Motivation: There is a great need to develop analytical methodology to analyze and to exploit the information contained in gene expression data. Because of the large number of genes and the complexity of biological networks, clustering is a useful exploratory technique for analysis of gene expression data. Other classical techniques, such as principal component analysis (PCA), have also been applied to analyze gene expression data. Using different data analysis techniques and different clustering algorithms to analyze the same data set can lead to very different conclusions. Our goal is to study the effectiveness of principal components (PCs) in capturing cluster structure. Specifically, using both real and synthetic gene expression data sets, we compared the quality of clusters obtained from the original data to the quality of clusters obtained after projecting onto subsets of the principal component axes. Results: Our empirical study showed that clustering with the PCs instead of the original variables does not necessarily improve, and often degrades, cluster quality. In particular, the first few PCs (which contain most of the variation in the data) do not necessarily capture most of the cluster structure. We also showed that clustering with PCs has different impact on different algorithms and different similarity metrics. Overall, we would not recommend PCA before clustering except in special circumstances. Contact: kayee@cs.washington.edu Supplementary information: http://www.cs.washington.edu/homes/kayee/pca * To whom correspondence should be addressed.

Motivation: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a ‘good’ clustering method and determining the ‘correct’ number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications. Results: We benchmarked the performance of model-based clustering on several synthetic and real gene expression data sets for which external evaluation criteria were available. The model-based approach has superior performance on our synthetic data sets, consistently selecting the correct model and the number of clusters. On real expression data, the model-based approach produced clusters of quality comparable to a leading heuristic clustering algorithm, but with the key advantage of suggesting the number of clusters and an appropriate model. We also explored the validity of the Gaussian mixture assumption on different transformations of real data. We also assessed the degree to which these real gene expression data sets fit multivariate Gaussian distributions both before and after subjecting them to commonly used data transformations. Suitably chosen transformations seem to result in reasonable fits. Availability: Mclust is available at http://www.stat.washington.edu/fraley/mclust. The software for the diagonal model is under development. Contact: kayee@cs.washington.edu Supplementary information: http://www.cs.washington.edu/homes/kayee/model * To whom all correspondence should be addressed.

Motivation: Many clustering algorithms have been proposed for the analysis of gene expression data, but little guidance is available to help choose among them. We provide a systematic framework for assessing the results of clustering algorithms. Clustering algorithms attempt to partition the genes into groups exhibiting similar patterns of variation in expression level. Our methodology is to apply a clustering algorithm to the data from all but one experimental condition. The remaining condition is used to assess the predictive power of the resulting clusters—meaningful clusters should exhibit less variation in the remaining condition than clusters formed by chance. Results: We successfully applied our methodology to compare six clustering algorithms on four gene expression data sets. We found our quantitative measures of cluster quality to be positively correlated with external standards of cluster quality. Availability: The software is under development. Contact: kayee@cs.washington.edu Supplementary information: http://www.cs.washington.edu/homes/kayee/cluster or http://www.cs.washington.edu/homes/ruzzo/cluster * To whom correspondence should be addressed.

Motivation: Selecting a small number of relevant genes for accurate classification of samples is essential for the development of diagnostic tests. We present the Bayesian model averaging (BMA) method for gene selection and classification of microarray data. Typical gene selection and classification procedures ignore model uncertainty and use a single set of relevant genes (model) to predict the class. BMA accounts for the uncertainty about the best set to choose by averaging over multiple models (sets of potentially overlapping relevant genes). Results: We have shown that BMA selects smaller numbers of relevant genes (compared with other methods) and achieves a high prediction accuracy on three microarray datasets. Our BMA algorithm is applicable to microarray datasets with any number of classes, and outputs posterior probabilities for the selected genes and models. Our selected models typically consist of only a few genes. The combination of high accuracy, small numbers of genes and posterior probabilities for the predictions should make BMA a powerful tool for developing diagnostics from expression data. Availability: The source codes and datasets used are available from our Supplementary website. Contact:kayee@u.washington.edu Supplementary information:http://www.expression.washington.edu/publications/kayee/bma

Network models are widely used in social sciences and genome sciences. The latent space model proposed by Hoff et al. ( 2002 Hoff, P. D. , Raftery, A. E. and Handcock, M. S. 2002. “Latent Space Approaches to Social Network Analysis,”. Journal of the American Statistical Association, 97: 1090–1098. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] ), and extended by Handcock et al. ( 2007 Handcock, M. S. , Raftery, A. E. and Tantrum, J. M. 2007. “Model-Based Clustering for Social Networks” (with discussion),. Journal of the Royal Statistical Society, Series A, 170: 301–354. [Crossref] , [Google Scholar] ) to incorporate clustering, provides a visually interpretable model-based spatial representation of relational data and takes account of several intrinsic network properties. Due to the structure of the likelihood function of the latent space model, the computational cost is of order O(N ²), where N is the number of nodes. This makes it infeasible for large networks. In this article, we propose an approximation of the log-likelihood function. We adapt the case-control idea from epidemiology and construct a case-control log-likelihood, which is an unbiased estimator of the log-full likelihood. Replacing the full likelihood by the case-control likelihood in the Markov chain Monte Carlo estimation of the latent space model reduces the computational time from O(N ²) to O(N), making it feasible for large networks. We evaluate its performance using simulated and real data. We fit the model to a large protein–protein interaction data using the case-control likelihood and use the model fitted link probabilities to identify false positive links. Supplemental materials are available online.

Clustering is a common methodology for the analysis of array data, and many research laboratories are generating array data with repeated measurements. We evaluated several clustering algorithms that incorporate repeated measurements, and show that algorithms that take advantage of repeated measurements yield more accurate and more stable clusters. In particular, we show that the infinite mixture model-based approach with a built-in error model produces superior results.