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Matrix Means, Distances, Kernels, and Geometric Optimization

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If you have a question about this talk, please contact Zoubin Ghahramani.

I will talk about a new distance function on hermitian positive definite (hpd) matrices that takes inspiration from both differential geometry and convex optimization. This distance function originally arose in a computer-vision application, but since then it took on a life of its own that is interesting enough to talk about.

In my talk, I will briefly describe the original application, followed by key results and wider mathematical connections of this distance function, e.g., to the theory of kernel functions on symmetric spaces; matrix theory; nonlinear matrix equations; symmetric polynomials in noncommutative variables, quantum information theory, and the expanding area of geometric optimization with hpd matrices. I will also mention a few challenging open problems.

This talk is part of the Machine Learning @ CUED series.

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