Total Variation Data Analysis - A Non-linear Spectral Framework for Machine Learning
Xavier Bresson

Seminar • 12 January 2015 • BIG 4.235

Abstract
Machine Learning develops algorithms to identify patterns in large-scale and multi-dimensional data. This field has recently seen tremendous advances with the emergence of new powerful techniques combining the key mathematical tools of sparsity, convex optimization and relaxation methods. In this talk, I will present how these concepts can be applied to find tight solutions of NP-hard balanced cut problems for unsupervised data clustering, significantly overcoming state-of-the-art spectral clustering methods including Shi-Malik's normalized cut. I will also show how to design fast algorithms for the proposed non-convex and non-differentiable optimization problems based on recent breakthroughs in total variation optimization problems borrowed from the compressed sensing field.