We introduce a very large family of binary features for two-dimensional shapes. The salient ones for separating particular shapes are determined by inductive learning during the construction of classi cation trees. There is a feature for every possible geometric arrangement of local topographic codes. The arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial a ne and non-linear deformations. They are also partially ordered, which makes it possible to narrow the search for informative ones at each node of the tree. Di erent trees correspond to di erent aspects of shape. They are statistically weakly dependent due to randomization and are aggregated in a simple way. Adapting the algorithm to a shape family is then fully automatic once training samples are provided. As an illustration, we classify handwritten digits from the NIST database � the error rate is:7%.

We describe an approach to shape recognition based on asking relational questions about the arrangement of landmarks, basically localized and oriented boundary segments. The questions are grouped into highly structured inquiries in the form of a tree. There are, in fact, many trees, each constructed from training data based on entropy reduction. The outcome of each tree is not a classification but rather a distribution over shape classes. The final classification is based on an aggregate distribution. The framework is non-Euclidean and there is no feature vector in the standard sense. Instead, the representation of the image data is graphical and each question is associated with a labeled subgraph. The ordering of the questions is highly constrained in order to maintain computational feasibility, and dependence among the trees is reduced by randomly sub-sampling from the available pool of questions. Experiments are reported on the recognition of handwritten digits. Although the amount ...

This paper deals with the problem of probability density estimation with the goal of finding a good probabilistic representation of the data. One of the most popular density estimation methods is the Gaussian mixture model (GMM). A promising alternative to GMMS are the recently proposed mixtures of latent variable models. Examples of the latter are principal component analysis and factor analysis. The advantage of these models is that they are capable of representing the covariance structure with less parameters by choosing the dimension of a subspace in a suitable way. An empirical evaluation on a large number of data sets shows that mixtures of latent variable models almost always outperform various GMMS both in density estimation and Bayes classifiers. To avoid having to choose a value for the dimension of the latent subspace by a computationally expensive search technique such as cross-validation, a Bayesian treatment of mixtures of latent variable models is proposed. This framework makes it possible to determine the appropriate dimension during training and experiments illustrate its viability.

Abstract. Trees are a powerful data structure for representing data for which hierarchical relations can be defined. It has been applied in a number of fields like image analysis, natural language processing, protein structure, or music retrieval, to name a few. Procedures for comparing trees are very relevant in many tasks where tree representations are involved. The computation of these measures is usually time consuming and different authors have proposed algorithms that are able to compute them in a reasonable time, by means of approximated versions of the similarity measure. Other methods require that the trees are fully labeled for the distance to be computed. The measure utilized in this paper is able to deal with trees labeled only at the leaves that runs in O(|T1 | × |T2|) time. Experiments and comparative results are provided.