Abstract:
I will describe new, probabilistic algorithms for two classical machine learning problems of wide practical applicability: manifold learning (dimensionality reduction) and clustering.

An important recent application of manifold learning is the problem of tracking the articulated 3D pose of a moving person from monocular video. Here, a pose is represented by a large number of joint angles or 3D marker locations, but the feasible or typical poses actually live in a nonlinear manifold of much smaller dimension because of correlations induced by body constraints. I will describe a probabilistic manifold learning method called Laplacian Eigenmaps Latent Variable Model (LELVM). LELVM unifies two traditionally separate classes of methods, probabilistic and spectral, neatly combining the advantages of both; in particular, it yields nonparametric mappings and densities efficiently. I will show how an LELVM model learned from motion-capture data and combined with a particle filter is able to track people robustly in the presence of missing, noisy and ambiguous image measurements.

In the second part of the talk I will describe theoretical and practical results about the mean-shift algorithm and its varieties. Mean-shift is an algorithm for finding the modes of a kernel density estimate, and has attracted considerable attention in recent years in nonparametric clustering, mapping inversion and other problems. I'll show that mean-shift is an expectation-maximisation (EM) algorithm which converges linearly and is often very slow. I'll introduce a much faster algorithm called Gaussian blurring mean-shift (GBMS) which converges cubically, is related to spectral clustering, and achieves excellent clustering results. I will show that GBMS is the optimal case of a large family of mean-shift-like algorithms. I will illustrate the results in the problem of image segmentation.

Bio:
Miguel A. Carreira-Perpinan is an assistant professor at the Department of Computer Science & Electrical Engineering of OGI, Oregon Health & Science University. He received a PhD in Computer Science from the University of Sheffield, UK in 2001, and did postdoctoral work at Georgetown University and the University of Toronto. He is the recipient of an NSF CAREER award for machine learning approaches to articulatory inversion. His research interests lie in machine learning, with applications to speech processing, computer vision and computational neuroscience.