Cluster analysis of high-dimensional data: A case study

Normal mixture models are often used to cluster continuous data. However, conventional approaches for fitting these models will have problems in producing nonsingular estimates of the component-covariance matrices when the dimension of the observations is large relative to the number of observations. In this case, methods such as principal components analysis (PCA) and the mixture of factor analyzers model can be adopted to avoid these estimation problems. We examine these approaches applied to the Cabernet wine data set of Ashenfelter (1999), considering the clustering of both the wines and the judges, and comparing our results with another analysis. The mixture of factor analyzers model proves particularly effective in clustering the wines, accurately classifying many of the wines by location.

Issues of robustness and high dimensionality in cluster analysis

Finite mixture models are being increasingly used to model the distributions of a wide variety of random phenomena. While normal mixture models are often used to cluster data sets of continuous multivariate data, a more robust clustering can be obtained by considering the t mixture model-based approach. Mixtures of factor analyzers enable model-based density estimation to be undertaken for high-dimensional data where the number of observations n is very large relative to their dimension p. As the approach using the multivariate normal family of distributions is sensitive to outliers, it is more robust to adopt the multivariate t family for the component error and factor distributions. The computational aspects associated with robustness and high dimensionality in these approaches to cluster analysis are discussed and illustrated.

Cluster analysis of self-awareness levels in adults with traumatic brain injury and relationship to outcome

The purpose of this study was to investigate the relationship between self-awareness, emotional distress, motivation, and outcome in adults with severe traumatic brain injury. A sample of 55 patients were selected from 120 consecutive patients with severe traumatic brain injury admitted to the rehabilitation unit of a large metropolitan public hospital. Subjects received multidisciplinary inpatient rehabilitation and different types of outpatient rehabilitation and community-based services according to availability and need, Measures used in the cluster analysis were the Patient Competency Rating Scale, Self-Awareness of Deficits Interview, Head Injury Behavior Scale, Change Assessment Questionnaire, the Beck Depression Inventory, and Beck Anxiety Inventory; outcome measures were the Disability Rating Scale, Community Integration Questionnaire, and Sickness Impact Profile. A three-cluster solution was selected, with groups labeled as high self-awareness (n = 23), low self-awareness (n = 23), and good recovery (n = 8). The high self-awareness cluster had significantly higher levels of self-awareness, motivation, and emotional distress than the low self-awareness cluster but did not differ significantly in outcome. Self-awareness after brain injury is associated with greater motivation to change behavior and higher levels of depression and anxiety; however, it was not clear that this heightened motivation actually led to any improvement in outcome. Rehabilitation timing and approach may need to be tailored to match the individual's level of self-awareness, motivation, and emotional distress.

Xmds: eXtensible multi-dimensional simulator

A software package that efficiently solves a comprehensive range of problems based on coupled complex nonlinear stochastic ODEs and PDEs is outlined. Its input and output syntax is formulated as a subset of XML, thus making a step towards a standard for specifying numerical simulations.

Mixture modelling for cluster analysis

Cluster analysis via a finite mixture model approach is considered. With this approach to clustering, the data can be partitioned into a specified number of clusters g by first fitting a mixture model with g components. An outright clustering of the data is then obtained by assigning an observation to the component to which it has the highest estimated posterior probability of belonging; that is, the ith cluster consists of those observations assigned to the ith component (i = 1,..., g). The focus is on the use of mixtures of normal components for the cluster analysis of data that can be regarded as being continuous. But attention is also given to the case of mixed data, where the observations consist of both continuous and discrete variables.

On the simultaneous use of clinical and microarray expression data in the cluster analysis of tissue samples

This paper considers a model-based approach to the clustering of tissue samples of a very large number of genes from microarray experiments. It is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. Frequently in practice, there are also clinical data available on those cases on which the tissue samples have been obtained. Here we investigate how to use the clinical data in conjunction with the microarray gene expression data to cluster the tissue samples. We propose two mixture model-based approaches in which the number of components in the mixture model corresponds to the number of clusters to be imposed on the tissue samples. One approach specifies the components of the mixture model to be the conditional distributions of the microarray data given the clinical data with the mixing proportions also conditioned on the latter data. Another takes the components of the mixture model to represent the joint distributions of the clinical and microarray data. The approaches are demonstrated on some breast cancer data, as studied recently in van't Veer et al. (2002).

A new perspective on service quality: A multi-dimensional, hierarchical scale

This study offers a new perspective on the nature, content and structure of perceived service quality. The Nordic and Gap schools of quality assessment are integrated with recent advances in the literature to develop and test a multidimensional, hierarchical scale. The scale provides a framework for assessing service quality within a high involvement, high contact, ongoing service environment. Empirical results indicated that service quality conforms to a multidimensional, hierarchical structure consisting of four primary dimensions, which in turn comprise nine sub-dimensions. The results obtained extend our understanding of service evaluation and have important implications for service providers seeking to improve the quality of the services they provide.

Cluster analysis of the p53 genetic regulatory network: topology and biology

We describe a network module detection approach which combines a rapid and robust clustering algorithm with an objective measure of the coherence of the modules identified. The approach is applied to the network of genetic regulatory interactions surrounding the tumor suppressor gene p53. This algorithm identifies ten clusters in the p53 network, which are visually coherent and biologically plausible.

A rough cluster analysis of shopping orientation data

This paper describes the application of a new technique, rough clustering, to the problem of market segmentation. Rough clustering produces different solutions to k-means analysis because of the possibility of multiple cluster membership of objects. Traditional clustering methods generate extensional descriptions of groups, that show which objects are members of each cluster. Clustering techniques based on rough sets theory generate intensional descriptions, which outline the main characteristics of each cluster. In this study, a rough cluster analysis was conducted on a sample of 437 responses from a larger study of the relationship between shopping orientation (the general predisposition of consumers toward the act of shopping) and intention to purchase products via the Internet. The cluster analysis was based on five measures of shopping orientation: enjoyment, personalization, convenience, loyalty, and price. The rough clusters obtained provide interpretations of different shopping orientations present in the data without the restriction of attempting to fit each object into only one segment. Such descriptions can be an aid to marketers attempting to identify potential segments of consumers.

Analysis of line x environment interactions for yield in navy beans. 2. Pattern analysis of lines and environment within years

Seven years of multi-environment yield trials of navy bean (Phaseolus vulgaris L.) grown in Queensland were examined. As is common with plant breeding evaluation trials, test entries and locations varied between years. Grain yield data were analysed for each year using cluster and ordination analyses (pattern analyses). These methods facilitate descriptions of genotype performance across environments and the discrimination among genotypes provided by the environments. The observed trends for genotypic yield performance across environments were partly consistent with agronomic and disease reactions at specific environments and also partly explainable by breeding and selection history. In some cases, similarities in discrimination among environments were related to geographic proximity, in others management practices, and in others similarities occurred between geographically widely separated environments which differed in management practices. One location was identified as having atypical line discrimination. The analysis indicated that the number of test locations was below requirements for adequate representation of line x environment interaction. The pattern analyses methods used were an effective aid in describing the patterns in data for each year and illustrated the variations in adaptive patterns from year to year. The study has implications for assessing the number and location of test sites for plant breeding multi-environment trials, and for the understanding of genetic traits contributing to line x environment interactions.

Cluster measurement and benchmarking - A recent Welsh approach

Drawing on extensive academic research and theory on clusters and their analysis, the methodology employed in this pilot study (sponsored by the Welsh Assembly Government’s Economic Research Grants Assessment Board) seeks to create a framework for reviewing and monitoring clusters in Wales on an ongoing basis, and generate the information necessary for successful cluster development policy to occur. The multi-method framework developed and tested in the pilot study is designed to map existing Welsh sectors with cluster characteristics, uncover existing linkages, and better understand areas of strength and weakness. The approach adopted relies on synthesising both quantitative and qualitative evidence. Statistical measures, including the size of potential clusters, are united with other evidence on input-output derived inter-linkages within clusters and to other sectors in Wales and the UK, as well as the export and import intensity of the cluster. Multi Sector Qualitative Analysis is then designed for competencies/capacity, risk factors, markets, types and crucially, the perceived strengths of cluster structures and relationships. The approach outlined above can, with the refinements recommended through the review process, provide policy-makers with a valuable tool for reviewing and monitoring individual sectors and ameliorating problems in sectors likely to decline further.

Prediction of the chemical composition of lamb carcasses from multi-frequency impedance data

Multi-frequency bioimpedance analysis (MFBIA) was used to determine the impedance, reactance and resistance of 103 lamb carcasses (17.1-34.2 kg) immediately after slaughter and evisceration. Carcasses were halved, frozen and one half subsequently homogenized and analysed for water, crude protein and fat content. Three measures of carcass length were obtained. Diagonal length between the electrodes (right side biceps femoris to left side of neck) explained a greater proportion of the variance in water mass than did estimates of spinal length and was selected for use in the index L-2/Z to predict the mass of chemical components in the carcass. Use of impedance (Z) measured at the characteristic frequency (Z(c)) instead of 50 kHz (Z(50)) did not improve the power of the model to predict the mass of water, protein or fat in the carcass. While L-2/Z(50) explained a significant proportion of variation in the masses of body water (r(2) 0.64), protein (r(2) 0.34) and fat (r(2) 0.35), its inclusion in multi-variate indices offered small or no increases in predictive capacity when hot carcass weight (HCW) and a measure of rib fat-depth (GR) were present in the model. Optimized equations were able to account for 65-90 % of the variance observed in the weight of chemical components in the carcass. It is concluded that single frequency impedance data do not provide better prediction of carcass composition than can be obtained from measures of HCW and GR. Indices of intracellular water mass derived from impedance at zero frequency and the characteristic frequency explained a similar proportion of the variance in carcass protein mass as did the index L-2/Z(50).