Nema Dean

Variable Selection and Updating In Model-Based Discriminant Analysis for High Dimensional Data with Food Authenticity Applications

Food authenticity studies are concerned with determining if food samples have been correctly labelled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity applications, a model-based discriminant analysis method that includes variable selection is presented. The discriminant analysis model is fitted in a semi-supervised manner using both labeled and unlabeled data. The method is shown to give excellent classification performance on several high-dimensional multiclass food authenticity datasets with more variables than observations. The variables selected by the proposed method provide information about which variables are meaningful for classification purposes. A headlong search strategy for variable selection is shown to be efficient in terms of computation and achieves excellent classification performance. In applications to several food authenticity datasets, our proposed method outperformed default implementations of Random Forests, AdaBoost, transductive SVMs and Bayesian Multinomial Regression by substantial margins.

Identifying clusters in Bayesian disease mapping

Disease mapping is the field of spatial epidemiology interested in estimating the spatial pattern in disease risk across [Formula: see text] areal units. One aim is to identify units exhibiting elevated disease risks, so that public health interventions can be made. Bayesian hierarchical models with a spatially smooth conditional autoregressive prior are used for this purpose, but they cannot identify the spatial extent of high-risk clusters. Therefore, we propose a two-stage solution to this problem, with the first stage being a spatially adjusted hierarchical agglomerative clustering algorithm. This algorithm is applied to data prior to the study period, and produces [Formula: see text] potential cluster structures for the disease data. The second stage fits a separate Poisson log-linear model to the study data for each cluster structure, which allows for step-changes in risk where two clusters meet. The most appropriate cluster structure is chosen by model comparison techniques, specifically by minimizing the Deviance Information Criterion. The efficacy of the methodology is established by a simulation study, and is illustrated by a study of respiratory disease risk in Glasgow, Scotland.

Hybrid approach combining chemometrics and likelihood ratio framework for reporting the evidential value of spectra.

Many chemometric tools are invaluable and have proven effective in data mining and substantial dimensionality reduction of highly multivariate data. This becomes vital for interpreting various physicochemical data due to rapid development of advanced analytical techniques, delivering much information in a single measurement run. This concerns especially spectra, which are frequently used as the subject of comparative analysis in e.g. forensic sciences. In the presented study the microtraces collected from the scenarios of hit-and-run accidents were analysed. Plastic containers and automotive plastics (e.g. bumpers, headlamp lenses) were subjected to Fourier transform infrared spectrometry and car paints were analysed using Raman spectroscopy. In the forensic context analytical results must be interpreted and reported according to the standards of the interpretation schemes acknowledged in forensic sciences using the likelihood ratio approach. However, for proper construction of LR models for highly multivariate data, such as spectra, chemometric tools must be employed for substantial data compression. Conversion from classical feature representation to distance representation was proposed for revealing hidden data peculiarities and linear discriminant analysis was further applied for minimising the within-sample variability while maximising the between-sample variability. Both techniques enabled substantial reduction of data dimensionality. Univariate and multivariate likelihood ratio models were proposed for such data. It was shown that the combination of chemometric tools and the likelihood ratio approach is capable of solving the comparison problem of highly multivariate and correlated data after proper extraction of the most relevant features and variance information hidden in the data structure.

Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas

This paper presents a finite mixture of multivariate betas as a new model-based clustering method tailored to applications where the feature space is constrained to the unit hypercube. The mixture component densities are taken to be conditionally independent, univariate unimodal beta densities (from the subclass of reparameterized beta densities given by Bagnato and Punzo in Comput Stat 28(4):10.1007/s00180-012-367-4, 2013). The EM algorithm used to fit this mixture is discussed in detail, and results from both this beta mixture model and the more standard Gaussian model-based clustering are presented for simulated skill mastery data from a common cognitive diagnosis model and for real data from the Assistment System online mathematics tutor (Feng et al. in J User Model User Adap Inter 19(3):243–266, 2009). The multivariate beta mixture appears to outperform the standard Gaussian model-based clustering approach, as would be expected on the constrained space. Fewer components are selected (by BIC-ICL) in the beta mixture than in the Gaussian mixture, and the resulting clusters seem more reasonable and interpretable.

Bayesian cluster detection via adjacency modelling

Disease mapping aims to estimate the spatial pattern in disease risk across an area, identifying units which have elevated disease risk. Existing methods use Bayesian hierarchical models with spatially smooth conditional autoregressive priors to estimate risk, but these methods are unable to identify the geographical extent of spatially contiguous high-risk clusters of areal units. Our proposed solution to this problem is a two-stage approach, which produces a set of potential cluster structures for the data and then chooses the optimal structure via a Bayesian hierarchical model. The first stage uses a spatially adjusted hierarchical agglomerative clustering algorithm. The second stage fits a Poisson log-linear model to the data to estimate the optimal cluster structure and the spatial pattern in disease risk. The methodology was applied to a study of chronic obstructive pulmonary disease (COPD) in local authorities in England, where a number of high risk clusters were identified.

A Survey of Popular R Packages for Cluster Analysis

Cluster analysis is a set of statistical methods for discovering new group/class structure when exploring data sets. This article reviews the following popular libraries/commands in the R software language for applying different types of cluster analysis: from the stats library, the kmeans, and hclust functions; the mclust library; the poLCA library; and the clustMD library. The packages/functions cover a variety of cluster analysis methods for continuous data, categorical data, or a collection of the two. The contrasting methods in the different packages are briefly introduced, and basic usage of the functions is discussed. The use of the different methods is compared and contrasted and then illustrated on example data. In the discussion, links to information on other available libraries for different clustering methods and extensions beyond basic clustering methods are given. The code for the worked examples in Section 2 is available at http://www.stats.gla.ac.uk/∼nd29c/Software/ClusterReviewCode.R

Spatial clustering of average risks and risk trends in Bayesian disease mapping

Spatiotemporal disease mapping focuses on estimating the spatial pattern in disease risk across a set of nonoverlapping areal units over a fixed period of time. The key aim of such research is to identify areas that have a high average level of disease risk or where disease risk is increasing over time, thus allowing public health interventions to be focused on these areas. Such aims are well suited to the statistical approach of clustering, and while much research has been done in this area in a purely spatial setting, only a handful of approaches have focused on spatiotemporal clustering of disease risk. Therefore, this paper outlines a new modeling approach for clustering spatiotemporal disease risk data, by clustering areas based on both their mean risk levels and the behavior of their temporal trends. The efficacy of the methodology is established by a simulation study, and is illustrated by a study of respiratory disease risk in Glasgow, Scotland.

sARI: a soft agreement measure for class partitions incorporating assignment probabilities

Agreement indices are commonly used to summarize the performance of both classification and clustering methods. The easy interpretation/intuition and desirable properties that result from the Rand and adjusted Rand indices, has led to their popularity over other available indices. While more algorithmic clustering approaches like k-means and hierarchical clustering produce hard partition assignments (assigning observations to a single cluster), other techniques like model-based clustering include information about the certainty of allocation of objects through class membership probabilities (soft partitions). To assess performance using traditional indices, e.g., the adjusted Rand index (ARI), the soft partition is mapped to a hard set of assignments, which commonly overstates the certainty of correct assignments. This paper proposes an extension of the ARI, the soft adjusted Rand index (sARI), with similar intuition and interpretation but also incorporating information from one or two soft partitions. It can be used in conjunction with the ARI, comparing the similarities of hard to soft, or soft to soft partitions to the similarities of the mapped hard partitions. Simulation study results support the intuition that in general, mapping to hard partitions tends to increase the measure of similarity between partitions. In applications, the sARI more accurately reflects the cluster boundary overlap commonly seen in real data.

Is the housing market blind to religion? A perceived substitutability approach to homophily and social integration

Housing markets are unlikely to be impervious to the preferences and prejudices associated with urban segregation. For example, two neighbourhoods with very different religious attributes are unlikely to be perceived as close substitutes by homebuyers that have a strong preference for neighbours of a particular religion. This paper offers a new framework for the conception and measurement of social integration, defined in terms of perceived homophily. Homophily is the tendency for links to form between similar nodes in a network and we can think of perceived homophily as the tendency for any pair of neighbourhoods to be considered by the housing market to be close substitutes. Textbook economic theory suggests that we should expect the degree of perceived substitutability to affect cross-price elasticities. These can be measured empirically to reveal discontinuities in the network of perceived substitutability of different housing locations. Applying homophily coefficients to substitutability measures allows us to estimate perceived religious homophily between neighbourhoods. The approach can be applied to any city or region that has geocoded house transactions and socio-demographic data. We illustrate the method using data on Glasgow and find strong evidence of religious homophily. This suggests an underlying lack of social integration/cohesion and implies that the Glaswegian housing market is by no means blind to religion.