Later-stage fusion multi-kernel clustering method and system based on tensor learning and active reconstruction

Abstract

The invention discloses a later fusion multi-kernel clustering method and system based on tensor learning and active reconstruction, and relates to the technical field of information clustering, and the method comprises the steps: firstly obtaining a target data sample and a clustering task, mapping the target data sample to a Hilbert space, and generating a multi-kernel matrix; carrying out active reconstruction on a base division matrix in later fusion multi-kernel clustering; applying low-rank tensor constraint to the actively reconstructed basis division matrix; establishing an objective function of a later fusion multi-kernel clustering method; performing initialization operation on all variables; by utilizing an alternating direction multiplier method, updating and optimizing a certain variable in sequence by fixing other variables; the convergence threshold value of the target function is limited, and when the change fluctuation of the target function value is smaller than the threshold value, the optimization process is stopped; and taking the directly learned consistency division matrix as input, and obtaining sample label information and a clustering result through a K-means clustering algorithm. The clustering scheme provided by the invention has remarkable effectiveness and high efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of information clustering, and more specifically to a late-stage fusion multi-core clustering method and system based on tensor learning and active reconstruction. Background Art

[0002] The Late Fusion Multiple Kernel Clustering (LFMKC) method solves the computational complexity challenge of multi-core clustering. Different from the multi-core K-means clustering method to represent the distribution information from different views, the late fusion multi-core clustering is fused at the clustering decision level and uses a smaller basis partition matrix to capture the data distribution of each core view. This strategy significantly reduces the time and memory overhead in the multi-core clustering process.

[0003] Late fusion multi-core clustering aims to fuse each basis partition matrix To learn the consensus clustering matrix H∈ n×k , its target formula can be expressed as follows:

[0004]

[0005] Where γ represents the weight coefficient of different kernel views, T p ∈ k×k is the p-th column permutation matrix, which is used to effectively align the basis partition matrices of different views. It can be observed from the expression that late fusion multi-core clustering aims to optimize the objective function by maximizing all variables.

[0006] Multi-core clustering based on late fusion strategy improves the computational efficiency of multi-core clustering to quasi-linear computational complexity by fusing at the clustering decision level, achieving encouraging clustering performance, but they are still limited by the following two shortcomings:

[0007] (1) The basis partition matrix they focus on cannot be learned and optimized during the clustering process, so their performance is directly limited by the bottleneck of the cluster structure representation ability of the basis partition matrix;

[0008] (2) They study the consistency and complementarity between views by adjusting view weights, but ignore the inherent high-order correlations between views, resulting in a lack of ability to mine multi-core information. Summary of the invention

[0009] In view of this, the present invention provides a late-fusion multi-core clustering method and system based on tensor learning and active reconstruction, which breaks through the bottleneck of the basis partition matrix representation capability in the traditional late-fusion strategy and can learn meaningful high-order cross-view information. The present invention actively reconstructs the decision layer and calibrates and optimizes it during the late-fusion process, stacks the reconstructed representation into a tensor to condense a clearer cluster structure between views, and can directly learn consistent clustering divisions.

[0010] In order to achieve the above object, the present invention provides the following technical solutions:

[0011] A late fusion multi-core clustering method based on tensor learning and active reconstruction includes the following steps:

[0012] Step S1, obtaining a target data sample and a clustering task, mapping the target data sample to a Hilbert space, and generating a multi-core matrix;

[0013] Step S2, actively reconstructing the basis partition matrix in the late fusion multi-core clustering;

[0014] Step S3, applying a low-rank tensor constraint to the actively reconstructed basis partition matrix;

[0015] Step S4, establishing the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction;

[0016] Step S5, initializing all variables;

[0017] Step S6, using the alternating direction multiplier method, by fixing other variables, updating and optimizing one variable in turn;

[0018] Step S7, limiting the convergence threshold of the objective function, when the fluctuation of the objective function value is less than the threshold, the optimization process in step S6 stops;

[0019] Step S8: Using the directly learned consistency partition matrix as input, the sample label information and clustering results are obtained through the K-means clustering algorithm.

[0020] Furthermore, in step S1, the features of the multi-view data samples are first obtained, and then the data samples are mapped to the Hilbert space through the Gaussian kernel function, and each view forms an N×N kernel matrix, where N represents the number of samples, thereby generating a multi-kernel matrix; and a clustering task is obtained, that is, how many classes the data samples need to be divided into.

[0021] Furthermore, in step S2, the Basis partition matrix for late fusion multi-core clustering Reconstruct the image, ensure the quality of the reconstruction by using the F-norm, and impose the same column orthogonality constraint on it, and continuously calibrate and optimize it dynamically in subsequent iterations;

[0022] Introducing learnable column permutation matrices To integrate the clustering structures between different views, the formula is as follows:

[0023]

[0024] in, are the basis partition matrices of the later fusion multi-core clustering, The partition matrix obtained by reconstructing each basis partition matrix of the late fusion multi-core clustering.

[0025] Furthermore, in step S3, the dynamically reconstructed basis partition matrix Stack them into tensor form, and introduce the tensor nuclear norm based on singular value decomposition to impose constraints on them. The expression is as follows:

[0026]

[0027] H p H p =T p T p =I.

[0028] Furthermore, in step S4, the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction is specifically:

[0029]

[0030] H * H * =H p H p =T p T p =T p T p =I;

[0031] Among them, H * is a consistent consensus partition matrix, are the basis partition matrices of the later fusion multi-core clustering, The partition matrix obtained by reconstructing each base partition matrix of the late fusion multi-core clustering, and is a learnable column permutation matrix, and λ and ρ are trade-off parameters.

[0032] Furthermore, in step S5, H is first initialized by solving the following m sub-problems: The solution is to first perform eigenvalue decomposition on K to obtain the eigenvalues ​​and corresponding eigenvectors. The optimal solution is a matrix constructed by the eigenvectors corresponding to the largest k eigenvalues; then initialize other variables by assignment:

[0033]

[0034] Furthermore, in step S6, the alternating direction multiplier method is used to update and optimize a certain variable in turn by fixing other variables. The specific process is as follows:

[0035] Following the principle of ADMM, the auxiliary tensor variable A is introduced and the augmented Lagrangian function is obtained as follows:

[0036]

[0037] Where Y∈n×k×m represents the Lagrangian multiplier, μ>0 is the penalty factor, and the alternating minimization strategy is used to divide the problem in the augmented Lagrangian function into five sub-problems. Each sub-problem optimizes its own variables separately while keeping other variables fixed.

[0038] Furthermore, in step S7, the change of the variable is first calculated, and the formula is as follows:

[0039]

[0040] Then set the threshold to 10 -4 , so in each round of iteration, when When , the convergence condition is considered to be reached and the above optimization process stops.

[0041] Furthermore, in step S8, the directly learned consistency partition matrix is ​​used as the input of the K-means clustering algorithm to directly obtain the sample label information and clustering results.

[0042] A late fusion multi-core clustering system based on tensor learning and active reconstruction, clustering is performed according to any of the above-mentioned late fusion multi-core clustering methods based on tensor learning and active reconstruction, comprising:

[0043] An acquisition module, used for acquiring target data samples and clustering tasks, mapping the target data samples to the Hilbert space, and generating a multi-core matrix;

[0044] A building block for actively reconstructing the basis partition matrix in late fusion multi-core clustering; applying low-rank tensor constraints to the actively reconstructed basis partition matrix;

[0045] Function module, used to establish the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction;

[0046] Initialization module, used to initialize all variables;

[0047] An optimization module is used to update and optimize a certain variable in turn by fixing other variables using an alternating direction multiplier method;

[0048] A threshold limiting module is used to limit the convergence threshold of the objective function. When the fluctuation of the objective function value is less than the threshold, the optimization process stops;

[0049] The clustering module is used to take the directly learned consistency partition matrix as input and obtain sample label information and clustering results through the K-means clustering algorithm.

[0050] It can be seen from the above technical solutions that the present invention provides a late fusion multi-core clustering method and system based on tensor learning and active reconstruction, which has the following beneficial effects compared with the prior art:

[0051] The present invention proposes a novel late-fusion multi-core clustering algorithm - low-rank tensor and active reconstruction induced late-fusion multi-core clustering. It proposes for the first time to actively reconstruct the basis partition matrix, and calibrate and optimize it during the late fusion process, thereby breaking through the bottleneck of the cluster structure representation capability of the multi-core clustering algorithm based on late fusion that is limited by the basis partition matrix.

[0052] The present invention uses the emerging tensor nuclear norm technology based on tensor singular value decomposition (t-SVD) and uses the active reconstruction dynamic basis partitioning matrix to construct tensors for the first time, so as to capture the spatial structure and high-order correlations across views in the data. It can also enable the two processes of active reconstruction strategy and tensor learning to assist each other to jointly achieve the optimal clustering effect, and effectively extract clearer cluster structures from multiple perspectives, thereby solving the defect that the existing technology lacks the ability to mine multi-core information.

[0053] In summary, compared with the prior art, the clustering scheme proposed in the present invention has significant effectiveness and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0055] Figure 1 Schematic diagram of clustering performance evolution process in the embodiment;

[0056] Figure 2Schematic diagram of the variable error evolution process in the embodiment;

[0057] Figure 3 Schematic diagram of the analysis of the impact of different values ​​of λ1 on clustering performance;

[0058] Figure 4 Schematic diagram of the analysis of the impact of different values ​​of λ2 on clustering performance;

[0059] Figure 5 It is a schematic diagram of the method steps of the present invention. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] The embodiment of the present invention discloses a late fusion multi-core clustering method based on tensor learning and active reconstruction, see Figure 5 , including the following steps:

[0062] Step S1, obtaining a target data sample and a clustering task, mapping the target data sample to a Hilbert space, and generating a multi-core matrix.

[0063] First, the features of multi-view data samples are obtained, and then the data samples are mapped to the Hilbert space through the Gaussian kernel function. Each view forms an N×N kernel matrix, where N represents the number of samples, thereby generating a multi-kernel matrix; and the clustering task is obtained, that is, how many classes the data samples need to be divided into.

[0064] Step S2: actively reconstruct the basis partition matrix in the late fusion multi-core clustering, and update and correct it in subsequent steps.

[0065] In this embodiment, the first Basis partition matrix for late fusion multi-core clustering Reconstruction is performed, the quality of reconstruction is guaranteed by the F norm, and the same column orthogonality constraint is imposed on it, and it is dynamically calibrated and optimized in the subsequent iteration process. In addition, since clustering is an unsupervised learning task, and The clustering structure in may not be well aligned with the sample labels in different views at the same time. To solve this problem, this embodiment introduces a learnable column permutation matrix To integrate the clustering structures between different views, the formula is as follows:

[0066]

[0067] in, are the basis partition matrices of the later fusion multi-core clustering, The partition matrix obtained by reconstructing each basis partition matrix of the late fusion multi-core clustering.

[0068] On this basis, in order to build an end-to-end one-step multi-core clustering model, the consensus clustering matrix H across views is partitioned into * The learning of is integrated into the objective function. Similarly, we further introduce the learnable column permutation matrix To align the clustering divisions of different views. The expression is as follows:

[0069]

[0070] Step S3: applying a low-rank tensor constraint to the actively reconstructed basis partition matrix.

[0071] In order to explore and mine the inherent high-order correlation information between views, the dynamically reconstructed basis partition matrix Stack them into tensor form, and introduce the tensor nuclear norm based on singular value decomposition to impose constraints on them. The expression is as follows:

[0072]

[0073] H p H p =T p T p =I.

[0074] Step S4: Establishing the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction.

[0075] The objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction is as follows:

[0076]

[0077] H * H * =H p H p =T p T p =T p T p =I;

[0078] Among them, H * is a consistent consensus partition matrix, are the basis partition matrices of the later fusion multi-core clustering, The partition matrix obtained by reconstructing each base partition matrix of the late fusion multi-core clustering, and is a learnable column permutation matrix, and λ and ρ are trade-off parameters.

[0079] Step S5: Initialize all variables.

[0080] First, H is initialized by solving the following m subproblems: The solution is to first perform eigenvalue decomposition on K to obtain the eigenvalues ​​and corresponding eigenvectors. The optimal solution is a matrix constructed from the eigenvectors corresponding to the largest k eigenvalues; then initialize other variables by assignment:

[0081] Step S6: using the alternating direction multiplier method, by fixing other variables, update and optimize one variable in turn.

[0082] The alternating direction multiplier method (ADMM) is used to solve LTAR-LFMKC, which updates a specific variable while keeping other variables unchanged. The specific process is as follows:

[0083] In order to ensure the independence of the tensor H in the formula, the auxiliary tensor variable A is introduced according to the principle of ADMM and the augmented Lagrangian function is obtained as follows:

[0084]

[0085]

[0086] where Y∈ n×k×m represents the Lagrangian multiplier, μ>0 is the penalty factor, and the alternating minimization strategy is used to divide the problem in the augmented Lagrangian function into five sub-problems. Each sub-problem optimizes its own variable separately while keeping other variables fixed.

[0087] {H * Sub-problem: By fixing other variables, * The sub-problem can be expressed as follows:

[0088] By expanding the Frobenius norm and simplifying it, we can get the following equivalent form of the matrix alignment problem: max H*H*＝I Tr(H * B), where T is calculated by performing economic rank-$k$ SVD on M pClosed-form solution. Assume that the matrix M has a truncated singular value decomposition (truncatedSVD) of rank $k$ such as M=UΣV, where U∈ n×k ,Σ∈ k×k , V∈ k×k The optimal closed-form solution to this problem is H * =UV, where U and V are the left and right singular value matrices of the truncated SVD of B, respectively.

[0089] {H subproblem:} By fixing other variables, {H} can be updated by the following question:

[0090]

[0091] For each core view, the problem can be expressed as the following m sub-problems:

[0092]

[0093] By expanding the Frobenius norm, we can simplify the following equivalent problem:

[0094]

[0095] Where Q p express Let M p =H * T p +λH p T p +ρμQ p , use and optimize H * The same method can get the optimal solution as follows: p =U p V p Among them, U p and V p M p The left and right singular value matrices of the truncated SVD of .

[0096] {T subproblem:} By fixing other variables, update T by the following problem:

[0097]

[0098] For each core view, the problem can be expressed as the following m independent sub-problems: The optimal solution obtained by calculation is as follows: T p =U tp V tp , where U tp and V tp H p H* The left and right singular value matrices of the truncated SVD of .

[0099] {T subproblem:} Similar to the process of updating T, first simplify the problem of solving T into the following m independent subproblems:

[0100] Similarly, the optimal solution can be obtained as follows: T p =U tp V tp , where U tp and V tp H p H p The left and right singular value matrices of the truncated SVD of .

[0101] {Subproblem A:} By fixing other variables, subproblem {A} is a t-TNN minimization problem which can be solved by solving the following problem: make The solution is achieved by exploiting C's tensor tubal-shrinkage operation. in The i-th positive slice of is

[0102] {Update Y and μ:} The Lagrange multiplier Y and the penalty factor μ can be updated during the optimization process as follows:

[0103] Y=Y+μ(FA); μ=τ×μ, where τ>1 is intended to speed up the convergence, and τ=2 is set as a constant by default in the method.

[0104] Step S7: limit the convergence threshold of the objective function. When the fluctuation of the objective function value is less than the threshold, the optimization process in step S6 stops.

[0105] First, calculate the change in the variable. The formula is as follows:

[0106]

[0107]

[0108] Then set the threshold to 10 -4 , so in each round of iteration, when When , the convergence condition is considered to be reached and the above optimization process stops.

[0109] Step S8: Using the directly learned consistency partition matrix as input, the sample label information and clustering results are obtained through the K-means clustering algorithm.

[0110] The directly learned consistency partition matrix is ​​used as the input of the K-means clustering algorithm to directly obtain the sample label information and clustering results.

[0111] A late fusion multi-core clustering system based on tensor learning and active reconstruction, clustering is performed according to the late fusion multi-core clustering method based on tensor learning and active reconstruction, including:

[0112] An acquisition module, used for acquiring target data samples and clustering tasks, mapping the target data samples to the Hilbert space, and generating a multi-core matrix;

[0113] A building block for actively reconstructing the basis partition matrix in late fusion multi-core clustering; applying low-rank tensor constraints to the actively reconstructed basis partition matrix;

[0114] Function module, used to establish the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction;

[0115] Initialization module, used to initialize all variables;

[0116] An optimization module is used to update and optimize a certain variable in turn by fixing other variables using an alternating direction multiplier method;

[0117] A threshold limiting module is used to limit the convergence threshold of the objective function. When the fluctuation of the objective function value is less than the threshold, the optimization process stops;

[0118] The clustering module is used to take the directly learned consistency partition matrix as input and obtain sample label information and clustering results through the K-means clustering algorithm.

[0119] Next, specific embodiments are listed to demonstrate the progressive significance of the solution of the present invention.

[0120] This example tests the clustering performance of the method of the present invention on 10 benchmark datasets, including ProteinFold, Plant, Nonpl, Caltech, 4Area, Scene15, CCV, Flower102, ALOI100, and Reuters. For relevant information of the datasets, see Table 1.

[0121] Table 1 Basic statistics of the dataset

[0122]

[0123] This experiment uses the average kernel K-means clustering algorithm (Avg-KKM) and the best single kernel K-means clustering algorithm (SB-KKM) as the baseline, and also selects some classic MKC algorithms, including multi-kernel k-means clustering (MKKM), localized multi-kernel K-means clustering (LMKKM), optimal neighbor multi-kernel clustering (ONKC), multi-kernel K-means clustering with matrix induced regularization term (MKKM-MR), and local alignment maximization multi-kernel clustering (LKAM). In addition, some of the latest methods were selected, including those based on late fusion strategy, namely late fusion multi-kernel clustering (LFMKC), one-step late fusion multi-view clustering (OPLFMVC); subspace-based and graph-based methods, namely neighbor kernel subspace segmentation multi-kernel clustering (NKSS), structure-preserving multi-kernel clustering (SPMKC), hierarchical multi-kernel clustering (HMKC), self-weighted integral space fast multi-view clustering (AIMC), efficient orthogonal multi-view subspace clustering (OMSC), graph-based multi-view clustering (GMC); and minimum-maximum optimization-based Methods, namely simple multi-core K-means clustering (SMKKM), localized simple multi-core K-means clustering (LSMKKM), localized simple multi-core K-means clustering without hyperparameters (HFLSMKKM); tensor-based methods, namely tensor learning-induced multi-view spectral clustering (TLIMSC), low-rank tensor-based multi-view clustering neighbor learning (LTBPL), unified low-rank tensor and graph learning multi-view clustering (UGLTL), tensor graph learning multi-view subspace clustering (WTNNM), coupled graph tensor learning multi-core clustering (KCGT). For consistency, for each comparison algorithm, their public source code is used, and all experiments are carried out in the same experimental environment. Regarding the setting of algorithm parameters, the guidelines of the literature or the author must be strictly followed. All methods are randomly initialized and repeated 50 times and the best results are shown to reduce the randomness caused by K-means. This experiment uses the common clustering accuracy (ACC), normalized mutual information (NMI) and Rand index (RI) to show the clustering performance of each method.

[0124] Table 2 Performance comparison experiment table of clustering accuracy ACC:

[0125]

[0126] Table 3 Performance comparison experiment table of clustering standard mutual information NMI:

[0127]

[0128] Table 4 Performance comparison experiment table of cluster purity PUR:

[0129]

[0130] Table 5 Performance comparison experiment table of clustering Rand index RI:

[0131]

[0132] Table 6 Running time table:

[0133]

[0134] Table 7 Ablation experiment:

[0135]

[0136] Experimental description:

[0137] Tables 2 and 3 show the clustering performance comparison results of the algorithms mentioned above, where "-" indicates that the corresponding results are not available due to insufficient memory or unacceptable overhead. The TLIMSC algorithm does not support the situation where the number of core views is greater than the number of clusters. We bold and mark the best results in red, and the second best and third best results are represented in blue and orange respectively. By comparing the experimental results, we can observe the following conclusions:

[0138] (1) LFMKC significantly improves the computational efficiency of the algorithm, and its clustering performance also exceeds that of many comparative algorithms, but its clustering performance still has obvious bottlenecks. On the other hand, HMKC introduces a hierarchical method to maximize favorable details and achieves performance improvement. For example, the average ACC performance index of LFMKC on all data sets exceeds that of ONKC, MKKM-MR, LKAM, NKSS, and SPMKC by 3.42%, 2.93%, 5.05%, 6.42%, and 9.50%, respectively; while the average ACC performance index of HMKC on all data sets exceeds that of LFMKC, NKSS, SPMKC, SMKKM, OPLFMVC, and LSMKKM by 4.81%, 11.64%, 14.76%, 7.34%, 11.99%, and 3.70%, respectively. It can be seen that among all non-tensor algorithms, the clustering performance of HMKC has basically reached the best level.

[0139] (2) Looking at all the compared algorithms, it is easy to find that the clustering performance of tensor learning-based clustering algorithms, such as LTBPL, UGLTL, WTNNM and KCGT, remains at a significant leading position. This demonstrates the effectiveness of tensor learning aimed at mining potential high-order associations between views. For example, WTNNM leads the average performance of all non-tensor algorithms by 17% in terms of ACC performance indicators on seven datasets; UGLTL leads the average ACC performance indicator on nine datasets by about 24%, that is, except for the LTAR-LFMKC algorithm we proposed, the average ACC performance indicator of UGLTL reaches the best by a significant gap. For a single dataset, different tensor algorithms show a certain degree of ups and downs. At the same time, LTAR-LFMKC proposed the idea of ​​active reconstruction, breaking through the bottleneck of the representation ability of the basis partition matrix, and achieved a stable and consistent optimal level on all data sets. Among them, the ACC performance index surpassed UGLTL by 11.1%, 20.2%, 5%, 0.4%, 25.9%, 2.4%, 35.3%, 13.8%, and 1.9% on nine data sets, and surpassed KCGT by 8.2%, 32.4%, 32.4%, 1.4%, 13.2%, 19.2%, 39.3%, 0.8%, and 4.6%. At the same time, the results of the analysis on indicators such as NMI, PUR, and RI are also similar. It is easy to see that the algorithm proposed by the present invention maintains a significant leading position.

[0140] In summary, LTAR-LFMKC showed significantly better clustering performance than the comparison algorithms on all data sets, improving the average performance of all comparison algorithms by 22.9% to 53.4%, verifying the effectiveness and efficiency of the low-rank tensor and active reconstruction learning proposed in the present invention.

[0141] In addition, in order to study the evolution process of LTAR-LFMKC, this example calculates the clustering performance and function loss in each round of iteration. Figure 1 and Figure 2 The loss and performance curves of LTAR-LFMKC in iterations are plotted in Figure 2. The experimental results show that the function loss value will fluctuate several times in the early learning process, generally stabilize after 5 to 6 iterations, and then rapidly decrease and converge to the local optimal solution; while the clustering performance first rises rapidly and then tends to stabilize, which can correspondingly reflect that the clustering quality continues to improve in the learning process and then reaches stability. This evolution process fully proves the effectiveness and necessity of the LTAR-LFMKC learning process.

[0142] In order to evaluate the computational complexity of the algorithm, this embodiment records the time overhead of all methods (in seconds) and reports it in Table 4. For the algorithm with hyperparameters, this embodiment reports its average running time (i.e., assuming that there are 2 hyperparameters, each hyperparameter has 5 possible values, and the algorithm is run 25 times in total, then its average running time = total running time / 25 times). As shown in the table, the LTAR-LFMKC proposed in the present invention runs the fastest or almost the fastest on all benchmark data sets. Although WTNNM has superior clustering performance, it is usually the least computationally efficient among all comparison algorithms. For example, a single run time on the Nonpl data set is about 20 hours, and on a larger data set, even if the memory can meet its computing requirements, its time overhead is unbearable. Except for TLIMSC, whose running time is significantly lower than the average running time, other comparison algorithms based on tensor learning, namely LTBPL, UGLTL, WTNNM, and KGCT, all require longer time overhead. In summary, the LTAR-LFMKC proposed in the present invention not only greatly improves the clustering performance, but also has superior computational efficiency than most common multi-core clustering algorithms and tensor clustering algorithms, and has achieved a significant reduction in computational complexity.

[0143] The proposed LTAR-LFMKC introduces two trade-off parameters λ1 and λ2, which are only roughly adjusted in the algorithm. To further study the impact of these two parameters on the algorithm on different datasets, a separate experiment was conducted to analyze their sensitivity and effects, and the results are plotted in Figure 3 and Figure 4 As shown in the figure, these two parameters have a significant impact on the clustering performance, which shows that each item in the formula plays an important role; the impact of this parameter on the clustering performance on different data sets has a very similar pattern, and a stable clustering effect is achieved in the small range of 10^[0,1] and 2^[3-5] respectively. It can be seen that the two trade-off parameters introduced by LTAR-LFMKC have a significant effect on improving the clustering performance, and have regularity and consistency across data sets. At the same time, the clustering parameter analysis can guide the present invention to propose an adjustment strategy for the algorithm on each data set.

[0144] In order to further study the factors that contribute to the superior performance, we also conduct ablation experiments on various parts of the proposed LTAR-LFMKC, including the role of active reconstruction of the basis partition matrix, the role of tensor learning guidance, and the strategy of aligning basis partitions between views through column permutation matrices.

[0145] From a large number of comparative experiments in Table 2, it can be seen that multi-core clustering (such as LFMKC and OPLFMVC) ​​using only the late fusion strategy cannot obtain sufficiently satisfactory clustering results, and methods that only learn low-rank tensor subspace representations (such as LTBPL, UGLTL, WTNNM, and KCGT) cannot achieve further improvement. Therefore, the present invention proposes an LTAR-LFMKC algorithm to actively reconstruct and learn the basis partition matrix, capture high-order cross-view associations through tensor learning, and introduce a column permutation matrix to align views during the optimization process. In order to study the contributions of the three parts of LTAR-LFMKC respectively, the present invention designs four ablation tests for further experiments, wherein the first test L1 indicates that neither the basis partition matrix is ​​actively reconstructed nor the tensor nuclear norm based on tensor singular value decomposition is discarded, the second test L2 indicates that the basis partition matrix is ​​not actively reconstructed, the third test L3 indicates that the tensor nuclear norm based on tensor singular value decomposition is discarded, and the fourth test L4 indicates that the column permutation matrix is ​​not used to align views. These tests are performed on all benchmark datasets, and we report their clustering performance ACC index in Table 7. The results of other indicators are similar and are provided in the Appendix. From the experimental results in Table 7, it can be seen that on all benchmark datasets, compared with L1 discarding both parts at the same time, L2 and L3 have achieved significant performance improvements, and LTAR-LFMKC has also achieved consistent improvements compared with L2 and L3, which shows that both the active reconstruction of the basis partition matrix and the tensor learning guidance have a significant effect on improving the clustering performance, and they can better improve the clustering effect when they are performed simultaneously. Compared with L4 that does not use the column permutation matrix to align views, LTAR-LFMKC also achieves a more significant performance improvement. These tests show the importance of active reconstruction and tensor learning, and also verify the necessity of the basis partition strategy between views aligned by the column permutation matrix.

[0146] The technical solution of the present invention can be applied to the following technical fields:

[0147] 1. Image and video processing:

[0148] Image classification and annotation:

[0149] Tensor learning is used to process multidimensional data and multi-kernel clustering methods are combined to improve the accuracy and efficiency of image classification.

[0150] Video content analysis: Extract features from video frames and use clustering methods to automatically classify and label video content. It is suitable for video surveillance and content recommendation systems.

[0151] 2. Medical Image Analysis:

[0152] Disease diagnosis: Through efficient feature extraction and cluster analysis of medical images (such as MRI and CT images), doctors can be assisted in early diagnosis and classification of diseases.

[0153] Image reconstruction: Use active reconstruction technology to improve the resolution and quality of medical images, helping doctors obtain clearer diagnostic images.

[0154] 3. Natural Language Processing:

[0155] Text classification and clustering: Classify and cluster text data (such as news and social media content) to improve information retrieval and content recommendation.

[0156] Sentiment analysis: Use multi-core clustering methods to perform sentiment analysis on text data, which is applied to market research and user feedback systems.

[0157] 4. Recommendation system:

[0158] Personalized recommendations: Combine user historical behavior data and multi-core learning methods to improve the accuracy of the recommendation system and achieve personalized recommendations (such as movies, music, products, etc.).

[0159] User portrait construction: Through cluster analysis of user behavior data, fine-grained user portraits are constructed to improve the accuracy of marketing strategies.

[0160] 5. Bioinformatics:

[0161] Gene expression data analysis: Feature extraction and clustering of high-dimensional gene expression data help identify gene expression patterns and promote disease research and drug development.

[0162] Protein structure prediction: Using tensor learning and multi-core clustering methods to improve the accuracy of protein structure prediction.

[0163] 6. Cybersecurity:

[0164] Anomaly detection: Perform multi-dimensional feature extraction and cluster analysis in network traffic data to detect network attacks and abnormal behaviors and improve network security protection capabilities.

[0165] Threat intelligence analysis: Through clustering and multi-core learning, it analyzes network security threat intelligence and provides accurate security warnings.

[0166] 7. Intelligent Transportation:

[0167] Traffic flow prediction: Use multi-kernel learning and clustering methods to analyze and predict traffic flow data and optimize traffic management.

[0168] Vehicle Path Planning: Apply this method in intelligent transportation systems to improve the efficiency and accuracy of vehicle path planning.

[0169] Potential technologies and applications: While maintaining computational efficiency, extend the algorithm to solve challenging problems such as data noise and data missing in actual clustering applications. For example:

[0170] Medical image analysis: Noise may exist in medical images (such as MRI and CT scans), such as image noise caused by equipment problems, patient movement, or scanning environment. Medical image data of some patients may be incomplete, such as part of the scan image is missing or the data is not fully collected.

[0171] Intelligent Transportation System: During the traffic flow data collection process, due to sensor failure or environmental interference, erroneous data records (such as abnormally high or abnormally low flow values) may occur. Traffic flow sensors on some sections of the road may fail, resulting in missing data.

[0172] E-commerce recommendation system: There may be noise in user behavior data, such as user mistaken clicks, robot clicks, or abnormal purchase behavior. There is less behavior data for new users, which is called the cold start problem, resulting in incomplete data.

[0173] Bioinformatics: Gene expression data may be disturbed by experimental conditions, human manipulation or environmental factors during the experiment, resulting in noise. Gene chip or sequencing data may be partially missing, and the expression values ​​of some genes cannot be successfully measured.

[0174] Social network analysis: Social network data may contain a lot of noise, such as fake accounts, spam, and robot behavior. Due to user privacy settings or platform restrictions, some social network data may be incomplete, such as missing social relationship or behavior data of some users. The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same and similar parts between the various embodiments can be referenced to each other. For the system module disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part description.

[0175] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A late fusion multi-core clustering method based on tensor learning and active reconstruction, characterized in that: The following steps are involved: Step S1, obtaining a target data sample and a clustering task, mapping the target data sample to a Hilbert space, and generating a multi-core matrix; Step S2, actively reconstructing the basis partition matrix in the late fusion multi-core clustering; Step S3, applying a low-rank tensor constraint to the actively reconstructed basis partition matrix; Step S4, establishing the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction; Step S5, initializing all variables; Step S6: using the alternating direction multiplier method, by fixing other variables, update and optimize one variable in turn; Step S7, limiting the convergence threshold of the objective function, when the fluctuation of the objective function value is less than the threshold, the optimization process in step S6 stops; Step S8: Using the directly learned consistency partition matrix as input, the sample label information and clustering results are obtained through the K-means clustering algorithm.

2. A late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In the step S1, the features of the multi-view data samples are first obtained, and then the data samples are mapped to the Hilbert space through the Gaussian kernel function, and each view forms an N×N kernel matrix, where N represents the number of samples, thereby generating a multi-kernel matrix; And obtain the clustering task, that is, how many classes the data samples need to be divided into.

3. A late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In step S2, the Basis partition matrix for late fusion multi-core clustering Reconstruct the image, ensure the quality of the reconstruction by using the F-norm, and impose the same column orthogonality constraint on it, and continuously calibrate and optimize it dynamically in subsequent iterations; Introducing learnable column permutation matrices To integrate the clustering structures between different views, the formula is as follows: in, are the basis partition matrices of the later fusion multi-core clustering, The partition matrix obtained by reconstructing each basis partition matrix of the late fusion multi-core clustering.

4. A late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In step S3, the dynamically reconstructed basis partition matrix Stack them into tensor form, and introduce the tensor nuclear norm based on singular value decomposition to impose constraints on them. The expression is as follows: s.t.H p H p =T p T p =I。 5. The late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In step S4, the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction is specifically: s.t.H * H * =H p H p =T p T p =T p T p =I; Among them, H * is a consistent consensus partition matrix, are the basis partition matrices of the later fusion multi-core clustering, The partition matrix obtained by reconstructing each base partition matrix of the late fusion multi-core clustering is and is a learnable column permutation matrix, and λ and ρ are trade-off parameters.

6. A late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In step S5, H is first initialized by solving the following m sub-problems: The solution is to first perform eigenvalue decomposition on K to obtain the eigenvalues ​​and corresponding eigenvectors. The optimal solution is a matrix constructed from the eigenvectors corresponding to the largest k eigenvalues; then initialize other variables by assignment:

7. The late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In step S6, the alternating direction multiplier method is used to update and optimize a certain variable in turn by fixing other variables. The specific process is as follows: Following the principle of ADMM, the auxiliary tensor variable A is introduced and the augmented Lagrangian function is obtained as follows: where Y∈ n×k×m represents the Lagrangian multiplier, μ>0 is the penalty factor, and the alternating minimization strategy is used to divide the problem in the augmented Lagrangian function into five sub-problems. Each sub-problem optimizes its own variable separately while keeping other variables fixed.

8. The late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In step S7, the change of the variable is first calculated, and the formula is as follows: Then set the threshold to 10 -4 , so in each round of iteration, when When , the convergence condition is considered to be reached and the above optimization process stops.

9. The late fusion multi-core clustering method based on tensor learning and active reconstruction according to claim 1, characterized in that: In step S8, the directly learned consistency partition matrix is ​​used as the input of the K-means clustering algorithm to directly obtain sample label information and clustering results.

10. A late fusion multi-core clustering system based on tensor learning and active reconstruction, clustering is performed according to a late fusion multi-core clustering method based on tensor learning and active reconstruction according to any one of claims 1 to 9, characterized in that: include: An acquisition module, used for acquiring target data samples and clustering tasks, mapping the target data samples to the Hilbert space, and generating a multi-core matrix; Building blocks for active reconstruction of the basis partition matrix in late-fusion multi-core clustering; Apply low-rank tensor constraints to the actively reconstructed basis partition matrix; Function module, used to establish the objective function of the late fusion multi-core clustering method based on tensor learning and active reconstruction; Initialization module, used to initialize all variables; An optimization module is used to update and optimize a certain variable in turn by fixing other variables using an alternating direction multiplier method; A threshold limiting module is used to limit the convergence threshold of the objective function. When the fluctuation of the objective function value is less than the threshold, the optimization process stops; The clustering module is used to take the directly learned consistency partition matrix as input and obtain sample label information and clustering results through the K-means clustering algorithm.

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