-2326);

[0077] By processing the data through the PCAW algorithm, the redundant features of the data are reduced.

[0078] The smaller the better, that is, the points x i and x j (W ij is large), P T x i and P T x j should be as close as possible after dimensionality reduction. The smaller the denominator in formula (2) is, the larger the numerator is, so that formula (2) is larger under the condition of satisfying the small denominator and the large numerator at the same time. can be written as:

[0079]

[0080] Here

[0081]

[0082] Therefore, formula (2) can be transformed into:

[0083]

[0084] The Lagrange function of formula (2-4) is:

[0085]

[0086] wherein, λ is a symmetric Lagrange multiplier matrix, and the eigenvalue decomposition of λ is λ=AΛA T , wherein Λ is a diagonal matrix, each element on the diagonal is an eigenvalue of λ, A is a characteristic matrix composed of the eigenvectors corresponding to each eigenvalue of λ, and formula (2-5) is derived with respect to P, and the derived formula is set to 0:

[0087]

[0088] Equation (2-6) can be transformed into:

[0089]

[0090] in Equation (2-7) is clearly a process of orthogonal diagonalizing a symmetric matrix, therefore yes The feature matrix composed of the eigenvalues, For matrix The matrix consisting of the eigenvectors corresponding to the m smallest eigenvalues. Because It contains the variable P, therefore the solution is required. It needs to be iterated until the t-th iteration is obtained. And the result obtained in the (t+1)th iteration The difference between them continues until the convergence condition is met. If P is the optimal solution to equation (2-4), then... (A is any orthogonal matrix) is also the optimal solution of equation (2-4).

[0091] S103. Calculate the density of each data point for the data after removing redundancy;

[0092] In one feasible implementation, Euclidean distance is used to calculate the distance between each point in the dataset when calculating density. However, due to the influence of redundant features, the density calculation is inaccurate. Therefore, PCAW is first used to process the data to reduce the impact of data redundancy features on the density calculation.

[0093] In one feasible implementation, the data after redundancy removal is obtained;

[0094] Different distances d are selected for different datasets in the data after redundancy removal. e , where the selected distance d e The average number of neighbors for each data point should be 1% to 2% of the total number of data points.

[0095] The density of data point i is calculated according to the following formula (3):

[0096]

[0097] Where, p i Ω represents the density of data point i. k d represents the number of neighbors of data point i. ik It is represented as the Euclidean distance between data point i and data point k.

[0098] In one feasible implementation, the neighbors of data point i are those whose distance from data point i is less than d. edata points.

[0099] In an embodiment, the Euclidean distance is affected by redundant features when calculating high-dimensional data, which causes the fuzzy clustering algorithm to degrade in performance, and the redundant features need to be removed before clustering when performing fuzzy clustering on high-dimensional data. The PCAW algorithm combines the advantages of PCA and LLE dimension reduction algorithms, retains the principal components (main information) and neighborhood structure information of the data points, reduces information loss, and improves clustering accuracy.

[0100] In an embodiment, when calculating the density of high-dimensional data, the PCAW algorithm is used to remove the redundant features of the high-dimensional data, and then the density is calculated, which reduces the negative impact of redundant features on the Euclidean distance in the density calculation process, thereby improving the accuracy of density calculation.

[0101] In S104, the sum of the membership degrees of each data point with respect to all clusters is changed from 1 to a density value function of the data point, and the membership degrees are updated.

[0102] In an embodiment, since noise data and outliers are usually scattered in low-density areas, if the sum of the membership degrees of any data point with respect to all clusters is changed from 1 to a function of the respective density value ((the density value of the point - the minimum density value of all points) ÷ (the maximum density value of all points - the minimum density value of all points)), then the noise data points and outliers have smaller membership degrees, and their influence on the cluster centers can be suppressed.

[0103] In an embodiment, the following formula is the objective function of RDFCM:

[0104]

[0105] In an embodiment, the sum of the membership degrees of any data point with respect to all clusters is changed from 1 to a function of the respective density value, wherein the density value function is: density value function = (the density value of the data point - the minimum density value of all data points) ÷ (the maximum density value of all data points - the minimum density value of all data points).

[0106] The membership degrees are updated according to the following membership degree update formula (4):

[0107]

[0108] wherein x j is the jth data point, v i is the ith cluster center, u ij is the membership degree of the jth data point x j belongs to the ith cluster, p j is the density of the jth data point, pmin is the density minimum of all data points, p max is the density maximum of all data points.

[0109] S105, update the cluster center based on the updated membership, judge whether the updated cluster center function meets the convergence condition, if not, update the membership and the cluster center again, if yes, complete the fuzzy mean clustering based on the de-redundancy and density constraint.

[0110] In a feasible implementation, in step S105, the cluster center is updated based on the updated membership, it is judged whether the updated cluster center function meets the convergence condition, if not, the membership and the cluster center are updated again, if yes, the fuzzy mean clustering based on the de-redundancy and density constraint is completed, including:

[0111] The cluster center is updated according to the cluster center updating formula of formula (5) as follows:

[0112]

[0113] It is judged whether the updated cluster center function meets the convergence condition, if not, the membership and the cluster center are updated again, if yes, the fuzzy mean clustering based on the de-redundancy and density constraint is completed.

[0114] In a feasible implementation, the convergence condition includes:

[0115] The l 21 norm of the difference between the t+1th updated cluster center and the tth updated cluster center is less than 1e-6, where V is a k-row d-column matrix, k is the number of clusters, and d is the dimension of data.

[0116] In a feasible implementation, because the noise point is far away from other data points and sparse, the density of the noise point is small, so the sum of the membership of each cluster of the noise point is small, and therefore the role of the noise point in updating the cluster center is small. The degree of the cluster center offset to the noise point is small or even not offset. As shown in formula (4), u ij is the membership of the jth point belonging to the ith cluster, and the membership of the noise point is small, so the role of the noise point in updating the cluster center of the ith cluster is small.

[0117] In the embodiment of the application, the PCAW de-redundancy method is proposed to solve the problem of performance degradation of the fuzzy clustering algorithm caused by redundant features, which can effectively reduce the information loss while reducing the dimension of high-dimensional data, thereby improving the clustering accuracy. The constraint condition that the sum of the membership of each cluster of the data point is 1 is replaced by the sum of the membership being the density normalized value of the data point, and the influence of the noise point and the abnormal value on the updating of the cluster center is suppressed.

[0118] Figure 2 is a schematic diagram of a fuzzy mean clustering system based on de-redundancy and density constraint, the system 200 is used for the fuzzy mean clustering based on de-redundancy and density constraint described above, and the system 200 comprises:

[0119] an information acquisition module 210, configured to acquire system data; the system data comprises: a dimension reduction dimension m, a cluster number c, an initial membership matrix U, an initial clustering center matrix V, and an initial projection matrix P;

[0120] a redundancy removal module 220, configured to construct a de-redundancy algorithm PCAW algorithm based on a traditional PCA dimension reduction principle; remove redundancy through the PCAW algorithm; and calculate the density of each data point based on the data after removing the redundancy;

[0121] a membership update module 240, configured to change the sum of the membership of all clusters in the each data point from 1 to a density value function of the data point, and update the membership;

[0122] a clustering center update module 250, configured to update the clustering center based on the updated membership, judge whether the updated clustering center function satisfies a convergence condition, if not, re-update the clustering center; and if yes, complete the fuzzy mean clustering based on de-redundancy and density constraint.

[0123] Preferably, the redundancy removal module 220 is configured to obtain a PCA objective function as shown in the following formula (1) based on the PCA dimension reduction principle:

[0124]

[0125] wherein n is the number of data; X is a data set matrix; x i (i∈1,…n) represents the ith column of X, that is, the ith data point; P is a projection matrix; tr(B) represents the trace of the matrix B; I represents a unit matrix; 1=[1,1,…1] T , represents a vector with all elements being 1;

[0126] based on the PCA objective function, a de-redundancy algorithm PCAW algorithm as shown in the following formula (2) is constructed:

[0127]

[0128] wherein, is used to maintain the neighborhood structure property between data; W is an affinity matrix, W ij represents the relationship between the data point i and the data point j;

[0129] The PCAW algorithm is used to process the data, and reduce the data redundancy.

[0130] Preferably, the data dimension reduction module 230 is configured to obtain the data after removing the redundancy.

[0131] Different distances d are selected for different data sets in the data after removing the redundancy. e The selected distance d is e The average number of neighbors of each data point is required to be 1% to 2% of the total number of data points.

[0132] The density of the data point i is calculated according to the following formula (3):

[0133]

[0134] Where p is i The density of the data point i, Ω is k The number of neighbors of the data point i, d is ik The Euclidean distance between the data point i and the data point k.

[0135] Preferably, the neighbors of the data point i are the data points with a distance less than d e from the data point i.

[0136] Preferably, the membership degree updating module 240 is configured to change the sum of the membership degrees of any data point with respect to all clusters from 1 to a function of the respective density values, wherein the function of the density values is: density value function = (density value of the data point - minimum density value of all data points) ÷ (maximum density value of all data points - minimum density value of all data points).

[0137] The membership degree is updated according to the following membership degree updating formula (4):

[0138]

[0139] Where x is the jth data point, v is the ith cluster center, u is the jth data point x belongs to the ith cluster, p is the density of the jth data point, p is the minimum density value of all data points, and p is the maximum density value of all data points. j i ij j j min max

[0140] Preferably, the cluster center updating module 250 is configured to update the cluster center according to the following cluster center updating formula (5):

[0141] ​​​​​​​ determine whether the updated cluster center function satisfies a convergence condition, if not, update the membership and the cluster center again, if yes, complete the fuzzy mean clustering based on the redundancy elimination and the density constraint.

[0142] Preferably, the convergence condition comprises:

[0143] the l 21 norm of the difference between the t+1th updated cluster center and the tth updated cluster center is less than 1e-6, where V is a k-row d-column matrix, k is the number of clusters, and d is the dimension of data.

[0144] In the embodiment of the present application, a fuzzy mean clustering system based on redundancy elimination and density constraint is provided, aiming at the problem that redundant features cause the performance of fuzzy clustering algorithm to decline, a PCAW redundancy elimination method is provided, which can effectively reduce information loss while reducing the dimension of high-dimensional data, thereby improving clustering accuracy. The constraint condition that the sum of the membership of data points about each cluster is 1 is replaced by the constraint condition that the sum of the membership is the density normalized value of the data points, thereby suppressing the influence of noise points and outliers on the update of the cluster center.

[0145] Figure 3 is a structural schematic diagram of an electronic device 300 provided by the embodiment of the present application, the electronic device 300 can have relatively large differences due to different configurations or performances, and can include one or more processors (central processing units, CPUs) 301 and one or more memories 302, wherein the memory 302 stores at least one instruction, the at least one instruction is loaded and executed by the processor 301 to realize the steps of the following fuzzy mean clustering method based on redundancy elimination and density constraint:

[0146] S1, input a preset data set X; obtain system data; the system data includes: a dimension reduction dimension m, a cluster number c, an initial membership matrix U, an initial cluster center matrix V, and an initial projection matrix P;

[0147] S2, based on the traditional PCA dimension reduction principle, construct a redundancy elimination algorithm PCAW algorithm; remove redundancy through the PCAW algorithm;

[0148] S3, calculate the density of each data point after removing the redundancy;

[0149] S4, change the sum of the membership of each data point about all clusters from 1 to the density value function of the data point, and update the membership;

[0150] S5, updating the clustering center based on the updated membership, judging whether the updated clustering center function meets the convergence condition, if not, updating the membership and the clustering center again; if yes, completing the fuzzy mean clustering based on the de-redundancy and density constraint.

[0151] In the exemplary embodiments, a computer readable storage medium, such as a memory including instructions executable by a processor in a terminal to perform the above fuzzy mean clustering based on the de-redundancy and density constraint is also provided. For example, the computer readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0152] Those skilled in the art can understand that all or part of the steps of the above-mentioned embodiments can be completed by hardware, or by a program instructing related hardware to complete, and the program can be stored in a computer readable storage medium, such as a read-only memory, a magnetic disk or an optical disk.

Claims

1. A fuzzy means clustering method based on de-redundancy and density constraints, applied to image classification, characterized in that, The method steps comprise: S1, inputting a preset image data set X; acquiring system data; the system data comprises: a dimension reduction dimension m, a cluster number c, an initial membership matrix U, an initial clustering center matrix V, and an initial projection matrix P; S2, constructing a de-redundancy algorithm PCAW algorithm based on a traditional PCA dimension reduction principle; and removing redundancy through the PCAW algorithm; S3, calculating the density of each data point after removing the redundancy; S4, changing the sum of the membership degrees of all clusters in each data point from 1 to a density value function of the data point, and updating the membership degrees; S5, updating the clustering center based on the updated membership degrees, judging whether the updated clustering center function satisfies a convergence condition, if not, re-updating the membership degrees and the clustering center; and if yes, completing the fuzzy mean clustering based on de-redundancy and density constraint. In the step S2, the de-redundancy algorithm PCAW algorithm is constructed based on the traditional PCA dimension reduction principle; and the redundancy is removed through the PCAW algorithm, which comprises: Based on the PCA dimension reduction principle, the PCA target function shown in the following formula (1) is obtained: where n is the number of data; X is the dataset matrix; x i (i∈1,…n) represents the i-th column of X, i.e., the i-th data point; P is the projection matrix; tr(B) denotes the trace of matrix B; I represents the identity matrix; 1 = [1, 1, …1] T , represents a vector with all elements being 1; Based on the PCA target function, the de-redundancy algorithm PCAW algorithm shown in the following formula (2) is constructed: wherein, for preserving the neighborhood structure property among data; W is an affinity matrix, W ij represents the relationship between data point i and data point j, and W can be obtained by LLE. The data is processed through the PCAW algorithm to reduce the data redundancy features; In the step S3, the density of each data point is calculated through dimension reduction calculation on the data after removing the redundancy, which comprises: The data after removing the redundancy is acquired; selecting a different distance d for different data sets in the de-redundant data e wherein the selected distance d e The average number of neighbors for each data point needs to be 1% to 2% of the total number of data points. The density of the data point i is calculated according to the following formula (3): where p i denotes the density of data point i, Ω k denotes the number of neighbors of data point i, d ik denotes the Euclidean distance between data point i and data point k.

2. The method of claim 1, wherein, The neighbors of the data point i are the data points with a distance to data point i less than d e .

3. The method of claim 2, wherein, In the step S4, the sum of the membership degrees of all clusters in each data point is changed from 1 to a density value function of the data point, and the membership degrees are updated, which comprises: The sum of the membership degrees of all clusters of any data point is changed from 1 to a function of the respective density value, wherein the function of the density value is: density value function=(density value of the data point-minimum density value of all data points)÷(maximum density value of all data points-minimum density value of all data points); The membership degrees are updated according to the following formula (4) membership degree update formula: where x j is the jth data point, v i is the ith cluster center, u ij is the jth data point x j is the membership of the jth data point to the ith cluster, p j is the density of the jth data point, p min is the minimum density of all data points, and p max is the maximum density of all data points.

4. The method of claim 3, wherein, In the step S5, the clustering center is updated based on the updated membership degrees, and it is judged whether the updated clustering center function satisfies a convergence condition, if not, the clustering center is re-updated; If yes, the fuzzy mean clustering based on de-redundancy and density constraint is completed, which comprises: The clustering center is updated according to the following formula (5) clustering center update formula: It is judged whether the updated clustering center function satisfies a convergence condition, if not, the membership degrees and the clustering center are re-updated; and if yes, the fuzzy mean clustering based on de-redundancy and density constraint is completed.

5. The method of claim 4, wherein, The convergence condition comprises: l 21 norm of the difference between the (t+1)th updated cluster centers and the tth updated cluster centers is less than 1e-6, where V is k by d, k is the number of clusters, and d is the dimension of the data.

6. A fuzzy means clustering system based on de-redundancy and density constraints, applied to image classification, characterized in that, The system is used for the fuzzy mean clustering based on de-redundancy and density constraint as claimed in any one of claims 1 to 5, and the system comprises: An information acquisition module is configured to input a preset image data set X; acquire system data; and the system data comprises: a dimension reduction dimension m, a cluster number c, an initial membership matrix U, an initial clustering center matrix V, and an initial projection matrix P; The redundancy removing module is configured to construct a redundancy removing algorithm PCAW algorithm based on a traditional PCA dimension reduction principle, remove redundancy through the PCAW algorithm, and calculate the density of each data point after removing the redundancy. The membership updating module is configured to update the membership by changing the sum of the membership of all clusters in each data point from 1 to a density value function of the data point. The cluster center updating module is configured to update the cluster center based on the updated membership, determine whether the updated cluster center function satisfies a convergence condition, and if not, update the membership and the cluster center again, and if yes, complete the fuzzy mean clustering based on the redundancy removing and the density constraint.

7. The system of claim 6, wherein, The redundancy removing module is configured to obtain a PCA target function as shown in the following formula (1) based on the PCA dimension reduction principle. where n is the number of data; X is the dataset matrix; x i (i∈1,…n) represents the i-th column of X, i.e., the i-th data point; P is the projection matrix; tr(B) denotes the trace of matrix B; I represents the identity matrix; 1 = [1, 1, …1] T , represents a vector with all elements being 1; Based on the PCA target function, a redundancy removing algorithm PCAW algorithm as shown in the following formula (2) is constructed. wherein, for preserving the neighborhood structure property among data; W is an affinity matrix, W ij denotes the relationship between data point i and data point j; The data is processed through the PCAW algorithm to reduce the redundant features of the data.

8. The system of claim 7, wherein, The redundancy removing module is configured to acquire the data after removing the redundancy, and select different distances d for different data sets in the data after removing the redundancy e wherein the selected distance d e The number of neighbors of each data point needs to be 1% to 2% of the total number of data points. The density of the data point i is calculated according to the following formula (3). where p i denotes the density of data point i, Ω k denotes the number of neighbors of data point i, d ik denotes the Euclidean distance between data point i and data point k.

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