Structured SUMCOR Multiview Canonical Correlation Analysis for Large-Scale Data

TL;DR

This paper introduces a scalable computational framework for large-scale SUMCOR GCCA that incorporates structural regularization, enabling better performance in real-world data analytics while maintaining low memory usage and parallel implementation capabilities.

Contribution

The paper presents a novel algorithm for large-scale SUMCOR GCCA that integrates structural regularizers and is efficient, parallelizable, and converges to a KKT point.

Findings

Effective in handling large-scale data

Incorporates structural regularization

Converges to a KKT point

Abstract

The sum-of-correlations (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 CCA 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.