The sum-of-correlation (SUMCOR) formulation of generalized canonical correlation analysis (GCCA) seeks highly correlated low-dimensional representations of different views via maximizing pairwise latent similarity of the views. SUMCOR is considered arguably the most natural extension of classical two-view canonical correlation analysis to the multiview case and, thus, has numerous applications in signal processing and data analytics. Recent work has proposed effective algorithms for handling the SUMCOR problem at very large scale. However, the existing scalable algorithms cannot incorporate structural regularization and prior information-which are critical for good performance in real-world applications. In this work, we propose a new computational framework for large-scale SUMCOR GCCA that can easily incorporate a suite of structural regularizers, which are frequently used in data analytics. The updates of the proposed algorithm are lightweight, and the memory complexity is also low. In addition, the proposed algorithm can be readily implemented in a parallel fashion. We show that the proposed algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the regularized SUMCOR problem. Judiciously designed simulations and real-data experiments are employed to demonstrate the effectiveness of the proposed algorithm.
Bibliographical noteFunding Information:
Manuscript received December 30, 2017; revised June 22, 2018 and October 1, 2018; accepted October 2, 2018. Date of publication October 29, 2018; date of current version December 5, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Athanasios A. Rontogiannis. The work of C. I. Kanatsoulis, X. Fu and N. D. Sidiropoulos was supported in part by the National Science Foundation (NSF) under projects NSF ECCS 1808159, NSF ECCS 1608961 and NSF IIS-1447788. The work of M. Hong was supported in part by the NSF under Grant CMMI-1727757 and Grant CCF-1526078, and in part by the Air Force Office of Scientific Research under Grant 15RT0767. (Corresponding author: Nicholas D. Sidiropoulos.) C. I. Kanatsoulis and M. Hong are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,email@example.com; firstname.lastname@example.org).
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- Canonical correlation analysis (CCA)
- cross-modality retrieval
- feature selection
- multiview CCA