Total Variation Data Analysis - A Non-linear Spectral Framework for Machine Learning
Time and place
1 PM on Thursday, February 13th, 2014; NAC 6113
Xavier Bresson (University of Lausanne)
Abstract
With enormous and daily flows of data in finance, security, health, social network and multimedia (sound/text/image/video), there is a strong need to process information as efficiently as possible for smart decisions to be made. Machine Learning develops analytical methods and strong algorithms to deal with this massive large-scale, multi-dimensional and multi-modal 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 excellent approximate 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. This new total variation clustering technique paves the way to a new generation of learning algorithms that can provide simultaneously accurate, fast and robust solutions to other fundamental problems in data science such as Support Vector Machine data classification. These new methodologies have a wide range of applications including data retrieval (search engines), neuroimaging (diseases detection and analysis) and social network analysis (community detection).
