Regularized Consensus PCA

TL;DR

This paper introduces a flexible framework for multiblock PCA methods using regularized consensus PCA, which unifies various existing techniques and provides an efficient gradient algorithm for solution convergence.

Contribution

It proposes a novel regularized consensus PCA framework that generalizes multiple multiblock component methods through a unified optimization scheme.

Findings

Unified framework for multiblock PCA methods.

Gradient algorithm for convergence to stationary solutions.

Recovery of existing methods for specific parameter choices.

Abstract

A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of all blocks. Regularized consensus PCA is obtained by applying regularized generalized canonical correlation analysis to this scheme for the function $g(x) = x^m$ where $m \ge 1$. A gradient algorithm is proposed. At convergence, a solution of the stationary equation related to the optimization problem is obtained. For m = 1, 2 or 4 and shrinkage constants equal to 0 or 1, many multiblock component methods are recovered.