SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

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

Daniel L. Pimentel-AlarcĂłn and Krishna Kumar,

Date and Time: Nov 05, 2014 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

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.