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Classification on the Grassmann Manifold: Performance Limits of Compressive Classifiers

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If you have a question about this talk, please contact Dr Ramji Venkataramanan.

The reliable classification of high-dimensional signals from low-dimensional measurements is an increasingly crucial task in the age of the data deluge. This talk demonstrates that tools and intuitions from Shannon theory enable the derivation of fundamental limits on the performance of such classification systems, by focusing on the classification of high-dimensional (rank-deficient) Gaussian signals from noisy, low-dimensional signal projections.

Leveraging the syntactic equivalence of discrimination between Gaussian classes and communication over vector wireless channels, bounds on classifier performance will be presented that are asymptotic in two regimes. First, the notion of classification capacity is introduced, which characterizes the number of classes that can be discriminated reliably as the signal dimensionality approaches infinity; tight bounds on the classification capacity associated with Gaussian classes are presented. Second, the notion of diversity-discrimination tradeoff is also introduced, which, by analogy with the diversity-multiplexing tradeoff of vector channels, characterizes the tradeoff between the misclassification probability and the number of discernible classes as the signal-to-noise ratio goes to infinity; again tight bounds on this tradeoff are also proven.

These results reveal that the “easiest” classes to discriminate correspond to (affine) subspaces drawn from an appropriate Grassmann manifold; they further reveal a precise relationship between signal and measurement geometry and classifier performance. Numerical results, including a face recognition application, validate this relationship in practice.

This represents joint work with Matthew Nokleby (Duke University, USA ) and Robert Calderbank (Duke University, USA )

BIO: Miguel Rodrigues is a Senior Lecturer with the Department of Electronic and Electrical Engineering, University College London, U.K. He was previously with the Department of Computer Science, University of Porto, Portugal, rising through the ranks from Assistant to Associate Professor, where he also led the Information Theory and Communications Research Group at Instituto de Telecomunicações – Porto. He received the Licenciatura degree in Electrical Engineering from the Faculty of Engineering of the University of Porto, Portugal in 1998 and the Ph.D. degree in Electronic and Electrical Engineering from University College London, UK in 2002. He has carried out postdoctoral research work both at Cambridge University, UK, as well as Princeton University, USA , in the period 2003 to 2007. He has also held visiting appointments at Princeton University, Duke University, Cambridge University, and University College London in the period 2007 to 2013.

His research interests are in the general areas of information theory, communications theory and statistical signal processing. He was the recipient of the IEEE Communications and Information Theory Societies Joint Paper Award in 2011 for the work on Wireless Information-Theoretic Security (with M. Bloch, J. Barros and S. W. McLaughlin).

This talk is part of the Signal Processing and Communications Lab Seminars series.

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