Results 1 
3 of
3
Modefinding for mixtures of Gaussian distributions
 Dept. of Computer Science, University of Sheffield
, 1999
"... I consider the problem of finding all the modes of a mixture of multivariate Gaussian distributions, which has applications in clustering and regression. I derive exact formulas for the gradient and Hessian and give a partial proof that the number of modes cannot be more than the number of component ..."
Abstract

Cited by 34 (8 self)
 Add to MetaCart
I consider the problem of finding all the modes of a mixture of multivariate Gaussian distributions, which has applications in clustering and regression. I derive exact formulas for the gradient and Hessian and give a partial proof that the number of modes cannot be more than the number of components, and are contained in the convex hull of the component centroids. Then, I develop two exhaustive mode search algorithms: one based on combined quadratic maximisation and gradient ascent and the other one based on a fixedpoint iterative scheme. Appropriate values for the search control parameters are derived by taking into account theoretical results regarding the bounds for the gradient and Hessian of the mixture. The significance of the modes is quantified locally (for each mode) by error bars, or confidence intervals (estimated using the values of the Hessian at each mode); and globally by the sparseness of the mixture, measured by its differential entropy (estimated through bounds). I conclude with some reflections about bumpfinding.
Towards Formal Structural Representation of Spoken Language: An Evolving Transformation System (ETS) Approach
, 2005
"... Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new approaches are needed. The motivation ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new approaches are needed. The motivation behind the undertaken research is an observation that the notion of representation of objects and concepts that once was considered to be central in the early days of pattern recognition, has been largely marginalised by the advent of statistical approaches. As a consequence of a predominantly statistical approach to speech recognition problem, due to the numeric, feature vectorbased, nature of representation, the classes inductively discovered from real data using decisiontheoretic techniques have little meaning outside the statistical framework. This is because decision surfaces or probability distributions are difficult to analyse linguistically. Because of the later limitation it is doubtful that the gap between speech recognition and linguistic research can be bridged by the numeric representations. This thesis investigates an alternative, structural, approach to spoken language representation and categorisa
Mixtures of Latent Variable Models for Density Estimation and Classification
, 2000
"... 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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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 crossvalidation, 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.