Department of Mathematics
Sparse canonical correlation analysis: New formulation and algorithm
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. © 2013 IEEE.
canonical correlation analysis, linear discriminant analysis, multivariate data, orthogonality, Sparsity
Source Publication Title
IEEE Transactions on Pattern Analysis and Machine Intelligence
Institute of Electrical and Electronics Engineers
Link to Publisher's Edition
Chu, Delin, Li-Zhi Liao, Michael K. Ng, and Xiaowei Zhang. "Sparse canonical correlation analysis: New formulation and algorithm." IEEE Transactions on Pattern Analysis and Machine Intelligence 35.12 (2013): 3050-3065.