A clustering method based on self-weighted multi-view k-means

Abstract

The application discloses a clustering method based on self-weighted multi-view k-means, and relates to the technical field of data processing, and comprises the following steps: acquiring multi-view data and constructing an original data matrix; constructing a clustering model based on the original data matrix; adding a projection matrix to the clustering model for low-dimensional subspace learning, and using a norm penalty term of the projection matrix for constraint; the clustering model uses a minimum absolute criterion to induce and self-weight constraint, iteratively self-weights the clustering model, and outputs an optimal clustering model; and clustering the multi-view data through the optimal clustering model. The application uses the minimum absolute criterion to induce robustness, effectively reduces the influence of abnormal values, applies the self-weighting technology to the multi-view k-means, realizes dimension reduction and noise suppression, and has excellent clustering effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing, and more particularly to a clustering method based on self-weighted multi-view k-means. BACKGROUND

[0002] The speed and scale of information dissemination and collection have reached an unprecedented level, and various data have begun to proliferate. These data are often described in different ways or perspectives, such as representing the features of each class as a view. Data information described by multiple views is richer, and much of the information can help build reliable and robust clustering models. However, the more information, the higher the probability of involving noise and redundancy. This curse of dimensionality and the ineffective features and noise of multi-view pose great challenges to large-scale, noisy multi-view data clustering.

[0003] To address this challenge, many multi-view clustering (MVC) methods have played a key role in real-world applications by fusing complementary information from multiple views to cluster data points into different clusters. Since they have different similarity structures, MVC methods based on discriminative methods are applied to common feature vector matrices, common coefficient matrices, and common indicator matrices. The first two methods are view-based clustering methods, so the construction of views is a key problem. Using different kernels to construct views greatly affects the final clustering performance. In addition, for certain specific kernels, the influence of parameter selection must be considered, making the clustering results sensitive to parameter tuning. More importantly, these view-based methods cannot be used to solve large-scale data clustering problems because they cannot solve large-scale data clustering problems. The most representative third method is multi-view K-means clustering, which is more suitable for processing large data sets due to its high efficiency and simplicity.

[0004] Therefore, how to propose a clustering method based on self-weighted multi-view k-means, with optimization and convergence, effectively solving the objective function through unsupervised learning, realizing the robustness and efficient outlier suppression in the multi-view clustering process, is a problem that the person skilled in the art needs to solve. SUMMARY

[0005] Therefore, the present application provides a clustering method based on self-weighted multi-view k-means, which realizes subspace learning by adding a projection matrix. At the same time, by introducing the l 2,1 norm penalty term, feature selection and noise suppression are realized, the clustering center matrix is represented as a convex combination of the data matrix, and a good clustering result can be quickly obtained in the weighted feature subspace. In order to achieve the above purpose, the present application adopts the following technical solutions:

[0006] A clustering method based on self-weighted multi-view k-means, comprising:

[0007] obtaining multi-view data and constructing an original data matrix;

[0008] constructing a clustering model based on the original data matrix;

[0009] adding a projection matrix to the clustering model for low-dimensional subspace learning and using a norm penalty term of the projection matrix for constraint;

[0010] performing minimum absolute criterion induction and self-weighting constraint on the clustering model and outputting an optimal clustering model through iteration and self-weighting;

[0011] performing clustering on the multi-view data through the optimal clustering model.

[0012] Optionally, the multi-view data comprises multi-view and high-dimensional data.

[0013] Optionally, the constructing a clustering model based on the original data matrix comprises:

[0014] constructing a multi-view K-means clustering model based on the original data matrix X;

[0015] inducing robustness of the multi-view K-means clustering model through minimum absolute criterion and obtaining a robust K-means clustering model;

[0016] performing non-negative matrix factorization on the robust K-means clustering model, defining a basis vector F in a convex combination of a column space of the original data matrix X in the non-negative matrix factorization, and obtaining a clustering model in the form of NMF.

[0017] Optionally, the clustering model in the form of NMF is:

[0018]

[0019]

[0020] wherein, D∈R n×k is a clustering centroid capture matrix, XD∈R m×k is a clustering centroid matrix, S∈R k×n is a clustering assignment matrix.

[0021] Optionally, the adding a projection matrix to the clustering model for low-dimensional subspace learning and using a norm penalty term of the projection matrix for constraint comprises:

[0022] projecting a vth view of the original data matrix X to a low-dimensional subspace, introducing a new projection matrix W into the clustering model, and defining the projection matrix d (v)' ≤d (v) ; wherein, d(v)' is the feature dimension of the low-dimensional subspace, and the low-dimensional subspace is denoted as W (v)T X (v) .

[0023] Optionally, the optimization objective of the low-dimensional subspace is:

[0024]

[0025]

[0026] where β is a tuning parameter, and ||W (v) || 2,1 is the l 2,1 norm of the projection matrix W, D ∈ R n×k is a clustering centroid capturing matrix, and S ∈ R k×n is a clustering assignment matrix.

[0027] Optionally, the clustering model is subjected to a least absolute criterion induction and a self-weighting constraint, and an optimal clustering model is outputted through iterative self-weighting, including:

[0028] The optimization objective of the low-dimensional subspace is changed to:

[0029]

[0030]

[0031] Definition The clustering indicator matrix is calculated through an l 2,1 norm, where α (v) is a view weight coefficient, S is a matrix, D is an affinity matrix, and W is a projection matrix.

[0032] Optionally, the calculation of the clustering indicator matrix includes:

[0033] Step one: calculating α (v) , updating the weight α k of each view, assigning a higher weight to a more discriminative image feature, and obtaining a closed-form solution of α (v) ;

[0034] Step two: calculating W (v) , fixing other variables, and calculating W through the formula (v) ;

[0035] Step three: calculating D, fixing other variables, and calculating D through the formula ;

[0036] Step four: calculating S, fixing other variables, and calculating S through the formula The solution for S is obtained;

[0037] Step 5: Iterate through steps 1 to 4 until the objective function value converges.

[0038] Optionally, it also includes initialization, which involves initializing the clustering indicator matrix:

[0039]

[0040] Among them, I C ∈Re C×C Z is the identity matrix. C ∈Re C×C Random sorting of binary matrices I C rows, 1∈Re [N ÷C]×1 Given a column vector containing all elements, use vector 1 and matrix Z. C Initialize G using the direct product of N and C. If N is not divisible by C, then start from Z. C Additional options Line, randomly fill in the indivisible parts.

[0041] Optionally, the multi-view data is subjected to dimensionality reduction settings, wherein the dimensionality reduction is set to reduce the dimension d of the multi-view data, and β is an optimization parameter, wherein the parameter β is within 10. -6 Up to 10 6 The search is performed between dimensions with a step size of 0.5, searching for the dimension d corresponding to the best clustering result by searching all dimensions of each view in the original data matrix.

[0042] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a clustering method based on self-weighted multi-view k-means, which has the following beneficial effects:

[0043] This invention achieves subspace learning by adding a projection matrix, and simultaneously introduces the l of the projection matrix. 2,1 A norm penalty term is used to achieve feature selection and noise suppression. The cluster center matrix is ​​represented as a convex combination of data matrices, and synchronous clustering in the weighted feature subspace can quickly yield good clustering results. This invention proposes a novel unsupervised clustering framework that achieves robustness and efficient outlier suppression in multi-view clustering, while also achieving dimensionality reduction. An iterative self-weighting method is employed, using a 2,1-norm penalty term of the projection matrix to suppress noise, and adaptively controlling the coordination between multiple views through iterative reweighting. Extensive experimental results on various synthetic and real-world datasets demonstrate that this algorithm outperforms other methods in terms of clustering performance and robustness. Attached Figure Description

[0044] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only aim at the embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of the provided drawings.

[0045] Figure 1 A flowchart of a clustering method based on self-weighted multi-view k-means is provided.

[0046] Figure 2 The change value of the objective function in each data set with the number of iterations is provided.

[0047] Figure 3 The weight of each view in each data set is provided.

[0048] Figure 4 The corresponding dimension reduction number of each view in each data set is provided.

[0049] Figure 5 The values of ACC, NMI and Purity in each data set under different β are provided. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present application.

[0051] The embodiments of the present application disclose a clustering method based on self-weighted multi-view k-means, as shown in the formula (1), comprising: Figure 1

[0052] Obtaining multi-view data and constructing an original data matrix;

[0053] Constructing a clustering model based on the original data matrix;

[0054] Adding a projection matrix to the clustering model for low-dimensional subspace learning, and using a norm penalty term of the projection matrix for constraint;

[0055] Performing minimum absolute criterion induction and self-weighting constraint on the clustering model, and outputting an optimal clustering model through iteration and self-weighting;

[0056] Clustering the multi-view data through the optimal clustering model. ​

[0057] Further, the multi-view k-means includes:

[0058] In order to cluster the data described by multi-view, it is inclined to integrate the advantages of various heterogeneous features by exploring the rich information between them. Therefore, the relaxed K-Means clustering can be extended to the multi-view setting, denoted as multi-view K-means clustering:

[0059]

[0060] Where X (v) ∈R m×n is the data matrix of n samples and m-dimensional features in the vth view, F (v) ∈R m×k is the clustering center matrix, S∈R k×n is the cluster assignment matrix, each column satisfies 1 encoding scheme, if the data point is assigned to the first cluster, S ki =1, otherwise 0, F (v) is the clustering center matrix of the vth view,

[0061] Further, in order to have more stable clustering performance for fixed initialization, it is necessary to explore the complementary aspects of information shared by different views, and to use a robust K-means clustering method (RMVKM):

[0062]

[0063]

[0064] Where, α (v) is the weight factor of the vth view, and γ is a parameter that controls the weight distribution, so that important views can obtain greater weight in the multi-view clustering process.

[0065] Further, the robust K-means clustering method RMVKM does not have any dimension reduction mechanism, and if high-dimensional multi-dimensional data is processed, the curse of dimensionality problem may occur. At the same time, considering that the least absolute criterion is usually used to induce robustness and has excellent effect, the following model is proposed for RMVKM:

[0066]

[0067]

[0068] Where W (v) ∈R dv ' ×dv represents the projection matrix of the vth view, which reduces the dimension of each view to dv' dimension, s.t.S ki is the relationship between the i th data and the k th class, A constraint is that one data belongs to a class under {0, 1}.

[0069] Further, Convex-NMF as a popular clustering method, k-means clustering is equivalent to non-negative matrix factorization (NMF). In NMF, there is no constraint on the basis vector F = (f1,..., f k ), but for the reason of interpretability, a constraint is imposed that the vectors defining F lie within the column space of X:

[0070] f i = d 1i x1+... + d ni x n = XD i , or F = XD (4);

[0071] where d ni is the relationship between the center matrix and the corresponding data point.

[0072] In addition, also for the reason of interpretability, restrict oneself to convex combinations of columns of X. The advantage of this constraint is that the columns can be interpreted as weighted sums of certain data points; in particular, these columns will capture the notion of centroids. Call this restricted form of the factor F Convex-NMF. Convex-NMF applies to non-negative matrix and mixed-sign data matrices. Thus, rewriting K-means in the form of signed NMF is as follows:

[0073]

[0074]

[0075] where D ∈ R n×k is the clustering centroid capturing matrix, XD ∈ R m×k is the clustering centroid matrix, S ∈ R k×n is the clustering assignment matrix.

[0076] In the detailed description, a robust self-weighted multi-view projection clustering (SwMKM) method includes:

[0077] Based on the superiority of subspace learning in high-dimensional data processing, a new projection matrix W is introduced in multi-view k-means clustering. The projection transformation matrix of the vth view is defined as d (v)' ≤ d (v) . The vth view of the original data matrix X is projected into a low-dimensional subspace, and the projection transformation matrix is defined, where d (v)' is the feature dimension of the low-dimensional subspace. This low-dimensional subspace is represented as W (v)TX (v) This approach preserves the valuable information in the data while mitigating the curse of dimensionality. Below, we present the optimization objective based on subspace learning:

[0078]

[0079]

[0080] Where β is the tuning parameter, ||W (v) || 2,1 It is the l of the projection matrix W 2,1 The norm is used in this algorithm to suppress noise and remove redundant features. Orthogonal constraints are applied to the scattering matrix W. (v)T X (v) X (v)T W (v) The application in this is actually for learning intrinsic subspaces, and the original dataset X (v) On the d (v) Transforming the d-dimensional feature space into statistically uncorrelated d (v)' The inherent subspace of the dimension. Simultaneously updating the cluster centers and subspace of the data accelerates the convergence speed.

[0081] In a specific implementation, a robust self-weighted multi-view projection clustering method is described, and the implementation process includes: the difficulty in achieving the proposed objective stems from the following two aspects. 2,1 The norm is a non-smooth clustering index matrix for each term.

[0082]

[0083]

[0084] when

[0085] Where I is a dimension of d (v)' The identity matrix.

[0086] Step 1: Calculate α (v) Update the weight α of each view. k By assigning more discriminative image features to higher weights, α is derived. (v) Closed form solution:

[0087]

[0088] W (v) Both S and α are independent of α (v) It can be regarded as a constant, using α (v) Iterative update W (v) And S and based on the currently updated W (v) Calculate α with S(v) .

[0089] Step two: Compute W (v) , fixing all other variables, by minimizing the following function in the subproblem (v) :

[0090]

[0091] It is difficult to solve W 2,1 directly due to the l (v) norm. The Lagrange multiplier method is used to solve the above problem. The Lagrangian function of L v is:

[0092]

[0093] where Λ is a diagonal matrix that imposes the constraint on L(W (v) ). Take the derivative of L(W) and set it equal to 0:

[0094]

[0095] where denotes the current solution, and is rearranged to:

[0096]

[0097] X is a matrix, x i is the i-th row of the matrix, x ij is the i-th row and j-th column element of the matrix, X T is the transpose of the matrix X, X -1 is the inverse of the matrix X, Tr() is the sum of the diagonal elements of the matrix, X (v) is the matrix or vector of the v-th view. Let Therefore, PW = WΛ, Λ is a diagonal matrix, and the eigen equation is Pω i = λ i ω i i = 1, 2, …, d', then W is composed of the eigenvectors corresponding to the c smallest eigenvalues other than 0. Here λ i is the i-th smallest eigenvalue in the eigen equation other than zero. ω i is the i-th smallest eigenvector in the eigen equation other than zero. The time complexity here is Od 2 .

[0098] Step three: Compute D, fixing all other variables, by minimizing the following function in the subproblem:

[0099]

[0100] where D (v) is calculated as

[0101] D = S T SS T-1 (15) ;

[0102] Step 4: Compute indicator matrix S, fix all other variables, compute the i-th column of S denoted as s i by minimizing the following function

[0103]

[0104]

[0105] Solving the above equation (16) and equation (7) gives s i , since the number of iterations of s i is the predefined number of clusters k, it is solved by finding the nearest center.

[0106] In summary, in a robust self-weighted multi-view projection clustering method, W (v) is obtained by step 2, i.e. by solving the trajectory optimization to reduce the dimension of each view. S is updated by step 4, which is equivalent to K-means clustering considering the relationship between multi-view features. The multiple weight learning is completed in a re-weighted way by step 1. W v is calculated by solving the Lagrangian function of LW (v) , and then this process is iterated repeatedly until the value of the objective function converges.

[0107] Further, a specific algorithm of a robust self-weighted multi-view projection clustering method is as follows:

[0108] Input: V views of cluster number k. Dimension reduction d (v) ' of each view, parameter β, output: projection matrix common clustering indicator matrix S, where the value of α (v) is 1 / V.

[0109] Initialize W (v) by solving the following:

[0110]

[0111]

[0112] Loop (until convergence):

[0113] (1) Update a by equation (8) (v) ;

[0114] (2) Update W by equation (13) (v) ;

[0115] (3) Update D by equation (15)

[0116] (4) Update S by equation (16)

[0117] Return W (v) , S and a (v) .

[0118] Time complexity analysis: In each iteration, the time complexity of updating the view weight coefficient a (v) , the matrix S, the affinity matrix D, and the projection matrix W are O(d'dn), O(d 2 ), O(k 2 n), O(kd'n), respectively. Usually, k << n, d' << d, and d = ck. Therefore, the time complexity of the algorithm is O(d'dn + kd'n + d 2 + k 2 n) ≈ O(n), which is a linear problem with respect to n and can solve large-scale clustering problems and even handle high-dimensional data.

[0119] In specific embodiments, the parameter setting includes:

[0120] Step one. Cluster initialization

[0121] Initialization: Use a stable method to initialize G, which greatly reduces the dependence of the clustering result on initialization. Initialize G as follows:

[0122]

[0123] where I C ∈ Re C×C is a unit matrix, Z C ∈ Re C×C is a binary matrix randomly sorted from the rows of I C , and 1 ∈ Re [N÷C]×1 is a column vector containing all elements. Use the direct product of the vector 1 and the matrix Z C to initialize G. If N cannot be divided by C, additional rows need to be selected from Z C and randomly filled in the unpartitionable part.

[0124] In specific embodiments, the dimension reduction setting includes:

[0125] Dimension of the view: In this invention, for the proposed algorithm, the parameter γ is in the range of 10. -6 Up to 10 6 The search is performed between these dimensions with a step size of 0.5. Furthermore, the dimension d corresponding to the best clustering result is searched by searching all dimensions of each view in the original dataset; for simplicity, the step size of parameter d is set to 3.

[0126] In a specific implementation, convergence analysis includes:

[0127] Lemma 1, for any nonzero vector u t+1 ,u t ∈R d The following inequalities hold:

[0128]

[0129] Theorem 1 states that in a robust self-weighted multi-view projection clustering method, the objective of formula (9) will be monotonically reduced in each iteration until the algorithm converges.

[0130] Proof: Suppose that after the t-th iteration, we obtain... and S t Due to the updated and S t+1 yes According to the formula Solve the following:

[0131]

[0132] Summarizing equations (18) and (19), we have:

[0133]

[0134] In a specific implementation, verification is carried out through experiments, including:

[0135] Experimental setup: CPU i5-11400k, GPU GeForce RTX 3070, operating system Windows 11, project environment MATLAB R2020b to implement the model. The performance of SwMKM on toy experiments and four real-world datasets was evaluated using three standard clustering evaluation metrics: accuracy (ACC), normalized mutual information (NMI), and purity.

[0136] (1) Toy Experiments: Toy experiments were used to verify the superiority of SwMKM. For simplicity, a toy dataset was used. The results corresponding to "Initialization", "Iteration = 2", "Iteration = 4", "Iteration = 6", and "Iteration = 8" are shown in Table 1.

[0137] Table 1

[0138]

[0139]

[0140] It can be seen that the optimal solution is obtained at iteration = 8, with ACC, NMI, and Purity reaching 0.9910, 0.9880, and 0.9910, respectively. In Table 2, SwMKM can achieve better and stable accuracy compared to other baseline methods.

[0141] Table 2

[0142]

[0143] (2) Real data sets

[0144] (2.1) Handwritten numerals (HW)

[0145] The data set is selected from the UCI machine learning repository, which contains 2000 samples divided into ten categories corresponding to numbers (0-9). Each instance has six views of features: 64 K-L coefficients, 76 Fourier coefficients of shape features, 240 pixel averages of 2x3 windows, and 47 Zernike moments, 216 contour-related 6 morphological features.

[0146] (2.2) Handwritten digit 2 sourced data set

[0147] This handwritten digit (0-9) data set comes from two sources, namely MNIST handwritten digits and 10 digits of US postal handwritten digits. The data set consists of 10000 samples.

[0148] (2.3) MSRC-vl

[0149] The data set is a scene recognition data set from Microsoft Research Cambridge. According to [Multi-view clustering with self-weighting graphs], 7 classes are selected, namely trees, buildings, airplanes, cows, faces, cars and bicycles, and 5 visualization feature extraction methods are used to generate each data view.

[0150] (2.4) Outdoor Scene

[0151] The data set contains 8 categories: coast, mountain, forest, street, city, open countryside, highway and high-rise building, a total of 2688 pictures. Independent and shared subspace discovery is used for multi-view feature learning.

[0152] (3) Comparison method

[0153] SwMKM is compared with various existing methods to evaluate its performance and advantages in the field of multi-view data clustering. First, SwK (SwMKM for each individual view) is compared with KM for each view to demonstrate the role of self-weighting in single-view. Then, SwMKM is compared with SwK. This analysis aims to demonstrate the efficacy of SwMKM as a multi-view method, taking full advantage of the inherent advantages of multiple views over single-view methods. Subsequently, SwMKM is compared with several baseline methods, including NMVKM (Naive Multi-View K-Means Clustering), SMVKM (NMVKM with 2,1-norm), and RMVKM. Through this comparison, the significant advantages brought by the low-dimensional subspace learning and iterative self-weighting mechanism adopted by SwMKM are highlighted. In addition, comparison with RDEKM is made to highlight the ability of SwMKM to effectively perform feature selection and noise suppression by utilizing the 2,1-norm penalty term of statistically uncorrelated intrinsic subspace and projection matrix.

[0154] (4) Experimental results comparison

[0155] A simplified version of SwMKM, labeled sSwMKM, is examined by ignoring the weights assigned to each view. To emphasize the importance of mutual coordination between multiple views, the results of SwMKM are compared with aSwMKM, which directly connects all views and performs self-weighted multi-view K-means. This process aims to verify the superiority of the iterative reweighting method adopted by SwMKM. The experimental results obtained by different clustering methods on four benchmark datasets are shown in Table 3, Table 4, and Table 5, which are algorithm accuracy comparison, algorithm normalized mutual information value comparison, and algorithm purity comparison, respectively, reported in ACC, NMI, and Purity indices.

[0156] Table 3

[0157]

[0158] Table 4

[0159]

[0160]

[0161] Table 5

[0162]

[0163]

[0164] From these three tables, it can be seen that the proposed method achieves the best clustering results on all test datasets. In particular, on the Outdoorscene and MSRCv1 datasets, the proposed method is significantly better than other methods. For single view, SwK performs better than k-means on each dataset. This demonstrates the effect of the iterative self-weighting mechanism. However, SwMKM performs better in multi-view, which directly proves the superiority of multi-view. Since the aSwMKM, sSwMKM and SwMKM methods adopt the method with embedded subspace learning, they are better than the NMVKM, SMVKM and RMVKM methods. However, it is worth noting that the performance of aSwMKM is lower than that of sSwMKM and SwMKM. This difference is attributed to the fact that directly connecting heterogeneous features of different views is not a reasonable method. In addition, since SwMKM can learn multiple weights, its performance is better than sdEKM. Compared with RDEKM, the proposed SwMKM method shows significant improvement on four datasets.

[0165] Specifically, on the two handwritten datasets (Handwritten and Hdghti), the average improvement of the SwMKM method is 0.74%, 1.77% and 2.72%, respectively. These improvements are based on three clustering evaluation indicators: accuracy (ACC), normalized mutual information (NMI) and purity (PUR). The advantage of the SwMKM method lies in its statistically independent intrinsic subspace learning mechanism and the 2,1-norm penalty term of the projection matrix. This robustness distinguishes it from the low-dimensional subspace learning mechanism of the RDEKM method, making SwMKM more efficient in dealing with challenging datasets. For example, in the more challenging MSRCv1 and Outdoorscene, the average improvement of the SwMKM method is 6.957%, 3.024% and 5.290%, respectively. This shows that SwMKM can introduce robustness and effectively reduce the impact of outliers. In addition, the convergence speed of SwMKM is tested on all datasets, Figures 2-5 The performance of the SwMKM algorithm described in the present application in actual tests is as follows: Figure 2 The change in the value of the objective function in each dataset provided by the present application with the number of iterations, Figure 3 The weight of each view in each dataset provided by the present application, Figure 4 The corresponding dimension reduction number of each view in each dataset provided by the present application, Figure 5 The values of ACC, NMI and Purity under different β in each dataset provided by the present application. It is observed that the SwMKM algorithm can quickly converge with only a few iteration steps.

[0166] The present application proposes a novel unsupervised clustering framework, which adopts a multi-view least absolute residual model to achieve robustness and efficient outlier suppression in the multi-view clustering process, and to achieve dimension reduction. An iterative self-weighting method is adopted, a 2,1-norm penalty term of the projection matrix is used to suppress noise, and the coordination between multiple perspectives is adaptively controlled in an iterative re-weighting manner. In addition, an unsupervised optimization scheme with optimization and convergence is proposed to effectively solve the objective function. Extensive evaluation on widely used benchmark datasets shows that SwMKM is effective in clustering high-dimensional multi-view data. The proposed clustering method will be applied to practical computer vision applications such as bioinformatics, image segmentation and natural language processing, and extended to incomplete multi-view clustering.

[0167] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts between various embodiments can be referred to each other. For the device disclosed by the embodiments, since it corresponds to the method disclosed by the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0168] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A clustering method based on self-weighted multi-view k-means, characterized in that, include: Acquire multi-view data, which comes from an image dataset, and construct an original data matrix; A clustering model is constructed based on the original data matrix; In the clustering model, a projection matrix is ​​added for low-dimensional subspace learning, and the norm penalty term of the projection matrix is ​​used for constraint. The clustering model is induced by the minimum absolute criterion and subjected to self-weighting constraints. The optimal clustering model is output through iterative self-weighting. The clustering model is induced by the minimum absolute criterion and subjected to self-weighting constraints. The optimal clustering model is output through iterative self-weighting, including: By changing the optimization objective of the low-dimensional subspace, we obtain: ； ； definition ,pass Norm calculation of clustering index matrix, where, For view weight coefficients, For a matrix, For the affinity matrix, ; The calculation of the clustering index matrix includes: Step 1: Calculation Update the weight of each view. By assigning more discriminative image features to higher weights, we obtain... The closed-form solution; Step 2: Calculation Fix other variables, and use formulas calculate ; Step 3: Calculate D, keeping other variables fixed, using the formula Calculate D; Step 4: Calculate S, fixing other variables, and then... The solution for S is obtained; Step 5: Iterate through steps 1 to 4 until the objective function value converges; Clustering of multi-view data using the optimal clustering model.

2. The clustering method based on self-weighted multi-view k-means according to claim 1, characterized in that, The multi-view data includes multiple views and high-dimensional data.

3. The clustering method based on self-weighted multi-view k-means according to claim 1, characterized in that, The clustering model constructed based on the original data matrix includes: Construct a multi-view K-means clustering model based on the original data matrix X; The robustness of the multi-view K-means clustering model is induced by the minimum absolute criterion, thus obtaining a robust K-means clustering model. The robust K-means clustering model is subjected to nonnegative matrix decomposition, and basis vectors are defined in the nonnegative matrix decomposition. Located in the original data matrix In the convex combination of the column space, a clustering model of the form NMF is obtained.

4. The clustering method based on self-weighted multi-view k-means according to claim 3, characterized in that, The clustering model in the form of NMF is: ； ； in, This is the centroid capture matrix for clustering. The centroid matrix for clustering. Assign a matrix to the clusters.

5. The clustering method based on self-weighted multi-view k-means according to claim 1, characterized in that, In the clustering model, a projection matrix is ​​added for low-dimensional subspace learning, and the norm penalty term of the projection matrix is ​​used for constraints, including: Original data matrix The v-th view is projected onto a low-dimensional subspace, introducing a new projection matrix into the clustering model. Define the projection matrix ;in, It is the characteristic dimension of the low-dimensional subspace, which is represented as: .

6. The clustering method based on self-weighted multi-view k-means according to claim 5, characterized in that, The optimization objective of the low-dimensional subspace is: ； ； in, These are tuning parameters. It is a projection matrix of Norm, This is the centroid capture matrix for clustering. Assign a matrix to the clusters.

7. The clustering method based on self-weighted multi-view k-means according to claim 1, characterized in that, It also includes initialization, which involves initializing the clustering indicator matrix: ； in, It is the identity matrix. Random sorting of binary matrices OK, For a column vector containing all elements, use vectors sum matrix Initialize with direct product If N cannot be Divisible by, then from Additional options Line, randomly fill in the indivisible parts.

8. A clustering method based on self-weighted multi-view k-means according to claim 1, characterized in that, The multi-view data is subjected to dimensionality reduction, wherein the dimensionality reduction is defined as reducing the dimension d of the multi-view data. These are tuning parameters. exist arrive The search is performed between dimensions with a step size of 0.5, searching for the dimension d corresponding to the best clustering result by searching all dimensions of each view in the original data matrix.

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