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.

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.

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).

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.

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.

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 the acute postoperative pain experience following oral surgery: identification of 'unaffected', 'disabled' and 'depressed, anxious and disabled' patient clusters

Background: Pain is defined as both a sensory and an emotional experience. Acute postoperative tooth extraction pain is assessed and treated as a physiological (sensory) pain while chronic pain is a biopsychosocial problem. The purpose of this study was to assess whether psychological and social changes Occur in the acute pain state. Methods: A biopsychosocial pain questionnaire was completed by 438 subjects (165 males, 273 females) with acute postoperative pain at 24 hours following the surgical extraction of teeth and compared with 273 subjects (78 males, 195 females) with chronic orofacial pain. Statistical methods used a k-means cluster analysis. Results: Three clusters were identified in the acute pain group: 'unaffected', 'disabled' and 'depressed, anxious and disabled'. Psychosocial effects showed 24.8 per cent feeling 'distress/suffering' and 15.1 per cent 'sad and depressed'. Females reported higher pain intensity and more distress, depression and inadequate medication for pain relief (p

Using multivariate analysis to predict the behaviour of soils under effluent irrigation

Onsite wastewater treatment systems aim to assimilate domestic effluent into the environment. Unfortunately failure of such systems is common and inadequate effluent treatment can have serious environmental implications. The capacity of a particular soil to treat wastewater will change over time. The physical properties influence the rate of effluent movement through the soil and its chemical properties dictate the ability to renovate effluent. A research project was undertaken to determine the role that physical and chemical soil properties play in predicting the long-term behaviour of soil under effluent irrigation and to determine if they have a potential function as early indicators of adverse effects of effluent irrigation on treatment sustainability. Principal Component Analysis (PCA) and Cluster Analysis grouped the soils independently of their soil classifications and allowed us to distinguish the most suitable soils for sustainable long term effluent irrigation and determine the most influential soil parameters to characterise them. Multivariate analysis allowed a clear distinction between soils based on the cation exchange capacities. This in turn correlated well with the soil mineralogy. Mixed mineralogy soils in particular sodium or magnesium dominant soils are the most susceptible to dispersion under effluent irrigation. The soil Exchangeable Sodium Percentage (ESP) was identified as a crucial parameter and was highly correlated with percentage clay, electrical conductivity, exchangeable sodium, exchangeable magnesium and low Ca:Mg ratios (less than 0.5).

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.

Characterization of acute whiplash-associated disorders

Study Design. An experimental study of motor and sensory function and psychological distress in subjects with acute whiplash injury. Objectives. To characterize acute whiplash injury in terms of motor and sensory systems dysfunction and psychological distress and to compare subjects with higher and lesser levels of pain and disability. Summary of Background Data. Motor system dysfunction, sensory hypersensitivity, and psychological distress are present in chronic whiplash associated disorders ( WAD), but little is known of such factors in the acute stage of injury. As higher levels of pain and disability in acute WAD are accepted as signs of poor outcome, further characterization of this group from those with lesser symptoms is important. Materials and Methods. Motor function ( cervical range of movement [ ROM], joint position error [JPE]; activity of the superficial neck flexors [EMG] during a test of craniocervical flexion), quantitative sensory testing ( pressure, thermal pain thresholds, and responses to the brachial plexus provocation test), and psychological distress (GHQ-28, TAMPA, IES) were measured in 80 whiplash subjects ( WAD II or III) within 1 month of injury, as were 20 control subjects. Results. Three subgroups were identified in the cohort using cluster analysis based on the Neck Disability Index: those with mild, moderate, or severe pain and disability. All whiplash groups demonstrated decreased ROM and increased EMG compared with the controls ( all P < 0.01). Only the moderate and severe groups demonstrated greater JPE and generalized hypersensitivity to all sensory tests ( all P < 0.01). The three whiplash subgroups demonstrated evidence of psychological distress, although this was greater in the moderate and severe groups. Measures of psychological distress did not impact on between group differences in motor or sensory tests. Conclusions. Acute whiplash subjects with higher levels of pain and disability were distinguished by sensory hypersensitivity to a variety of stimuli, suggestive of central nervous system sensitization occurring soon after injury. These responses occurred independently of psychological distress. These findings may be important for the differential diagnosis of acute whiplash injury and could be one reason why those with higher initial pain and disability demonstrate a poorer outcome.

Homologues of the maize rust resistance gene Rp1-D are genetically associated with a major rust resistance QTL in sorghum

As part of a comparative mapping study between sugarcane and sorghum, a sugarcane cDNA clone with homology to the maize Rp1-D rust resistance gene was mapped in sorghum. The cDNA probe hybridised to multiple loci, including one on sorghum linkage group (LG) E in a region where a major rust resistance QTL had been previously mapped. Partial sorghum Rp1-D homologues were isolated from genomic DNA of rust-resistant and -susceptible progeny selected from a sorghum mapping population. Sequencing of the Rp1-D homologues revealed five discrete sequence classes: three from resistant progeny and two from susceptible progeny. PCR primers specific to each sequence class were used to amplify products from the progeny and confirmed that the five sequence classes mapped to the same locus on LG E. Cluster analysis of these sorghum sequences and available sugarcane, maize and sorghum Rp1-D homologue sequences showed that the maize Rp1-D sequence and the partial sugarcane Rp1-D homologue were clustered with one of the sorghum resistant progeny sequence classes, while previously published sorghum Rp1-D homologue sequences clustered with the susceptible progeny sequence classes. Full-length sequence information was obtained for one member of a resistant progeny sequence class (Rp1-SO) and compared with the maize Rp1-D sequence and a previously identified sorghum Rp1 homologue (Rph1-2). There was considerable similarity between the two sorghum sequences and less similarity between the sorghum and maize sequences. These results suggest a conservation of function and gene sequence homology at the Rp1 loci of maize and sorghum and provide a basis for convenient PCR-based screening tools for putative rust resistance alleles in sorghum.

Metamorphosis of a scleractinian coral in response to microbial biofilms

Microorganisms have been reported to induce settlement and metamorphosis in a wide range of marine invertebrate species. However, the primary cue reported for metamorphosis of coral larvae is calcareous coralline algae (CCA). Herein we report the community structure of developing coral reef biofilms and the potential role they play in triggering the metamorphosis of a scleractinian coral. Two-week-old biofilms induced metamorphosis in less than 10% of larvae, whereas metamorphosis increased significantly on older biofilms, with a maximum of 41% occurring on 8-week-old microbial films. There was a significant influence of depth in 4- and 8-week biofilms, with greater levels of metamorphosis occurring in response to shallow-water communities. Importantly, larvae were found to settle and metamorphose in response to microbial biofilms lacking CCA from both shallow and deep treatments, indicating that microorganisms not associated with CCA may play a significant role in coral metamorphosis. A polyphasic approach consisting of scanning electron microscopy, fluorescence in situ hybridization (FISH), and denaturing gradient gel electrophoresis (DGGE) revealed that coral reef biofilms were comprised of complex bacterial and microalgal communities which were distinct at each depth and time. Principal-component analysis of FISH data showed that the Alphaproteobacteria, Betaproteobacteria, Gammaproteobacteria, and Cytophaga-Flavobacterium of Bacteroidetes had the largest influence on overall community composition. A low abundance of Archaea was detected in almost all biofilms, providing the first report of Archaea associated with coral reef biofilms. No differences in the relative densities of each subdivision of Proteobacteria were observed between slides that induced larval metamorphosis and those that did not. Comparative cluster analysis of bacterial DGGE patterns also revealed that there were clear age and depth distinctions in biofilm community structure; however, no difference was detected in banding profiles between biofilms which induced larval metamorphosis and those where no metamorphosis occurred. This investigation demonstrates that complex microbial communities can induce coral metamorphosis in the absence of CCA.

Using molecular markers to assess the effect of introgression on quantitative attributes of common bean in the Andean gene pool

Progress in bean breeding programs requires the exploitation of genetic variation that is present among races or through introgression across gene pools of Phaseolus vulgaris L. Of the two major common bean gene pools, the Andean gene pool seems to have a narrow genetic base, with about 10% of the accessions in the CIAT core collection presenting evidence of introgression. The objective of this study was to quantify the degree of spontaneous introgression in a sample of common bean landraces from the Andean gene pool. The effects of introgression on morphological, economic and nutritional attributes were also investigated. Homogeneity analysis was performed on molecular marker data from 426 Andean-type accessions from the primary centres of origin of the CIAT common bean core collection and two check varieties. Quantitative attribute diversity for 15 traits was studied based on the groups found from the cluster analysis of marker prevalence indices computed for each accession. The two-group summary consisted of one group of 58 accessions (14%) with low prevalence indices and another group of 370 accessions (86%) with high prevalence indices. The smaller group occupied the outlying area of points displayed from homogeneity analysis, yet their geographic origin was widely distributed over the Andean region. This group was regarded as introgressed, since its accessions displayed traits that are associated with the Middle American gene pool: high resistance to Andean disease isolates but low resistance to Middle American disease isolates, low seed weight and high scores for all nutrient elements. Genotypes generated by spontaneous introgression can be helpful for breeders to overcome the difficulties in transferring traits between gene pools.