Linear Non-Gaussian Component Analysis via Maximum Likelihood

TL;DR

This paper introduces likelihood component analysis (LCA), a novel method for linear non-Gaussian component analysis that improves over PCA+ICA by simultaneously reducing dimensions and estimating latent components, revealing hidden features in complex data.

Contribution

The paper proposes LCA, a new scalable likelihood-based method for linear non-Gaussian component analysis that orders components by likelihood, not variance, and demonstrates its effectiveness in simulations and real data.

Findings

LCA recovers latent components discarded by PCA+ICA.

LCA reveals features in data not visible with PCA or PCA+ICA.

LCA identifies artifacts in fMRI data missed by traditional methods.

Abstract

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate this model, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation are achieved simultaneously. Our method orders components by their marginal likelihood rather than ordering components by variance as in PCA. We present a parametric LCA using the logistic density and a semi-parametric LCA using tilted Gaussians with cubic B-splines. Our algorithm is scalable to datasets common in applications (e.g., hundreds of thousands of observations across hundreds of variables with dozens of latent components). In simulations, latent components are recovered that are discarded by PCA+ICA methods. We apply our method to multivariate data and demonstrate that LCA is a useful data visualization and dimension reduction tool that reveals features not apparent from PCA or PCA+ICA. We also apply our method to an fMRI experiment from the Human Connectome Project and identify artifacts missed by PCA+ICA. We present theoretical results on identifiability of the linear non-Gaussian component model and consistency of LCA.