Description:

High-order Singular Value Decomposition

Anru Zhang, Eugene Anson Stead, Jr. M.D. Associate Professor, Departments of Biostatistics & Bioinformatics, Computer Science, Mathematics, and Statistical Science, Duke University

Abstract: The analysis of high-order data, i.e., arrays with multiple directions, is motivated by a wide range of scientific applications and has become an important interdisciplinary topic in data science. In this talk, we discuss how to perform SVD on general tensors or tensors with structural assumptions, e.g., sparsity, smoothness, and longitudinality. Through the developed frameworks, we can achieve accurate denoising for 4D scanning transmission electron microscopy images; in longitudinal microbiome studies, we can extract key components in the trajectories of bacterial abundance, identify representative bacterial taxa for these key trajectories, and group subjects based on the change of bacteria abundance over time. We also illustrate how we develop new statistically optimal methods and computationally efficient algorithms that exploit useful information from high-dimensional high-order data based on the modern theories of computation and non-convex optimization.