We consider the problem of illusory or artefactual structure from the visualisation of high-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SS

We investigate the problem of learning a classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column objects may belong to different sets, and the entries in the matrix express the relationships between them. We interpret the matrix elements as being produced by an unknown kernel which operates on object pairs and we show that - under mild assumptions - these kernels correspond to dot products in some (unknown) feature space. Minimizing a bound for the generalization error of a linear classifier which has been obtained using covering numbers we derive an objective function for model selection according to the principle of structural risk minimization. The new objective function has the advantage that it allows the analysis of matrices which are not positive definite, and not even symmetric or square.

We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images. 1 Introduction In this article we consider the rather general learning problem of finding a dependency between inputs x E X and outputs y E Y given a training set (Xl,yl),...,(xm, Ym) E X x Y This includes conventional pattern recognition and regression estimation. It also encompasses more complex dependency estimation tasks, e.g mapping of a certain class of strings to a certain class of graphs (as in text parsing) or the mapping of text descriptions to images.

Low rank approximation techniques are widespread in pattern recognition research -- they include Latent Semantic Analysis (LSA), Probabilistic LSA, Principal Components Analysus (PCA), the Generative Aspect Model, and many forms of bibliometric analysis. All make use of a low-dimensional manifold onto which data are projected. Such techniques are generally "unsupervised," which allows them to model data in the absence of labels or categories. With many practical problems, however, some prior knowledge is available in the form of context. In this paper, I describe a principled approach to incorporating such information, and demonstrate its application to PCA-based approximations of several data sets.

The similarity between objects is a fundamental element of many learning algorithms. Most nonparametric methods take this similarity to be fixed, but much recent work has shown the advantages of learning it, in particular to exploit the local invariances in the data or to capture the possibly nonlinear manifold on which most of the data lies. We propose a new nonparametric kernel density estimation method which captures the local structure of an underlying manifold through the leading eigenvectors of regularized local covariance matrices.

Pairwise data in empirical sciences typically violate metricity, either due to noise or due to fallible estimates, and therefore are hard to analyze by conventional machine learning technology. In this paper we therefore study ways to work around this problem. First, we present an alternative embedding to multidimensional scaling (MDS) that allows us to apply a variety of classical machine learning and signal processing algorithms. The class of pairwise grouping algorithms which share the shift-invariance property is statistically invariant under this embedding procedure, leading to identical assignments of objects to clusters. Based on this new vectorial representation, denoising methods are applied in a second step. Both steps provide a theoretically well controlled setup to translate from pairwise data to the respective denoised metric representation. We demonstrate the practical usefulness of our theoretical reasoning by discovering structure in protein sequence data bases, visibly improving performance upon existing automatic methods. 1 Introduction Unsupervised grouping or clustering aims at extracting hidden structure from data (see e.g.

We focus on the problem of efficient learning of dependency trees. It is well-known that given the pairwise mutual information coefficients, a minimum-weight spanning tree algorithm solves this problem exactly and in polynomial time. However, for large data-sets it is the construction of the correlation matrix that dominates the running time. We have developed a new spanning-tree algorithm which is capable of exploiting partial knowledge about edge weights. The partial knowledge we maintain is a probabilistic confidence interval on the coefficients, which we derive by examining just a small sample of the data. The algorithm is able to flag the need to shrink an interval, which translates to inspection of more data for the particular attribute pair. Experimental results show running time that is near-constant in the number of records, without significant loss in accuracy of the generated trees. Interestingly, our spanning-tree algorithm is based solely on Tarjan's red-edge rule, which is generally considered a guaranteed recipe for bad performance.

In recent years variational methods have become a popular tool for approximate inference and learning in a wide variety of probabilistic models. For each new application, however, it is currently necessary first to derive the variational update equations, and then to implement them in application-specific code. Each of these steps is both time consuming and error prone. In this paper we describe a general purpose inference engine called VIBES ('Variational Inference for Bayesian Networks') which allows a wide variety of probabilistic models to be implemented and solved variationally without recourse to coding. New models are specified either through a simple script or via a graphical interface analogous to a drawing package. VIBES then automatically generates and solves the variational equations. We illustrate the power and flexibility of VIBES using examples from Bayesian mixture modelling.

We formulate the regression problem as one of maximizing the minimum probability, symbolized by Ω, that future predicted outputs of the regression model will be within some ε bound of the true regression function. Our formulation is unique in that we obtain a direct estimate of this lower probability bound Ω. The proposed framework, minimax probability machine regression (MPMR), is based on the recently described minimax probability machine classification algorithm [Lanckriet et al.] and uses Mercer Kernels to obtain nonlinear regression models. MPMR is tested on both toy and real world data, verifying the accuracy of the Ω bound, and the efficacy of the regression models.

Problems in which abnormal or novel situations should be detected can be approached by describing the domain of the class of typical examples. These applications come from the areas of machine diagnostics, fault detection, illness identification or, in principle, refer to any problem where little knowledge is available outside the typical class. In this paper we explain why proximities are natural representations for domain descriptors and we propose a simple one-class classifier for dissimilarity representations. By the use of linear programming an efficient one-class description can be found, based on a small number of prototype objects. This classifier can be made (1) more robust by transforming the dissimilarities and (2) cheaper to compute by using a reduced representation set. Finally, a comparison to a comparable one-class classifier by Campbell and Bennett is given.