Fundamental Limits on the Classification of Gaussian Signals: Classification on the Grassmann Manifold

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• Matthew Nokleby, Duke University
• Wednesday 09 October 2013, 11:00-12:00
• Dennis Gabor Seminar Room (611), EEE Department.

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: The reliable classification of high-dimensional signals is an increasingly crucial task in the age of the data deluge. In this talk, I argue that tools and intuitions from information theory enable the derivation of fundamental limits on the performance of such classification systems. My focus is the classification of high-dimensional Gaussian signals from noisy, low-dimensional signal projections. Leveraging the syntactic equivalence of discrimination between Gaussian classes and communication over vector wireless channels, I derive asymptotic bounds on classifier performance. First, I prove outer bounds on the number of classes that can be discriminated with low probability of error as the signal dimensionality goes to infinity. Second, I prove inner and outer bounds on the relationship between the number of classes to be discriminated and the probability of classification error as the signal-to-noise ratio goes to infinity. The proofs reveal that the “easiest” classes to discriminate have covariance matrices that correspond to subspaces drawn from an appropriate Grassmann manifold—an observation with implications for dictionary learning.

Biography: Matthew Nokleby is a postdoctoral fellow at Duke University in Durham, NC, USA . He received the B.S. and M.S. from Brigham Young University in 2006 and 2008, respectively, and the Ph.D. from Rice University in 2012, all in Electrical Engineering. His research interests include information theory for wireless communications, sensor networks, and machine learning.

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