Fast SDP Relaxations of Graph Cut Clustering, Transduction, and Other Combinatorial Problem

The rise of convex programming has changed the face of many research fields in recent years, machine learning being one of the ones that benefitted the most. A very recent developement, the relaxation of combinatorial problems to semi-definite programs (SDP), has gained considerable attention over the last decade (Helmberg, 2000; De Bie and Cristianini, 2004a). Although SDP problems can be solved in polynomial time, for many relaxations the exponent in the polynomial complexity bounds is too high for scaling to large problem sizes. This has hampered their uptake as a powerful new tool in machine learning. In this paper, we present a new and fast SDP relaxation of the normalized graph cut problem, and investigate its usefulness in unsupervised and semi-supervised learning. In particular, this provides a convex algorithm for transduction, as well as approaches to clustering. We further propose a whole cascade of fast relaxations that all hold the middle between older spectral relaxation...

• Type: Journal
• Year: 2006
• Where: JMLR
• Authors: Tijl De Bie, Nello Cristianini
• Keywords: Combinatorial Problems, Fast Sdp Relaxation, JMLR 2006, SDP Relaxation