Group Factor Analysis

TL;DR

This paper introduces a novel group factor analysis method that models relationships between variable groups, extending classical factor analysis and canonical correlation analysis with a hierarchical variational inference approach.

Contribution

It presents a new hierarchical variational inference model for group factor analysis that captures relationships between groups of variables and extends existing methods.

Findings

Outperforms existing factor analysis methods in accuracy

Successfully applied to brain activation data

Effectively analyzes high-dimensional biological data

Abstract

Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each group represents either a set of related variables or a data set. The model also naturally extends canonical correlation analysis to more than two sets, in a way that is more flexible than previous extensions. Our solution is formulated as variational inference of a latent variable model with structural sparsity, and it consists of two hierarchical levels: The higher level models the relationships between the groups, whereas the lower models the observed variables given the higher level. We show that the resulting solution solves the group factor analysis problem accurately, outperforming alternative factor analysis based solutions as well as more straightforward implementations of group factor analysis. The method is demonstrated on two life science data sets, one on brain activation and the other on systems biology, illustrating its applicability to the analysis of different types of high-dimensional data sources.