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Activity Number: 594 - Methods for Analysis of High-Dimensional Data
Type: Contributed
Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #326989
Title: The Two-To-Infinity Norm and Singular Subspace Geometry with Applications to High-Dimensional Statistics
Author(s): Joshua Cape* and Minh Tang and Carey E Priebe
Companies: Johns Hopkins; Dept. of Applied Math and Statistics and Johns Hopkins University and Johns Hopkins University
Keywords: high-dimensional statistics; dimension reduction; singular value decomposition; spectral methods; perturbation theory

The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric structure of singular values and singular vectors. We provide a novel collection of technical and theoretical tools for studying the geometry of singular subspaces using the two-to-infinity norm. Motivated by preliminary deterministic Procrustes analysis, we consider a general matrix perturbation setting in which we derive a new Procrustean matrix decomposition. Together with flexible machinery developed for the two-to-infinity norm, this allows for a refined analysis of the induced perturbation geometry with respect to the underlying singular vectors even in the presence of singular value multiplicity. Our analysis yields perturbation bounds for a range of popular matrix noise models, each of which has a meaningful associated statistical inference task. Specific applications include the problem of covariance estimation, singular subspace recovery, and multiple graph inference.

Authors who are presenting talks have a * after their name.

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