arXiv subjects

Ryan P. Browne

Publications and source records attributed to Ryan P. Browne.

25 records · Page 2Linked to original sources

arXiv2013

Parsimonious Shifted Asymmetric Laplace Mixtures

A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An explicit two-stage parameter estimation procedure is described, and the Bayesian information criterion and the integrated completed likelihood are compared for model selection. This novel family of models is applied to real data, where it is compared to its Gaussian analogue within clustering and classification paradigms.

stat.ME↗

arXiv2013

Mixtures of Common Skew-t Factor Analyzers

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used.

stat.ME↗

arXiv2013

Constrained Optimization for a Subset of the Gaussian Parsimonious Clustering Models

The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter estimation in applications of mixture models for clustering and classification. This despite the fact that even the Gaussian mixture model likelihood surface contains many local maxima and is singularity riddled. Previous work has focused on circumventing this problem by constraining the smallest eigenvalue of the component covariance matrices. In this paper, we consider constraining the smallest eigenvalue, the largest eigenvalue, and both the smallest and largest within the family setting. Specifically, a subset of the GPCM family is considered for model-based clustering, where we use a re-parameterized version of the famous eigenvalue decomposition of the component covariance matrices. Our approach is illustrated using various experiments with simulated and real data.

stat.CO↗

arXiv2013

Mixtures of Skew-t Factor Analyzers

In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic distributions. Like their Gaussian and t-distribution analogues, our mixture of skew-t factor analyzers are very well-suited to the model-based clustering of high-dimensional data. Imposing constraints on components of the decomposed covariance parameter results in the development of eight flexible models. The alternating expectation-conditional maximization algorithm is used for model parameter estimation and the Bayesian information criterion is used for model selection. The models are applied to both real and simulated data, giving superior clustering results compared to a well-established family of Gaussian mixture models.

stat.ME↗

arXiv2013

A Partial EM Algorithm for Clustering White Breads

The design of new products for consumer markets has undergone a major transformation over the last 50 years. Traditionally, inventors would create a new product that they thought might address a perceived need of consumers. Such products tended to be developed to meet the inventors own perception and not necessarily that of consumers. The social consequence of a top-down approach to product development has been a large failure rate in new product introduction. By surveying potential customers, a refined target is created that guides developers and reduces the failure rate. Today, however, the proliferation of products and the emergence of consumer choice has resulted in the identification of segments within the market. Understanding your target market typically involves conducting a product category assessment, where 12 to 30 commercial products are tested with consumers to create a preference map. Every consumer gets to test every product in a complete-block design; however, many classes of products do not lend themselves to such approaches because only a few samples can be evaluated before `fatigue' sets in. We consider an analysis of incomplete balanced-incomplete-block data on 12 different types of white bread. A latent Gaussian mixture model is used for this analysis, with a partial expectation-maximization (PEM) algorithm developed for parameter estimation. This PEM algorithm circumvents the need for a traditional E-step, by performing a partial E-step that reduces the Kullback-Leibler divergence between the conditional distribution of the missing data and the distribution of the missing data given the observed data. The results of the white bread analysis are discussed and some mathematical details are given in an appendix.

stat.AP↗

arXiv2013

Estimating Common Principal Components in High Dimensions

We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered when looking for common principal components, for example, and the Flury method is a popular approach. However, the Flury method is not effective for higher dimensional problems. We obtain several simple majorization-minizmation (MM) algorithms that provide solutions to this problem and are effective in higher dimensions. We then use simulated data to compare them with other approaches in terms of convergence and computational time.

stat.CO↗

arXiv2012

Mixtures of Shifted Asymmetric Laplace Distributions

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse Gaussian distribution. This approach is mathematically elegant and relatively computationally straightforward. Our novel mixture modelling approach is demonstrated on both simulated and real data to illustrate clustering and classification applications. In these analyses, our mixture of shifted asymmetric Laplace distributions performs favourably when compared to the popular Gaussian approach. This work, which marks an important step in the non-Gaussian model-based clustering and classification direction, concludes with discussion as well as suggestions for future work.

stat.ME↗