We present a novel method for clustering using the support vector machine approach.Data points are mapped to a high dimensional feature space, where support vectors are used to define a sphere enclosing them. The boundary of the sphere forms in data space a set of closed contours containing the data. Data points enclosed by each contour are defined as a cluster. As the width parameter of the Gaussian kernel is decreased, these contours fit the data more tightly and splitting of contours occurs. The algorithm works by separating clusters according to valleys in the underlying probabilitydistribution, and thus clusters can take on arbitrary geometrical shapes.

A central issue in principal component analysis (PCA) is choosing the number of principal components to be retained. By interpreting PCA as density estimation, we show how to use Bayesian model selection to estimate thetrue dimensionality of the data. The resulting estimate is simple to compute yet guaranteed to pick the correct dimensionality, given enough data. The estimate involves an integral over the Steifel manifold of k-frames, which is difficult to compute exactly. But after choosing an appropriate parameterization and applying Laplace's method, an accurate andpractical estimator is obtained. In simulations, it is convincingly better than cross-validation and other proposed algorithms, plus it runs much faster.

E lRP such as to achieve minimum Bayes error (or probability of misclassification). Two avenues will be explored: the first is to maximize the ()-average divergence between the class densities and the second is to minimize the union Bhattacharyya bound in the range of (). While both approaches yield similar performance in practice, they outperform standardLDA features and show a 10% relative improvement in the word error rate over state-of-the-art cepstral features on a large vocabulary telephony speech recognition task. 1 Introduction Modern speech recognition systems use cepstral features characterizing the short-term spectrum of the speech signal for classifying frames into phonetic classes. These features are augmented with dynamic information from the adjacent frames to capture transient spectral events in the signal.

Algebraic geometry is essential to learning theory. In hierarchical learning machines such as layered neural networks and gaussian mixtures, the asymptotic normality does not hold, since Fisher information matricesare singular. In this paper, the rigorous asymptotic form of the stochastic complexity is clarified based on resolution of singularities and two different problems are studied.

Although connectionist models have provided insights into the nature of perception and motor control, connectionist accounts of higher cognition seldom go beyond an implementation of traditional symbol-processing theories. We describe a connectionist constraint satisfaction model of how people solve anagram problems. The model exploits statistics of English orthography, but also addresses the interplay of subsymbolic and symbolic computation by a mechanism that extracts approximate symbolic representations (partial orderings of letters) from subsymbolic structures and injects the extracted representation back into the model to assist in the solution of the anagram. We show the computational benefit of this extraction-injection process and discuss its relationship to conscious mental processes and working memory. We also account for experimental data concerning the difficulty of anagram solution based on the orthographic structure of the anagram string and the target word.

It has long been known that lateral inhibition in neural networks can lead to a winner-take-all competition, so that only a single neuron is active at a steady state. Here we show how to organize lateral inhibition so that groups of neurons compete to be active. Given a collection of potentially overlappinggroups, the inhibitory connectivity is set by a formula that can be interpreted as arising from a simple learning rule. Our analysis demonstratesthat such inhibition generally results in winner-take-all competition between the given groups, with the exception of some degenerate cases.In a broader context, the network serves as a particular illustration of the general distinction between permitted and forbidden sets, which was introduced recently. From this viewpoint, the computational functionof our network is to store and retrieve memories as permitted setsof coactive neurons.

Incorporating prior knowledge of a particular task into the architecture of a learning algorithm can greatly improve generalization performance. We study here a case where we know that the function to be learned is non-decreasing in two of its arguments and convex in one of them. For this purpose we propose a class of functions similar to multi-layer neural networks but (1) that has those properties, (2) is a universal approximator of continuous functions with these and other properties. We apply this new class of functions to the task of modeling the price of call options. Experiments show improvements on regressing the price of call options using the new types of function classes that incorporate the a priori constraints. 1 Introduction Incorporating a priori knowledge of a particular task into a learning algorithm helps reducing thenecessary complexity of the learner and generally improves performance, if the incorporated knowledge is relevant to the task and really corresponds to the generating process ofthe data. In this paper we consider prior knowledge on the positivity of some first and second derivatives of the function to be learned. In particular such constraints have applications to modeling the price of European stock options. Based on the Black-Scholes formula, the price of a call stock option is monotonically increasing in both the "moneyness" andtime to maturity of the option, and it is convex in the "moneyness". Section 3 better explains these terms and stock options.

It has been shown that the receptive fields of simple cells in VI can be explained byassuming optimal encoding, provided that an extra constraint of sparseness is added. This finding suggests that there is a reason, independent ofoptimal representation, for sparseness. However this work used an ad hoc model for the noise. Here I show that, if a biologically more plausible noise model, describing neurons as Poisson processes, is used sparseness does not have to be added as a constraint. Thus I conclude thatsparseness is not a feature that evolution has striven for, but is simply the result of the evolutionary pressure towards an optimal representation. 1 Introduction Recently there has been an resurgence of interest in using optimal coding strategies to'explain' the response properties of neuron in the primary sensory areas [1].

The human visual system encodes the chromatic signals conveyed by the three types of retinal cone photoreceptors in an opponent fashion. This color opponency has been shown to constitute an efficient encoding by spectral decorrelation of the receptor signals. We analyze the spatial and chromatic structure of natural scenes by decomposing the spectral images into a set of linear basis functions such that they constitute a representation with minimal redundancy. Independentcomponent analysis finds the basis functions that transforms the spatiochromatic data such that the outputs (activations) are statistically as independent as possible, i.e. least redundant. The resulting basis functions show strong opponency along an achromatic direction (luminance edges), along a blueyellow direction,and along a red-blue direction.

We present an algorithm that samples the hypothesis space of kernel classifiers.Given a uniform prior over normalised weight vectors and a likelihood based on a model of label noise leads to a piecewise constantposterior that can be sampled by the kernel Gibbs sampler (KGS). The KGS is a Markov Chain Monte Carlo method that chooses a random direction in parameter space and samples from the resulting piecewise constant density along the line chosen. The KGS can be used as an analytical tool for the exploration of Bayesian transduction, Bayes point machines, active learning, and evidence-based model selection on small data sets that are contaminated withlabel noise. For a simple toy example we demonstrate experimentally how a Bayes point machine based on the KGS outperforms anSVM that is incapable of taking into account label noise. 1 Introduction Two great ideas have dominated recent developments in machine learning: the application ofkernel methods and the popularisation of Bayesian inference. Focusing on the task of classification, various connections between the two areas exist: kernels havelong been a part of Bayesian inference in the disguise of covariance nmctions thatcharacterise priors over functions [9].