Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and implementable.

We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is computationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.

This paper investigates the effect of Kernel Principal Component Analysis (KPCA)within the classification framework, essentially the regularization propertiesof this dimensionality reduction method. KPCA has been previously used as a pre-processing step before applying an SVM but we point out that this method is somewhat redundant from a regularization pointof view and we propose a new algorithm called Kernel Projection Machine to avoid this redundancy, based on an analogy with the statistical framework of regression for a Gaussian white noise model. Preliminary experimental results show that this algorithm reaches the same performances as an SVM.

In recent years, spectral clustering methods, i.e. data partitioning based on the

We describe a novel method for real-time, simultaneous multi-view face detection and facial pose estimation. The method employs a convolutional networkto map face images to points on a manifold, parametrized by pose, and non-face images to points far from that manifold. This network is trained by optimizing a loss function of three variables: image, pose,and face/non-face label. We test the resulting system, in a single configuration, on three standard data sets - one for frontal pose, one for rotated faces, and one for profiles - and find that its performance on each set is comparable to previous multi-view face detectors that can only handle one form of pose variation. We also show experimentally that the system's accuracy on both face detection and pose estimation is improved by training for the two tasks together.

For example, Yona et al.[10] uses profiles to align distant homologues from

Various problems in machine learning, databases, and statistics involve pairwise distances among a set of objects. It is often desirable for these distances to satisfy the properties of a metric, especially the triangle inequality. Applicationswhere metric data is useful include clustering, classification, metric-based indexing, and approximation algorithms for various graph problems. This paper presents the Metric Nearness Problem: Givena dissimilarity matrix, find the "nearest" matrix of distances that satisfy the triangle inequalities.

We consider the problem of geometrical surface reconstruction from one or several images using learned shape models. While humans can effortlessly retrieve3D shape information, this inverse problem has turned out to be difficult to perform automatically. We introduce a framework based on level set surface reconstruction and shape models for achieving this goal. Through this merging, we obtain an efficient and robust method for reconstructing surfaces of an object category of interest. The shape model includes surface cues such as point, curve and silhouette features.Based on ideas from Active Shape Models, we show how both the geometry and the appearance of these features can be modelled consistently in a multi-view context. The complete surface is obtained by evolving a level set driven by a PDE, which tries to fit the surface to the inferred 3D features. In addition, an a priori 3D surface model is used to regularize the solution, in particular, where surface features are sparse. Experiments are demonstrated on a database of real face images.

We show how to build hierarchical, reduced-rank representation for large stochastic matrices and use this representation to design an efficient algorithm forcomputing the largest eigenvalues, and the corresponding eigenvectors. In particular, the eigen problem is first solved at the coarsest levelof the representation. The approximate eigen solution is then interpolated over successive levels of the hierarchy. A small number of power iterations are employed at each stage to correct the eigen solution. The typical speedups obtained by a Matlab implementation of our fast eigensolver over a standard sparse matrix eigensolver [13] are at least a factor of ten for large image sizes. The hierarchical representation has proven to be effective in a min-cut based segmentation algorithm that we proposed recently [8].

The Bradley-Terry model for paired comparison has been popular in many areas. We propose a generalized version in which paired individual comparisons are extended to paired team comparisons. We introduce a simple algorithm with convergence proofs to solve the model and obtain individual skill. A useful application to multi-class probability estimates using error-correcting codes is demonstrated.