Nonlinear adaptive distance metric learning for clustering

Jianhui Chen, Zheng Zhao, Jieping Ye, Huan Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

50 Scopus citations

Abstract

A good distance metric is crucial for many data mining tasks. To learn a metric in the unsupervised setting, most metric learning algorithms project observed data to a low-dimensional manifold, where geometric relationships such as pairwise distances are preserved. It can be extended to the nonlinear case by applying the kernel trick, which embeds the data into a feature space by specifying the kernel function that computes the dot products between data points in the feature space. In this paper, we propose a novel unsupervised Nonlinear Adaptive Metric Learning algorithm, called NAML, which performs clustering and distance metric learning simultaneously. NAML firstmaps the data to a high-dimensional space through a kernel function; then applies a linear projection to find a low-dimensional manifold where the separability of the data is maximized; and finally performs clustering in the low-dimensional space. The performance of NAML depends on the selection of the kernel function and the projection. We show that the joint kernel learning, dimensionality reduction, and clustering can be formulated as a trace maximization problem, which can be solved via an iterative procedure in the EM framework. Experimental results demonstrated the efficacy of the proposed algorithm.

Original languageEnglish (US)
Title of host publicationKDD-2007
Subtitle of host publicationProceedings of the Thirteenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Pages123-132
Number of pages10
DOIs
StatePublished - Dec 14 2007
EventKDD-2007: 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - San Jose, CA, United States
Duration: Aug 12 2007Aug 15 2007

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Other

OtherKDD-2007: 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
CountryUnited States
CitySan Jose, CA
Period8/12/078/15/07

Keywords

  • Clustering
  • Convex programming
  • Distance metric
  • Kernel

ASJC Scopus subject areas

  • Software
  • Information Systems

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  • Cite this

    Chen, J., Zhao, Z., Ye, J., & Liu, H. (2007). Nonlinear adaptive distance metric learning for clustering. In KDD-2007: Proceedings of the Thirteenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 123-132). (Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining). https://doi.org/10.1145/1281192.1281209