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Murphy, Thomas Brendan
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Murphy, Thomas Brendan
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Murphy, Thomas Brendan
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Now showing 1 - 9 of 9
- PublicationVariable selection methods for model-based clustering(The American Statistical Association, the Bernoulli Society, the Institute of Mathematical Statistics, and the Statistical Society of Canada, 2018-04-26)
; Model-based clustering is a popular approach for clustering multivariate data which has seen applications in numerous fields. Nowadays, high-dimensional data are more and more common and the model-based clustering approach has adapted to deal with the increasing dimensionality. In particular, the development of variable selection techniques has received a lot of attention and research effort in recent years. Even for small size problems, variable selection has been advocated to facilitate the interpretation of the clustering results. This review provides a summary of the methods developed for variable selection in model-based clustering. Existing R packages implementing the different methods are indicated and illustrated in application to two data analysis examples.496Scopus© Citations 60 - PublicationModel-Based clustering of microarray expression data via latent Gaussian mixture modelsIn recent years, work has been carried out on clustering gene expression microarray data. Some approaches are developed from an algorithmic viewpoint whereas others are developed via the application of mixture models. In this article, a family of eight mixture models which utilizes the factor analysis covariance structure is extended to 12 models and applied to gene expression microarray data. This modelling approach builds on previous work by introducing a modified factor analysis covariance structure, leading to a family of 12 mixture models, including parsimonious models. This family of models allows for the modelling of the correlation between gene expression levels even when the number of samples is small. Parameter estimation is carried out using a variant of the expectation–maximization algorithm and model selection is achieved using the Bayesian information criterion. This expanded family of Gaussian mixture models, known as the expanded parsimonious Gaussian mixture model (EPGMM) family, is then applied to two well-known gene expression data sets.
438Scopus© Citations 117 - PublicationMixed-Membership of Experts Stochastic BlockmodelSocial network analysis is the study of how links between a set of actors are formed. Typically, it is believed that links are formed in a structured manner, which may be due to, for example, political or material incentives, and which often may not be directly observable. The stochastic blockmodel represents this structure using latent groups which exhibit different connective properties, so that conditional on the group membership of two actors, the probability of a link being formed between them is represented by a connectivity matrix. The mixed membership stochastic blockmodel extends this model to allow actors membership to different groups, depending on the interaction in question, providing further flexibility. Attribute information can also play an important role in explaining network formation. Network models which do not explicitly incorporate covariate information require the analyst to compare fitted network models to additional attributes in a post-hoc manner. We introduce the mixed membership of experts stochastic blockmodel, an extension to the mixed membership stochastic blockmodel which incorporates covariate actor information into the existing model. The method is illustrated with application to the Lazega Lawyers dataset. Model and variable selection methods are also discussed.
302Scopus© Citations 9 - PublicationVariable Selection for Latent Class Analysis with Application to Low Back Pain Diagnosis(The Institute of Mathematical Statistics, 2017-12-28)
; ; The identification of most relevant clinical criteria related to low back pain disordersis a crucial task for a quick and correct diagnosis of the nature of pain and its treatment.Data concerning low back pain can be of categorical nature, in form of check-list in whicheach item denotes presence or absence of a clinical condition. Latent class analysis is amodel-based clustering method for multivariate categorical responses which can be appliedto such data for a preliminary diagnosis of the type of pain. In this work we propose avariable selection method for latent class analysis applied to the selection of the mostuseful variables in detecting the group structure in the data. The method is based onthe comparison of two different models and allows the discarding of those variables withno group information and those variables carrying the same information as the alreadyselected ones. We consider a swap-stepwise algorithm where at each step the models arecompared through and approximation to their Bayes factor. The method is applied tothe selection of the clinical criteria most useful for the clustering of patients in differentclasses of pain. It is shown to perform a parsimonious variable selection and to give agood clustering performance. The quality of the approach is also assessed on simulateddataScopus© Citations 33 544 - PublicationModel-based clustering with sparse covariance matricesFinite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily over-parameterized. For this reason, parsimonious models have been developed via covariance matrix decompositions or assuming local independence. However, these remedies do not allow for direct estimation of sparse covariance matrices nor do they take into account that the structure of association among the variables can vary from one cluster to the other. To this end, we introduce mixtures of Gaussian covariance graph models for model-based clustering with sparse covariance matrices. A penalized likelihood approach is employed for estimation and a general penalty term on the graph configurations can be used to induce different levels of sparsity and incorporate prior knowledge. Model estimation is carried out using a structural-EM algorithm for parameters and graph structure estimation, where two alternative strategies based on a genetic algorithm and an efficient stepwise search are proposed for inference. With this approach, sparse component covariance matrices are directly obtained. The framework results in a parsimonious model-based clustering of the data via a flexible model for the within-group joint distribution of the variables. Extensive simulated data experiments and application to illustrative datasets show that the method attains good classification performance and model quality. The general methodology for model-based clustering with sparse covariance matrices is implemented in the R package mixggm, available on CRAN.
402Scopus© Citations 16 - PublicationGaussian parsimonious clustering models with covariates and a noise componentWe consider model-based clustering methods for continuous, correlated data that account for external information available in the presence of mixed-type fixed covariates by proposing the MoEClust suite of models. These models allow different subsets of covariates to influence the component weights and/or component densities by modelling the parameters of the mixture as functions of the covariates. A familiar range of constrained eigen-decomposition parameterisations of the component covariance matrices are also accommodated. This paper thus addresses the equivalent aims of including covariates in Gaussian parsimonious clustering models and incorporating parsimonious covariance structures into all special cases of the Gaussian mixture of experts framework. The MoEClust models demonstrate significant improvement from both perspectives in applications to both univariate and multivariate data sets. Novel extensions to include a uniform noise component for capturing outliers and to address initialisation of the EM algorithm, model selection, and the visualisation of results are also proposed.
13Scopus© Citations 22 - PublicationBayesLCA : An R Package for Bayesian Latent Class AnalysisThe BayesLCA package for R provides tools for performing latent class analysis within a Bayesian setting. Three methods for fitting the model are provided, incorporating an expectation-maximization algorithm, Gibbs sampling and a variational Bayes approximation. The article briefly outlines the methodology behind each of these techniques and discusses some of the technical difficulties associated with them. Methods to remedy these problems are also described. Visualization methods for each of these techniques are included, as well as criteria to aid model selection.
1237Scopus© Citations 46 - PublicationClustering with the multivariate normal inverse Gaussian distributionMany model-based clustering methods are based on a finite Gaussian mixture model. The Gaussian mixture model implies that the data scatter within each group is elliptically shaped. Hence non-elliptical groups are often modeled by more than one component, resulting in model over-fitting. An alternative is to use a mean–variance mixture of multivariate normal distributions with an inverse Gaussian mixing distribution (MNIG) in place of the Gaussian distribution, to yield a more flexible family of distributions. Under this model the component distributions may be skewed and have fatter tails than the Gaussian distribution. The MNIG based approach is extended to include a broad range of eigendecomposed covariance structures. Furthermore, MNIG models where the other distributional parameters are constrained is considered. The Bayesian Information Criterion is used to identify the optimal model and number of mixture components. The method is demonstrated on three sample data sets and a novel variation on the univariate Kolmogorov–Smirnov test is used to assess goodness of fit.
17539Scopus© Citations 60 - PublicationComputational Aspects of Fitting Mixture Models via the Expectation-Maximization AlgorithmThe Expectation–Maximization (EM) algorithm is a popular tool in a wide variety of statistical settings, in particular in the maximum likelihood estimation of parameters when clustering using mixture models. A serious pitfall is that in the case of a multimodal likelihood function the algorithm may become trapped at a local maximum, resulting in an inferior clustering solution. In addition, convergence to an optimal solution can be very slow. Methods are proposed to address these issues: optimizing starting values for the algorithm and targeting maximization steps efficiently. It is demonstrated that these approaches can produce superior outcomes to initialization via random starts or hierarchical clustering and that the rate of convergence to an optimal solution can be greatly improved.
659Scopus© Citations 34