Subspace Identifiability From Canonical Projections and Convergence Analysis of Canonical Correlation Analysis

Consider a generic r-dimensional subspace, and suppose that we are only given projections of this subspace onto small subsets of the canonical coordinates.
In this talk I will show the necessary and sufficient conditions on such subsets to guarantee that there is only one r-dimensional subspace
consistent with all the projections.
I will also explain how our main result can be used to obtain new guarantees for the well-known low-rank matrix completion problem, that do not require the usual incoherence nor sampling assumptions.

and

Canonical correlation analysis (CCA) is a classical statistical technique to measure associations among two sets of random variables, with applications to several fields like medicine, language processing, multimodal signal processing and machine learning. In this talk, we first provide a direct and general formulation of CCA. We next present theoretical results for estimating the canonical correlation directions and the associated projection operators. Our results are based on certain concentration inequalities for the sample covariance and sample cross-covariance operators which maybe of independent interest.

November 5 @ 12:30
12:30 pm (1h)

Discovery Building, Orchard View Room

Daniel L. Pimentel-Alarcón, Krishna Kumar