Multiple Kernel k-Means with Incomplete Kernels

Xinwang Liu, Xinzhong Zhu, Miaomiao Li, Lei Wang, En Zhu, Tongliang Liu, Marius Kloft, Dinggang Shen, Jianping Yin, Wen Gao

Research output: Contribution to journalArticlepeer-review

240 Citations (Scopus)


Multiple kernel clustering (MKC) algorithms optimally combine a group of pre-specified base kernel matrices to improve clustering performance. However, existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernel matrices are absent. This paper proposes two simple yet effective algorithms to address this issue. Different from existing approaches where incomplete kernel matrices are first imputed and a standard MKC algorithm is applied to the imputed kernel matrices, our first algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernel matrices, which are treated as auxiliary variables to be jointly optimized. Our algorithm does not require that there be at least one complete base kernel matrix over all the samples. Also, it adaptively imputes incomplete kernel matrices and combines them to best serve clustering. Moreover, we further improve this algorithm by encouraging these incomplete kernel matrices to mutually complete each other. The three-step iterative algorithm is designed to solve the resultant optimization problems. After that, we theoretically study the generalization bound of the proposed algorithms. Extensive experiments are conducted on 13 benchmark data sets to compare the proposed algorithms with existing imputation-based methods. Our algorithms consistently achieve superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering.

Original languageEnglish
Article number8611131
Pages (from-to)1191-1204
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number5
Publication statusPublished - 2020 May 1

Bibliographical note

Publisher Copyright:
© 1979-2012 IEEE.


  • Multiple kernel clustering
  • incomplete kernel learning
  • multiple view learning

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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