Significant progress in clustering has been achieved by algorithms that are based on pairwise affinities between the datapoints. In particular, spectral clustering methods have the advantage of being able to divide arbitrarily shaped clusters and are based on efficient eigenvector calculations. However, spectral methods lack a straightforward probabilistic interpretation which makes it difficult to automatically set parameters using training data. In this paper we use the previously proposed typical cut framework for pairwise clustering. We show an equivalence between calculating the typical cut and inference in an undirected graphical model. We show that for clustering problems with hundreds of datapoints exact inference may still be possible. For more complicated datasets, we show that loopy belief propagation (BP) and generalized belief propagation (GBP) can give excellent results on challenging clustering problems. We also use graphical models to derive a learning algorithm for affinity matrices based on labeled data.

The detection and pose estimation of people in images and video is made challenging by the variability of human appearance, the complexity of natural scenes, and the high dimensionality of articulated body models. To cope with these problems we represent the 3D human body as a graphical model in which the relationships between the body parts are represented by conditional probability distributions. We formulate the pose estimation problem as one of probabilistic inference over a graphical model where the random variables correspond to the individual limb parameters (position and orientation). Because the limbs are described by 6-dimensional vectors encoding pose in 3-space, discretization is impractical and the random variables in our model must be continuousvalued. To approximate belief propagation in such a graph we exploit a recently introduced generalization of the particle filter. This framework facilitates the automatic initialization of the body-model from low level cues and is robust to occlusion of body parts and scene clutter.

We present and empirically test a novel approach for categorizing 3-D free form object shapes represented by range data. In contrast to traditional surface-signature based systems that use alignment to match specific objects, we adapted the newly introduced symbolic-signature representation to classify deformable shapes [10]. Our approach constructs an abstract description of shape classes using an ensemble of classifiers that learn object class parts and their corresponding geometrical relationships from a set of numeric and symbolic descriptors. We used our classification engine in a series of large scale discrimination experiments on two well-defined classes that share many common distinctive features. The experimental results suggest that our method outperforms traditional numeric signature-based methodologies.

The problem of "Structure From Motion" is a central problem in vision: given the 2D locations of certain points we wish to recover the camera motion and the 3D coordinates of the points. Under simplified camera models, the problem reduces to factorizing a measurement matrix into the product of two low rank matrices. Each element of the measurement matrix contains the position of a point in a particular image. When all elements are observed, the problem can be solved trivially using SVD, but in any realistic situation many elements of the matrix are missing and the ones that are observed have a different directional uncertainty. Under these conditions, most existing factorization algorithms fail while human perception is relatively unchanged. In this paper we use the well known EM algorithm for factor analysis to perform factorization. This allows us to easily handle missing data and measurement uncertainty and more importantly allows us to place a prior on the temporal trajectory of the latent variables (the camera position). We show that incorporating this prior gives a significant improvement in performance in challenging image sequences.

Existing source location and recovery algorithms used in magnetoencephalographic imaging generally assume that the source activity at different brain locations is independent or that the correlation structure is known. However, electrophysiological recordings of local field potentials show strong correlations in aggregate activity over significant distances. Indeed, it seems very likely that stimulus-evoked activity would follow strongly correlated time-courses in different brain areas. Here, we present, and validate through simulations, a new approach to source reconstruction in which the correlation between sources is modelled and estimated explicitly by variational Bayesian methods, facilitating accurate recovery of source locations and the time-courses of their activation.

We propose a functional mixture model for simultaneous clustering and alignment of sets of curves measured on a discrete time grid. The model is specifically tailored to gene expression time course data. Each functional cluster center is a nonlinear combination of solutions of a simple linear differential equation that describes the change of individual mRNA levels when the synthesis and decay rates are constant. The mixture of continuous time parametric functional forms allows one to (a) account for the heterogeneity in the observed profiles, (b) align the profiles in time by estimating real-valued time shifts, (c) capture the synthesis and decay of mRNA in the course of an experiment, and (d) regularize noisy profiles by enforcing smoothness in the mean curves. We derive an EM algorithm for estimating the parameters of the model, and apply the proposed approach to the set of cycling genes in yeast. The experiments show consistent improvement in predictive power and within cluster variance compared to regular Gaussian mixtures.

The classifiers are based on dyadic classification trees (DCTs), which involve adaptively pruned partitions of the feature space. A key aspect of DCTs is their spatial adaptivity, which enables local (rather than global) fitting of the decision boundary. Our risk analysis involves a spatial decomposition of the usual concentration inequalities, leading to a spatially adaptive, data-dependent pruning criterion. For any distribution on (X, Y) whose Bayes decision boundary behaves locally like a Lipschitz smooth function, we show that the DCT error converges to the Bayes error at a rate within a logarithmic factor of the minimax optimal rate.

We present the software architecture of a robotic system for mapping abandoned mines. The software is capable of acquiring consistent 2D maps of large mines with many cycles, represented as Markov random £elds.

We propose an approach to learning the semantics of images which allows us to automatically annotate an image with keywords and to retrieve images based on text queries. We do this using a formalism that models the generation of annotated images. We assume that every image is divided into regions, each described by a continuous-valued feature vector. Given a training set of images with annotations, we compute a joint probabilistic model of image features and words which allow us to predict the probability of generating a word given the image regions. This may be used to automatically annotate and retrieve images given a word as a query. Experiments show that our model significantly outperforms the best of the previously reported results on the tasks of automatic image annotation and retrieval.

Autonomous helicopter flight represents a challenging control problem, with complex, noisy, dynamics. In this paper, we describe a successful application of reinforcement learning to autonomous helicopter flight.