Abstract: Canonical correlation analysis (CCA) is a classic tool in statistics and machine learning. It is used to mine for pairs of highly correlated random variables that are mixed in two datasets. CCA is widely used and arguably the most important example of multiview analysis. At the same time, CCA and its generalizations exhibit remarkable richness and depth - including fundamental open questions - when examined from different points of view, which are often missed. For example, under what conditions will CCA recover a random variable that is linearly mixed in all the views? In this talk, we will explore the fundamental concepts and principles of CCA, and discuss practical applications including wireless communications (spectrum reuse / underlay; cell-edge detection) and fMRI (multi-subject common task-related spatio-temporal response recovery). We will focus on an algebraic interpretation of CCA, through a natural generative model that links CCA to coupled matrix factorization and sheds new light on CCA identifiability and algorithms. Easy to check identifiability conditions will be discussed, along with an algebraic interpretation of CCA as (approximate) subspace intersection. Time permitting, we will also discuss nonlinear (``deep'') CCA from a multilinear algebra / probabilistic graphical model point of view.

Short Bio: Nicholas D. Sidiropoulos (Fellow, IEEE) received the Diploma in electrical engineering from the Aristotle University of Thessaloniki, Thessaloniki, Greece, and the M.S. and Ph.D. degrees in electrical engineering from the University of Maryland at College Park, College Park, MD, USA, in 1988, 1990, and 1992, respectively. He is the Louis T. Rader Professor with the Department of ECE, University of Virginia. He has previously served as a Faculty with the University of Minnesota and the Technical University of Crete, Greece. His research interests are in signal processing, communications, optimization, tensor decomposition, and machine learning. He received the NSF/CAREER award in 1998, IEEE Signal Processing Society (SPS) Best Paper Award for 2001, 2007, 2011, and 2022, and the IEEE SPS Donald G. Fink Overview Paper Award for 2022. He served as a IEEE SPS Distinguished Lecturer (2008–2009), the Vice President—Membership of the IEEE SPS (2017–2019), and the Chair of the SPS Fellow Evaluation Committee (2020–2021). He received the 2010 IEEE SPS Meritorious Service Award, the 2013 Distinguished Alumni Award of the ECE Department, University of Maryland, the 2022 EURASIP Technical Achievement Award, and the 2022 IEEE SPS Claude Shannon–Harry Nyquist Technical Achievement Award. He is a fellow of EURASIP (2014).