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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| Published in: | IEEE transactions on pattern analysis and machine intelligence Vol. 45; no. 4; pp. 5174 - 5186 |
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| Format: | Journal Article |
| Language: | English |
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United States
IEEE
01.04.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0162-8828, 1939-3539, 2160-9292, 1939-3539 |
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| Abstract | 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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| AbstractList | 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/. 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/.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/. |
| Author | Liu, Xinwang |
| Author_xml | – sequence: 1 givenname: Xinwang orcidid: 0000-0001-9066-1475 surname: Liu fullname: Liu, Xinwang email: xinwangliu@nudt.edu.cn organization: College of Computer, National University of Defense Technology, Changsha, China |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/35969570$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1109/TPAMI.2019.2895608 10.1609/aaai.v30i1.10249 10.1023/A:1012450327387 10.7551/mitpress/1120.003.0052 10.1162/NECO_a_00872 10.1109/TPAMI.2020.3001433 10.1109/TPAMI.2018.2879108 10.1109/TPAMI.2018.2847335 10.1109/tpami.2019.2892416 10.1016/j.patcog.2014.05.005 10.1109/TFUZZ.2011.2170175 10.1109/TPAMI.2020.3011148 10.1137/S0036144596302644 10.1137/1.9781611972795.55 10.1109/TPAMI.2011.255 10.1109/tpami.2021.3116948 10.1109/ICCV48922.2021.00916 10.1609/aaai.v31i1.10895 10.24963/ijcai.2019/524 10.1109/TIT.2010.2069250 10.1109/TPAMI.2020.3037734 10.1109/TPAMI.2020.2974828 10.1609/aaai.v31i1.10893 10.1109/ICDM.2012.43 |
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| References | ref13 Gönen (ref6) ref34 ref15 Cortes (ref36) ref14 Kloft (ref22) 2011; 12 ref31 ref30 ref11 ref33 ref10 ref32 ref2 ref1 ref17 Kumar (ref9) ref19 ref18 Rakotomamonjy (ref28) 2008; 9 Kloft (ref35) 2012; 13 Bang (ref16) 2018 Cortes (ref24) 2012; 13 Li (ref12) Kumar (ref8) ref26 ref25 ref20 ref21 Cortes (ref23) ref27 ref29 ref4 ref3 ref5 Peng (ref7) |
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| SubjectTerms | 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 |
| Title | SimpleMKKM: Simple Multiple Kernel K-Means |
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