Multiview canonical correlation analysis (MCCA) seeks latent low-dimensional representations encountered with multiview data of shared entities (a.k.a. common sources). However, existing MCCA approaches do not exploit the geometry of the common sources, which may be available a priori, or can be constructed using certain domain knowledge. This prior information about the common sources can be encoded by a graph, and be invoked as a regularizer to enrich the maximum variance MCCA framework. In this context, this paper's novel graph-regularized MCCA (GMCCA) approach minimizes the distance between the wanted canonical variables and the common low-dimensional representations, while accounting for graph-induced knowledge of the common sources. Relying on a function capturing the extent to which the low-dimensional representations of the multiple views are similar, a generalization bound of GMCCA is established based on Rademacher's complexity. Tailored for setups where the number of data pairs is smaller than the data vector dimensions, a graph-regularized dual MCCA approach is also developed. To further deal with nonlinearities present in the data, graph-regularized kernel MCCA variants are put forward too. Interestingly, solutions of the graph-regularized linear, dual, and kernel MCCA are all provided in terms of generalized eigenvalue decomposition. Several corroborating numerical tests using real datasets are provided to showcase the merits of the graph-regularized MCCA variants relative to several competing alternatives including MCCA, Laplacian-regularized MCCA, and (graph-regularized) PCA.
Bibliographical noteFunding Information:
Manuscript received November 26, 2018; revised March 9, 2019; accepted April 3, 2019. Date of publication April 11, 2019; date of current version April 26, 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Alexander Bertrand. This work was supported in part by the National Science Foundation under Grants 1500713, 1505970, 1514056, and 1711471. This paper was presented in part at the IEEE International Conference on Acoustics, Speech, and Signal Processing, Brighton, U.K., May 2019 . (Corresponding author: Georgios B. Giannakis.) The authors are with the Digital Technology Center and the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: firstname.lastname@example.org; email@example.com; firstname.lastname@example.org). Digital Object Identifier 10.1109/TSP.2019.2910475
© 1991-2012 IEEE.
- Dimensionality reduction
- Laplacian regularization
- canonical correlation analysis
- generalized eigen-decomposition
- multiview learning
- signal processing over graphs