Common component analysis for multiple covariance matrices

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

7 Scopus citations

Abstract

We consider the problem of finding a suitable common low dimensional subspace for accurately representing a given set of covariance matrices. With one covariance matrix, this is principal component analysis (PCA). For multiple covariance matrices, we term the problem Common Component Analysis (CCA).While CCA can be posed as a tensor decomposition problem, standard approaches to tensor decompositions have two critical issues: (i) tensor decomposition methods are iterative and rely on the initialization; (ii) for a given level of approximation error, it is difficult to choose a suitable low dimensionality. In this paper, we present a detailed analysis of CCA that yields an effective initialization and iterative algorithms for the problem. The proposed methodology has provable approximation guarantees w.r.t. the global maximum and also allows one to choose the dimensionality for a given level of approximation error. We also establish conditions under which the methodology will achieve the global maximum. We illustrate the effectiveness of the proposed method through extensive experiments on synthetic data as well as on two real stock market datasets, where major financial events can be visualized in low dimensions.

Original languageEnglish (US)
Title of host publicationProceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD'11
Pages956-964
Number of pages9
DOIs
StatePublished - 2011
Event17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD'11 - San Diego, CA, United States
Duration: Aug 21 2011Aug 24 2011

Publication series

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

Other

Other17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD'11
CountryUnited States
CitySan Diego, CA
Period8/21/118/24/11

Keywords

  • Dimensionality reduction
  • Parafac
  • Pca
  • Tensor decompositions
  • Tucker

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