# Scalable and Flexible Multiview MAX-VAR Canonical Correlation Analysis

arXiv: https://arxiv.org/abs/1605.09459 · HTML: https://mlsanity.com/paper/1605.09459/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2016.

## Built on by (most cited first, 3 of 3)

- [Multi-Way Representation Alignment](https://mlsanity.com/paper/2602.06205/) (2026)
- [Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data](https://mlsanity.com/paper/2502.18756/) (2025)
- [Communication-Efficient Federated Linear and Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2109.12400/) (2021)

## Abstract (arXiv)

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.