Efficient Dimensionality Reduction for Canonical Correlation Analysis

TL;DR

This paper introduces a fast, randomized algorithm for approximate Canonical Correlation Analysis that reduces computational complexity while providing provable guarantees on the approximation quality.

Contribution

It proposes a novel dimensionality reduction approach combined with existing CCA algorithms to achieve faster approximate solutions with theoretical guarantees.

Findings

Reduces computational complexity compared to exact algorithms

Provides provable approximation guarantees

Applicable to large, tall-and-thin matrices

Abstract

We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input matrices, and then applies any CCA algorithm to the new pair of matrices. The algorithm computes an approximate CCA to the original pair of matrices with provable guarantees, while requiring asymptotically less operations than the state-of-the-art exact algorithms.