SimpleMKKM: Simple Multiple Kernel K-Means

We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given by an intractable minimization-maximization problem in the k...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 45; no. 4; pp. 5174 - 5186
Main Author: Liu, Xinwang
Format: Journal Article
Language:English
Published: United States IEEE 01.04.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Ablation
Algorithms
Clustering
Clustering algorithms
Criteria
Kernel
kernel alignment maximization
Kernels
Linear programming
Matrix partitioning
Maximization
Minimization
Multi-view clustering
multiple kernel clustering
Optimization
Partitioning algorithms
Source code
Task analysis
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
Online Access:Get full text
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Summary:We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given by an intractable minimization-maximization problem in the kernel coefficient and clustering partition matrix. To optimize it, we equivalently rewrite the minimization-maximization formulation as a minimization of an optimal value function, prove its differenentiablity, and design a reduced gradient descent algorithm to decrease it. Furthermore, we prove that the resultant solution of SimpleMKKM is the global optimum . We theoretically analyze the performance of SimpleMKKM in terms of its clustering generalization error. After that, we develop extensive experiments to investigate the proposed SimpleMKKM from the perspectives of clustering accuracy, advantage on the formulation and optimization, variation of the learned consensus clustering matrix with iterations, clustering performance with varied number of samples and base kernels, analysis of the learned kernel weight, the running time and the global convergence. The experimental study demonstrates the effectiveness of the proposed SimpleMKKM by considerably and consistently outperforming state of the art multiple kernel clustering alternatives. In addition, the ablation study shows that the improved clustering performance is contributed by both the novel formulation and new optimization. Our work provides a more effective approach to integrate multi-view data for clustering, and this could trigger novel research on multiple kernel clustering. The source code and data for SimpleMKKM are available at https://github.com/xinwangliu/SimpleMKKMcodes/ .
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2022.3198638