Multi-channel factor analysis: properties, extensions, and applications

Abstract

Multi-channel Factor Analysis (MFA) extends factor analysis to the multi-channel or multi-view setting, where latent common factors influence all channels while distinct factors are specific to individual channels. The within- and across-channel covariance is determined by a low-rank matrix, a block-diagonal matrix with low-rank blocks, and a diagonal matrix, which provides a parsimonious model for both covariances. MFA and related multi-channel methods for data fusion are discussed in Chapter 1. Under conditions on the channel sizes and factor numbers, the results of Chapter 2 show that the generic global identifiability of the aforementioned covariance matrices can be guaranteed a priori, and the estimators obtained by maximizing a Gaussian likelihood are shown to be consistent and asymptotically normal even under misspecification. To handle temporal correlation in the latent factors, Chapter 3 introduces Multi-channel Factor Spectral Analysis (MFSA). Results for the identifiability and parameterization properties of the MFSA spectral density model are derived, and a Majorization-Minimization procedure to optimize the Whittle pseudo-likelihood is designed to estimate the MFSA parameters. A simulation study is conducted to explore how temporal correlations in the latent factors affect estimation, and it is demonstrated that MFSA significantly outperforms MFA when the factor series are highly autocorrelated. In Chapter 4, a locally stationary joint multivariate Gaussian process with MFA-type cross-sectional covariance is developed to model multi-vehicle trajectories in a highway environment. A dynamic model-based clustering procedure is designed to partition cohorts of nearby vehicles into pods based on the stability of the intra-pod relative vehicle configuration. The performance of this procedure is illustrated by its application to the Next GENeration SIMulation dataset of vehicle trajectories on U.S. Highway 101.