Scalable and Flexible Multiview MAX-VAR Canonical Correlation Analysis

TL;DR

This paper introduces a scalable, regularized MAX-VAR GCCA algorithm that efficiently handles large-scale, multi-view data with structural constraints, improving convergence and applicability in multilingual and speech processing tasks.

Contribution

It proposes an alternating optimization algorithm for regularized MAX-VAR GCCA that is scalable, handles structural constraints, and guarantees convergence to critical points.

Findings

The algorithm converges globally to a critical point at a sublinear rate.

It approaches a global optimum at a linear rate without regularization.

Experiments demonstrate effectiveness on large-scale word embedding tasks.

Abstract

Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that handles a single view, (G)CCA is able to integrate information from different feature spaces. Here we focus on MAX-VAR GCCA, a popular formulation which has recently gained renewed interest in multilingual processing and speech modeling. The classic MAX-VAR GCCA problem can be solved optimally via eigen-decomposition of a matrix that compounds the (whitened) correlation matrices of the views; but this solution has serious scalability issues, and is not directly amenable to incorporating pertinent structural constraints such as non-negativity and sparsity on the canonical components. We posit regularized MAX-VAR GCCA as a non-convex optimization problem and propose an alternating optimization (AO)-based algorithm to handle it. Our algorithm alternates between {\em inexact} solutions of a regularized least squares subproblem and a manifold-constrained non-convex subproblem, thereby achieving substantial memory and computational savings. An important benefit of our design is that it can easily handle structure-promoting regularization. We show that the algorithm globally converges to a critical point at a sublinear rate, and approaches a global optimal solution at a linear rate when no regularization is considered. Judiciously designed simulations and large-scale word embedding tasks are employed to showcase the effectiveness of the proposed algorithm.