Canonical Correlation Analysis With L2,1-Norm for Multiview Data Representation

For many machine learning algorithms, their success heavily depends on data representation. In this paper, we present an ${\ell }_{2,1}$ -norm constrained canonical correlation analysis (CCA) model, that is, $ {L}_{{2,1}}$ -CCA, toward discovering compact and discriminative representation for the data associated with multiple views. To well exploit the complementary and coherent information across multiple views, the ${\ell }_{{2,1}}$ -norm is employed to constrain the canonical loadings and measure the canonical correlation loss term simultaneously. It enables, on the one hand, the canonical loadings to be with the capacity of variable selection for facilitating the interpretability of the learned canonical variables, and on the other hand, the learned canonical common representation keeps highly consistent with the most canonical variables from each view of the data. Meanwhile, the proposed ${L}_{{2,1}}$ -CCA can also be provided with the desired insensitivity to noise (outliers) to some degree. To solve the optimization problem, we develop an efficient alternating optimization algorithm and give its convergence analysis both theoretically and experimentally. Considerable experiment results on several real-world datasets have demonstrated that ${L}_{{2,1}}$ -CCA can achieve competitive or better performance in comparison with some representative approaches for multiview representation learning.