Unsupervised Dimension Reduction via Maximization of a Non-Gaussian Likelihood

• Activity Number: 334
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Benjamin Risk*+ and David Scott Matteson and David Ruppert
• Companies: and Cornell University and Cornell University
• Keywords: neuroimaging ; resting-state fMRI ; independent component analysis ; principal component analysis ; ProDenICA ; projection pursuit

Abstract

The use of principal component analysis (PCA) for dimension reduction is popular in the natural, physical, and social sciences. However, it has long been recognized that directions containing the most variance, as recovered by PCA, may not be the most relevant for many scientific problems. In contrast to PCA, independent component analysis (ICA) estimates directions that maximize some measure of non-Gaussianity. Despite different objectives, PCA is often used as a prewhitening step to noise-free ICA such that ICA is performed on the principal subspace. We present a model wherein latent and noise components have tilted Gaussian and Gaussian densities, respectively. In contrast to ICA, we represent data on a lower-dimensional subspace that maximizes the non-Gaussian likelihood rather than variance. The model can be viewed as a probabilistic formulation of projection pursuit or as a noisy ICA model with an alternative error structure. The tilt function of each latent density is estimated using cubic B-splines. We apply our method to an fMRI experiment in social cognition from the Human Connectome Project, and we recover brain networks whose loadings are correlated with the task.