A0306
Title: Modeling and learning on high-dimensional matrix-variate sequences
Authors: Xu Zhang - South China Normal University (China) [presenting]
Catherine Liu - The Hong Kong Polytechnic University (Hong Kong)
Jianhua Guo - Beijing Technology and Business University (China)
KC Yuen - HKU (China)
Alan Welsh - the Australian National University (Australia)
Abstract: A new matrix factor model named RaDFaM is proposed, which is strictly derived based on the general rank decomposition, and a structure of a high-dimensional vector factor model for each basis vector is assumed. RaDFaM contributes a novel class of low-rank latent structure that makes a tradeoff between signal intensity and dimension reduction from the perspective of tensor subspace. Based on the intrinsic separable covariance structure of RaDFaM, for a collection of matrix-valued observations, a new class of PCA variants is derived to estimate loading matrices and the latent factor matrices sequentially. The peak signal-to-noise ratio of RaDFaM has been proven to be superior in the category of PCA-type estimations. The asymptotic theory is also established, including the consistency, convergence rates, and asymptotic distributions for components in the signal part. Numerically, the performance of RaDFaM is demonstrated in applications such as matrix reconstruction, supervised learning, and clustering on uncorrelated and correlated data, respectively.
