One of the intuitions underlying many graph-based methods for clustering and semi-supervised learning, is that class or cluster boundaries pass through areas of low probability density. In this paper we provide some formal analysis of that notion for a probability distribution. We introduce a notion of weighted boundary volume, which measures the length of the class/cluster boundary weighted by the density of the underlying probability distribution. We show that sizes of the cuts of certain commonly used data adjacency graphs converge to this continuous weighted volume of the boundary.

Spectral clustering methods are common graph-based approaches to clustering of data. Spectral clustering algorithms typically start from local information encoded in a weighted graph on the data and cluster according to the global eigenvectors of the corresponding (normalized) similarity matrix. One contribution of this paper is to present fundamental limitations of this general local to global approach. We show that based only on local information, the normalized cut functional is not a suitable measure for the quality of clustering. Further, even with a suitable similarity measure,we show that the first few eigenvectors of such adjacency matrices cannot successfully cluster datasets that contain structures at different scales of size and density. Based on these findings, a second contribution of this paper is a novel diffusion based measure to evaluate the coherence of individual clusters. Our measure can be used in conjunction with any bottom-up graph-based clustering method,it is scale-free and can determine coherent clusters at all scales. We present both synthetic examples and real image segmentation problems where various spectralclustering algorithms fail. In contrast, using this coherence measure finds the expected clusters at all scales.

Correspondence algorithms typically struggle with shapes that display part-based variation. We present a probabilistic approach that matches shapes using independent parttransformations, where the parts themselves are learnt during matching. Ideas from semi-supervised learning are used to bias the algorithm towards finding'perceptuallyvalid' part structures. Shapes are represented by unlabeled point sets of arbitrary size and a background component is used to handle occlusion, local dissimilarity and clutter. Thus, unlike many shape matching techniques, our approach can be applied to shapes extracted from real images. Model parameters areestimated using an EM algorithm that alternates between finding a soft correspondence and computing the optimal part transformations using Procrustes analysis.

We consider the well-studied problem of learning decision lists using few examples whenmany irrelevant features are present. We show that smooth boosting algorithms suchas MadaBoost can efficiently learn decision lists of length k over n boolean variables using poly(k, log n) many examples provided that the marginal distribution over the relevant variables is "not too concentrated" in an L

A reliable motion estimation algorithm must function under a wide range of conditions. Oneregime, which we consider here, is the case of moving objects with contours but no visible texture. Tracking distinctive features such as corners can disambiguate the motion of contours, but spurious features such as T-junctions can be badly misleading. It is difficult to determine the reliability of motion from local measurements, since a full rank covariance matrix can result from both real and spurious features. We propose a novel approach that avoids these points altogether, andderives global motion estimates by utilizing information from three levels of contour analysis: edgelets, boundary fragments and contours.

Kernel-based regularized learning seeks a model in a hypothesis space by minimizing the empirical error and the model's complexity.

Chemical reaction networks by which individual cells gather and process information abouttheir chemical environments have been dubbed "signal transduction" networks. Despite this suggestive terminology, there have been few attempts to analyze chemical signaling systems with the quantitative tools of information theory. Gradientsensing in the social amoeba Dictyostelium discoideum is a well characterized signal transduction system in which a cell estimates the direction of a source of diffusing chemoattractant molecules based on the spatiotemporal sequence of ligand-receptor binding events at the cell membrane. Using Monte Carlo techniques (MCell) we construct a simulation in which a collection of individual ligandparticles undergoing Brownian diffusion in a three-dimensional volume interact with receptors on the surface of a static amoeboid cell. Adapting a method for estimation of spike train entropies described by Victor (originally due to Kozachenko and Leonenko), we estimate lower bounds on the mutual information betweenthe transmitted signal (direction of ligand source) and the received signal (spatiotemporal pattern of receptor binding/unbinding events). Hence we provide a quantitative framework for addressing the question: how much could the cell know, and when could it know it? We show that the time course of the mutual informationbetween the cell's surface receptors and the (unknown) gradient direction is consistent with experimentally measured cellular response times. We find that the acquisition of directional information depends strongly on the time constant at which the intracellular response is filtered.

This paper introduces adaptor grammars, a class of probabilistic models of language thatgeneralize probabilistic context-free grammars (PCFGs). Adaptor grammars augment the probabilistic rules of PCFGs with "adaptors" that can induce dependenciesamong successive uses. With a particular choice of adaptor, based on the Pitman-Yor process, nonparametric Bayesian models of language using Dirichlet processes and hierarchical Dirichlet processes can be written as simple grammars. We present a general-purpose inference algorithm for adaptor grammars, making it easy to define and use such models, and illustrate how several existing nonparametric Bayesian models can be expressed within this framework.

The study of point cloud data sampled from a stratification, a collection of manifolds withpossible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality anddensity of such structures. The framework is based on a maximum likelihood estimationof a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

Sequence labeling, the task of assigning labels y: yl, ..., yL to an input sequence x: 1:1, ...,:cL, is