WO2022170840A1 - Procédé et système d'apprentissage automatique de regroupement multi-vues par fusion tardive basés sur un graphe bipartite - Google Patents

Procédé et système d'apprentissage automatique de regroupement multi-vues par fusion tardive basés sur un graphe bipartite Download PDF

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WO2022170840A1
WO2022170840A1 PCT/CN2021/136557 CN2021136557W WO2022170840A1 WO 2022170840 A1 WO2022170840 A1 WO 2022170840A1 CN 2021136557 W CN2021136557 W CN 2021136557W WO 2022170840 A1 WO2022170840 A1 WO 2022170840A1
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view
clustering
bipartite graph
kernel
fusion multi
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朱信忠
徐慧英
梁伟轩
赵建民
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浙江师范大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G06F18/232—Non-hierarchical techniques
    • G06F18/2323—Non-hierarchical techniques based on graph theory, e.g. minimum spanning trees [MST] or graph cuts
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/25—Fusion techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound

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  • the present application relates to the technical fields of computer vision and pattern recognition, and in particular, to a method and system for late fusion multi-view clustering machine learning based on bipartite graphs.
  • the existing multi-view clustering algorithms can be roughly divided into the following two categories: (1) Multi-view clustering algorithms based on previous fusion. Early fusion refers to the fusion of representations of multiple views to obtain a unified representation before clustering. Then, run the clustering algorithm on it to get the final clustering result. The more classic algorithms are multi-core clustering algorithm, multi-view spectral clustering algorithm and multi-view subspace clustering algorithm. (2) Multi-view clustering algorithm based on late fusion. Different from pre-fusion, post-fusion multi-view clustering first obtains basic divisions from each single view, and then uses these basic divisions to obtain an optimal clustering result. All ensemble clustering algorithms can be regarded as a late fusion method.
  • the basic division uses the basic division to first construct the correlation matrix of each view, that is, an n ⁇ n-dimensional 0-1 matrix that judges whether the samples are classified into the same class, and learns a unified matrix through low-rank and sparse matrix decomposition. or after constructing the correlation matrix of each view, given a measure of the difficulty of sample learning, use self-paced learning to cluster the samples in an order from simple to difficult; or, maximize the linearity between the consistent partition and the basic partition The inner product between combinations; alternatively, use the late fusion method to deal with the missing multi-view clustering problem.
  • the purpose of this application is to provide a bipartite graph-based late fusion multi-view clustering machine learning method and system for the defects of the prior art.
  • a late-fusion multi-view clustering machine learning method based on bipartite graphs including:
  • the basic division is obtained by running kernel k-means clustering on each view corresponding to the obtained clustering task and the target data sample, and the diversification regular term of each view is calculated;
  • the kernel k-means clustering is performed, specifically:
  • the goal of kernel k-means clustering is to minimize the sum of squared errors based on the partition matrix B ⁇ ⁇ 0,1 ⁇ n ⁇ k , expressed as:
  • K represents the kernel matrix
  • I k represents the k-dimensional identity matrix.
  • the multi-view clustering objective function of later fusion based on the bipartite graph in the step S3 is expressed as:
  • the bipartite graph-based late fusion multi-view clustering objective function that is established in a cyclic manner is specifically:
  • step S4 the three-step alternating method is used to solve the formula (3), wherein the three-step alternating method termination condition is expressed as:
  • obj (t-1) and obj (t) represent the values of formula (3) in the t and t-1 iterations, respectively, and ⁇ represents the set precision.
  • the acquisition module is used to acquire clustering tasks and target data samples
  • the operation module is used to obtain the basic division by running the kernel k-means clustering on each view corresponding to the obtained clustering task and the target data sample, and calculate the diversification regular term of each view;
  • the solving module is used to solve the established bipartite graph-based late fusion multi-view clustering objective function in a cyclic manner, and obtain the bipartite graph after view fusion;
  • the clustering module is used to perform spectral clustering on the obtained bipartite graph to obtain the clustering result.
  • running kernel k-means clustering in the running module is specifically:
  • the goal of kernel k-means clustering is to minimize the sum of squared errors based on the partition matrix B ⁇ ⁇ 0,1 ⁇ n ⁇ k , expressed as:
  • K represents the kernel matrix
  • I k represents the k-dimensional identity matrix.
  • late fusion multi-view clustering objective function based on the bipartite graph in the establishment module is expressed as:
  • bipartite graph-based late-stage fusion multi-view clustering objective function that is established in the solving module using a cyclic method is specifically:
  • Second fixation module for fixing ⁇ and Z optimized The closed-form solution is obtained by setting the partial derivative of the objective function with respect to A p equal to 0
  • Third fixing module for fixing and Z, optimizing ⁇ transforms the objective function into a quadratic programming problem with linear constraints, expressed as:
  • the three-step alternating method is used to solve formula (3) in the solving module, and the termination condition of the three-step alternating method is expressed as:
  • obj (t-1) and obj (t) represent the values of formula (3) in the t and t-1 iterations, respectively, and ⁇ represents the set precision.
  • the present application proposes a novel bipartite graph-based late fusion multi-view clustering machine learning method.
  • the method includes acquiring basic clustering divisions and computing graph diversification regular terms, and optimizing objective function acquisition. Modules such as bipartite graph and clustering using bipartite graph.
  • the present application enables the optimized representative points not only to represent the information of a single view, but also to better serve the view fusion, so that the learned bipartite graph can better fuse the information of each view. information to achieve the purpose of improving the clustering effect.
  • Experimental results on six public datasets demonstrate that the present application outperforms existing methods.
  • Embodiment 1 is a flowchart of a later fusion multi-view clustering machine learning method based on a bipartite graph provided by Embodiment 1;
  • FIG. 2 is a schematic diagram of a parameter ⁇ sensitivity map provided in Embodiment 2;
  • Embodiment 3 is a schematic diagram of the influence of different representative points s provided in Embodiment 2 on the clustering effect;
  • Embodiment 4 is a schematic diagram of changes in clustering performance and objective function values as the number of iterations increases provided by Embodiment 2;
  • FIG. 5 is a structural diagram of a later fusion multi-view clustering machine learning system based on a bipartite graph provided in Embodiment 3.
  • FIG. 5 is a structural diagram of a later fusion multi-view clustering machine learning system based on a bipartite graph provided in Embodiment 3.
  • the present application provides a bipartite graph-based late fusion multi-view clustering machine learning method and system.
  • the bipartite graph-based late fusion multi-view clustering machine learning method provided in this embodiment, as shown in Figure 1, includes:
  • a new method for clustering by learning multi-view information through later fusion proposed in this embodiment is used to represent the view representative point method.
  • the representative point can better serve It is used for multi-view clustering; and the method of using bipartite graph for graph learning in the later fusion algorithm reduces the computational and storage complexity.
  • step S12 the basic division is obtained by running kernel k-means clustering on each view corresponding to the acquired clustering task and the target data sample, and the diversification regular term of each view is calculated. Specifically:
  • the goal of kernel k-means clustering is to minimize the sum of squared errors based on the partition matrix B ⁇ ⁇ 0,1 ⁇ n ⁇ k , expressed as:
  • Formula (1) can be transformed into:
  • K represents the kernel matrix
  • I k represents the k-dimensional identity matrix.
  • step S13 the representative points of each view are selected by random initialization, and a bipartite graph-based late fusion multi-view clustering objective function is established.
  • the later fusion multi-view clustering objective function based on bipartite graph is expressed as:
  • step S14 the established bipartite graph-based late fusion multi-view clustering objective function is solved in a circular manner, and a bipartite graph after view fusion is obtained, specifically:
  • obj (t-1) and obj (t) represent the values of formula (3) in the t and t-1 iterations, respectively, and ⁇ represents the set precision.
  • step S15 spectral clustering is performed on the obtained bipartite graph to obtain a clustering result.
  • this embodiment proposes a novel bipartite graph-based late fusion multi-view clustering machine learning method.
  • the method includes acquiring basic clustering division and computing graph diversification regular terms, optimizing the objective function. Modules for obtaining bipartite graphs and clustering using bipartite graphs.
  • the optimized representative points can not only represent the information of a single view, but also better serve the view fusion, so that the learned bipartite graph can better fuse each view information to achieve the purpose of improving the clustering effect.
  • the clustering performance of the proposed method was tested on 6 MKL standard datasets, including Oxford Flower17, Oxford Flower102, Protein fold prediction, UCI-Digital, Columbia Consumer Video (CCV) and Caltech102. See Table 1 for information about the dataset.
  • this example generates 12 benchmark kernel matrices, of which the first 10 feature sets use second-order polynomial kernels, and the last two use cosine inner product kernels.
  • kernel matrices For ProteinFold, this example generates 12 benchmark kernel matrices, of which the first 10 feature sets use second-order polynomial kernels, and the last two use cosine inner product kernels.
  • CCV three base kernels are generated by applying a Gaussian kernel on the SIFT, STIP and MFCC features, and the width of the three Gaussian kernels is set as the mean of the distances of each pair of samples. Kernel matrices for other datasets can be downloaded from the Internet.
  • A-MKKM average multi-kernel clustering algorithm
  • SB-MKKM optimal single-view kernel k-means clustering algorithm
  • MKKM multi-kernel k-means clustering
  • RKKM robust multi-kernel clustering
  • MKKM-MR matrix-induced regularization term
  • ONKC optimal neighbor multi-kernel clustering
  • MVC-LFA late fusion-based maximally aligned multi-view clustering
  • this experiment uses the grid search parameters of RMKKM, MKKM-MR, ONKC and MVC-LFA.
  • This experiment uses Common Clustering Accuracy (ACC), Normalized Mutual Information (NMI), and Purity (Purity) to show the clustering performance of each method. All methods are randomly initialized and repeated 50 times and show the best results to reduce randomness caused by k-means.
  • ACC Common Clustering Accuracy
  • NMI Normalized Mutual Information
  • Purity Purity
  • Table 2 shows the clustering effects of the above methods and the comparison algorithms on all datasets. According to the table, it can be observed that: 1. The proposed algorithm outperforms all comparison algorithms under the three evaluation criteria. 2.
  • ONKC is an important benchmark algorithm in multi-core algorithms, and the performance of the proposed algorithm on the six datasets ACC is 7.14%, 10.22%, 3.17%, 3.45%, 6.07% better than ONKC, respectively and 10.2%.
  • 3.MVC-LFA is a late fusion algorithm, which usually performs better than most other multi-view algorithms, and the proposed algorithm exceeds its average by 7.58%, 7.07% and 7.34% under the three clustering indicators, respectively. .
  • This embodiment introduces a regularization parameter ⁇ to balance the weight of bipartite graph learning and diversification of regular terms.
  • ⁇ varies in the range of [ 2-15,2-12 ,..., 215 ], taking the best comparison algorithm on this dataset as the basic reference. From this figure, it can be seen that: 1) the best NMI is always obtained when the two terms are properly balanced; 2) the proposed algorithm outperforms the best contrasting algorithm on most datasets regardless of the variation of ⁇ .
  • This embodiment also gives the objective function value and changes in clustering performance at each iteration, as shown in FIG. 4 . It can be seen that the objective function value decreases monotonically and usually converges within 25 iterations. It can be seen that with the decrease of the objective function, the clustering effect will fluctuate, but the overall trend is upward. This example shows that the algorithm can continuously improve the clustering performance during the training process.
  • This embodiment provides a later fusion multi-view clustering machine learning system based on bipartite graph, as shown in Figure 5, including:
  • an acquisition module 11 for acquiring clustering tasks and target data samples
  • the operation module 12 is used for running the kernel k-means clustering on each view corresponding to the obtained clustering task and the target data sample to obtain the basic division, and calculate the diversification regular term of each view;
  • the establishment module 13 is used to select the representative points of each view by random initialization, and establish the later fusion multi-view clustering objective function based on the bipartite graph;
  • the solving module 14 is used to solve the established bipartite graph-based later fusion multi-view clustering objective function in a cyclic manner, and obtain a bipartite graph after view fusion;
  • the clustering module 15 is configured to perform spectral clustering on the obtained bipartite graph to obtain a clustering result.
  • running kernel k-means clustering in the running module is specifically:
  • the goal of kernel k-means clustering is to minimize the sum of squared errors based on the partition matrix B ⁇ ⁇ 0,1 ⁇ n ⁇ k , expressed as:
  • K represents the kernel matrix
  • I k represents the k-dimensional identity matrix.
  • late fusion multi-view clustering objective function based on the bipartite graph in the establishment module is expressed as:
  • bipartite graph-based late-stage fusion multi-view clustering objective function that is established in the solving module using a cyclic method is specifically:
  • Second fixation module for fixing ⁇ and Z optimized The closed-form solution is obtained by setting the partial derivative of the objective function with respect to A p equal to 0
  • Third fixing module for fixing and Z, optimizing ⁇ transforms the objective function into a quadratic programming problem with linear constraints, expressed as:
  • the three-step alternating method is used to solve formula (3) in the solving module, and the termination condition of the three-step alternating method is expressed as:
  • obj (t-1) and obj (t) represent the values of formula (3) in the t and t-1 iterations, respectively, and ⁇ represents the set precision.
  • bipartite graph-based late fusion multi-view clustering machine learning system provided in this embodiment is similar to that of the first embodiment, and details are not repeated here.
  • this embodiment includes modules such as acquiring basic clustering division and computing graph diversification regular terms, optimizing objective function to acquire bipartite graph, and using bipartite graph for clustering.
  • the optimized representative points can not only represent the information of a single view, but also better serve the view fusion, so that the learned bipartite graph can better fuse each view information to achieve the purpose of improving the clustering effect.

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Abstract

La présente demande concerne un procédé d'apprentissage automatique de regroupement multi-vues par fusion tardive basé sur un graphe bipartite. Le procédé consiste à : S11, acquérir une tâche de regroupement et un échantillon de données cible ; S12, effectuer un regroupement de k moyennes de noyau sur chaque vue correspondant à la tâche de regroupement acquise et à l'échantillon de données cible afin d'obtenir une division de base, puis calculer des termes réguliers diversifiés de chaque vue ; S13, sélectionner des points représentatifs de chaque vue en utilisant une initialisation aléatoire, puis établir une fonction cible de regroupement multi-vues par fusion tardive d'après un graphe bipartite ; S14, résoudre de façon circulaire la fonction cible de regroupement multi-vues par fusion tardive établie d'après un graphe bipartite afin d'obtenir un graphe bipartite après la fusion de la vue ; et S15, effectuer un regroupement spectral sur le graphe bipartite obtenu afin d'obtenir un résultat de regroupement. Au moyen de la présente demande, les points représentatifs optimisés peuvent représenter des informations d'une seule vue et mieux servir à la fusion de vues, de façon à ce qu'un graphe bipartite obtenu au moyen d'un apprentissage puisse mieux fusionner les informations de toutes les vues, ce qui permet d'améliorer une effet de regroupement.
PCT/CN2021/136557 2021-02-09 2021-12-08 Procédé et système d'apprentissage automatique de regroupement multi-vues par fusion tardive basés sur un graphe bipartite WO2022170840A1 (fr)

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