Sparse canonical correlation analysis: New formulation and algorithm

Delin Chu, Lizhi Liao, Kwok Po Ng, Xiaowei Zhang

Research output: Contribution to journalJournal articlepeer-review

90 Citations (Scopus)


In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms.

Original languageEnglish
Article number6520858
Pages (from-to)3050-3065
Number of pages16
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number12
Publication statusPublished - Dec 2013

Scopus Subject Areas

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

User-Defined Keywords

  • canonical correlation analysis
  • linear discriminant analysis
  • multivariate data
  • orthogonality
  • Sparsity


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