Scoring clustering solutions by their biological relevance

MOTIVATION: A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering gene expression data into homogeneous groups was shown to be instrumental in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on clustering algorithms for gene expression analysis, very few works addressed the systematic comparison and evaluation of clustering results. Typically, different clustering algorithms yield different clustering solutions on the same data, and there is no agreed upon guideline for choosing among them. RESULTS: We developed a novel statistically based method for assessing a clustering solution according to prior biological knowledge. Our method can be used to compare different clustering solutions or to optimize the parameters of a clustering algorithm. The method is based on projecting vectors of biological attributes of the clustered elements onto the real line, such that the ratio of between-groups and within-group variance estimators is maximized. The projected data are then scored using a non-parametric analysis of variance test, and the score's confidence is evaluated. We validate our approach using simulated data and show that our scoring method outperforms several extant methods, including the separation to homogeneity ratio and the silhouette measure. We apply our method to evaluate results of several clustering methods on yeast cell-cycle gene expression data. AVAILABILITY: The software is available from the authors upon request.     

Supervised cluster analysis for microarray data based on multivariate Gaussian mixture

MOTIVATION: Grouping genes having similar expression patterns is called gene clustering, which has been proved to be a useful tool for extracting underlying biological information of gene expression data. Many clustering procedures have shown success in microarray gene clustering; most of them belong to the family of heuristic clustering algorithms. Model-based algorithms are alternative clustering algorithms, which are based on the assumption that the whole set of microarray data is a finite mixture of a certain type of distributions with different parameters. Application of the model-based algorithms to unsupervised clustering has been reported. Here, for the first time, we demonstrated the use of the model-based algorithm in supervised clustering of microarray data. RESULTS: We applied the proposed methods to real gene expression data and simulated data. We showed that the supervised model-based algorithm is superior over the unsupervised method and the support vector machines (SVM) method. AVAILABILITY: The program written in the SAS language implementing methods I-III in this report is available upon request. The software of SVMs is available in the website http://svm.sdsc.edu/cgi-bin/nph-SVMsubmit.cgi     

Evaluation and optimization of clustering in gene expression data analysis

MOTIVATION: A measurement of cluster quality is needed to choose potential clusters of genes that contain biologically relevant patterns of gene expression. This is strongly desirable when a large number of gene expression profiles have to be analyzed and proper clusters of genes need to be identified for further analysis, such as the search for meaningful patterns, identification of gene functions or gene response analysis. RESULTS: We propose a new cluster quality method, called stability, by which unsupervised learning of gene expression data can be performed efficiently. The method takes into account a cluster's stability on partition. We evaluate this method and demonstrate its performance using four independent, real gene expression and three simulated datasets. We demonstrate that our method outperforms other techniques listed in the literature. The method has applications in evaluating clustering validity as well as identifying stable clusters. AVAILABILITY: Please contact the first author.     

Gene ordering in partitive clustering using microarray expressions

A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering and ordering the genes using gene expression data into homogeneous groups was shown to be useful in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on gene ordering in hierarchical clustering framework for gene expression analysis, there is no work addressing and evaluating the importance of gene ordering in partitive clustering framework, to the best knowledge of the authors. Outside the framework of hierarchical clustering, different gene ordering algorithms are applied on the whole data set, and the domain of partitive clustering is still unexplored with gene ordering approaches. A new hybrid method is proposed for ordering genes in each of the clusters obtained from partitive clustering solution, using microarray gene expressions.Two existing algorithms for optimally ordering cities in travelling salesman problem (TSP), namely, FRAG_GALK and Concorde, are hybridized individually with self organizing MAP to show the importance of gene ordering in partitive clustering framework. We validated our hybrid approach using yeast and fibroblast data and showed that our approach improves the result quality of partitive clustering solution, by identifying subclusters within big clusters, grouping functionally correlated genes within clusters, minimization of summation of gene expression distances, and the maximization of biological gene ordering using MIPS categorization. Moreover, the new hybrid approach, finds comparable or sometimes superior biological gene order in less computation time than those obtained by optimal leaf ordering in hierarchical clustering solution.     

Validating clustering for gene expression data

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.     

Gene expression profiles of normal proliferating and differentiating human intestinal epithelial cells: a comparison with the Caco-2 cell model

cDNA microarray technology enables detailed analysis of gene expression throughout complex processes such as differentiation. The aim of this study was to analyze the gene expression profile of normal human intestinal epithelial cells using cell models that recapitulate the crypt-villus axis of intestinal differentiation in comparison with the widely used Caco-2 cell model. cDNA microarrays (19,200 human genes) and a clustering algorithm were used to identify patterns of gene expression in the crypt-like proliferative HIEC and tsFHI cells, and villus epithelial cells as well as Caco-2/15 cells at two distinct stages of differentiation. Unsupervised hierarchical clustering analysis of global gene expression among the cell lines identified two branches: one for the HIEC cells versus a second comprised of two sub-groups: (a) the proliferative Caco-2 cells and (b) the differentiated Caco-2 cells and closely related villus epithelial cells. At the gene level, supervised hierarchical clustering with 272 differentially expressed genes revealed distinct expression patterns specific to each cell phenotype. We identified several upregulated genes that could lead to the identification of new regulatory pathways involved in cell differentiation and carcinogenesis. The combined use of microarray analysis and human intestinal cell models thus provides a powerful tool for establishing detailed gene expression profiles of proliferative to terminally differentiated intestinal cells. Furthermore, the molecular differences between the normal human intestinal cell models and Caco-2 cells clearly point out the strengths and limitations of this widely used experimental model for studying intestinal cell proliferation and differentiation.     

Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters

MOTIVATION: Cluster analysis of genome-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and samples. In the present paper, we focus on several important issues related to clustering algorithms that have not yet been fully studied. RESULTS: We describe a simple and robust algorithm for the clustering of temporal gene expression profiles that is based on the simulated annealing procedure. In general, this algorithm guarantees to eventually find the globally optimal distribution of genes over clusters. We introduce an iterative scheme that serves to evaluate quantitatively the optimal number of clusters for each specific data set. The scheme is based on standard approaches used in regular statistical tests. The basic idea is to organize the search of the optimal number of clusters simultaneously with the optimization of the distribution of genes over clusters. The efficiency of the proposed algorithm has been evaluated by means of a reverse engineering experiment, that is, a situation in which the correct distribution of genes over clusters is known a priori. The employment of this statistically rigorous test has shown that our algorithm places greater than 90% genes into correct clusters. Finally, the algorithm has been tested on real gene expression data (expression changes during yeast cell cycle) for which the fundamental patterns of gene expression and the assignment of genes to clusters are well understood from numerous previous studies.     

A new algorithm for comparing and visualizing relationships between hierarchical and flat gene expression data clusterings

MOTIVATION: Clustering is one of the most widely used methods in unsupervised gene expression data analysis. The use of different clustering algorithms or different parameters often produces rather different results on the same data. Biological interpretation of multiple clustering results requires understanding how different clusters relate to each other. It is particularly non-trivial to compare the results of a hierarchical and a flat, e.g. k-means, clustering. RESULTS: We present a new method for comparing and visualizing relationships between different clustering results, either flat versus flat, or flat versus hierarchical. When comparing a flat clustering to a hierarchical clustering, the algorithm cuts different branches in the hierarchical tree at different levels to optimize the correspondence between the clusters. The optimization function is based on graph layout aesthetics or on mutual information. The clusters are displayed using a bipartite graph where the edges are weighted proportionally to the number of common elements in the respective clusters and the weighted number of crossings is minimized. The performance of the algorithm is tested using simulated and real gene expression data. The algorithm is implemented in the online gene expression data analysis tool Expression Profiler. AVAILABILITY: http://www.ebi.ac.uk/expressionprofiler     

EXCAVATOR: a computer program for efficiently mining gene expression data

Massive amounts of gene expression data are generated using microarrays for functional studies of genes and gene expression data clustering is a useful tool for studying the functional relationship among genes in a biological process. We have developed a computer package EXCAVATOR for clustering gene expression profiles based on our new framework for representing gene expression data as a minimum spanning tree. EXCAVATOR uses a number of rigorous and efficient clustering algorithms. This program has a number of unique features, including capabilities for: (i) data- constrained clustering; (ii) identification of genes with similar expression profiles to pre-specified seed genes; (iii) cluster identification from a noisy background; (iv) computational comparison between different clustering results of the same data set. EXCAVATOR can be run from a Unix/Linux/DOS shell, from a Java interface or from a Web server. The clustering results can be visualized as colored figures and 2-dimensional plots. Moreover, EXCAVATOR provides a wide range of options for data formats, distance measures, objective functions, clustering algorithms, methods to choose number of clusters, etc. The effectiveness of EXCAVATOR has been demonstrated on several experimental data sets. Its performance compares favorably against the popular K-means clustering method in terms of clustering quality and computing time.     

An algorithm to infer similarity among cell types and organisms by examining the most expressed sequences

Following sequence alignment, clustering algorithms are among the most utilized techniques in gene expression data analysis. Clustering gene expression patterns allows researchers to determine which gene expression patterns are alike and most likely to participate in the same biological process being investigated. Gene expression data also allow the clustering of whole samples of data, which makes it possible to find which samples are similar and, consequently, which sampled biological conditions are alike. Here, a novel similarity measure calculation and the resulting rank-based clustering algorithm are presented. The clustering was applied in 418 gene expression samples from 13 data series spanning three model organisms: Homo sapiens, Mus musculus, and Arabidopsis thaliana. The initial results are striking: more than 91% of the samples were clustered as expected. The MESs (most expressed sequences) approach outperformed some of the most used clustering algorithms applied to this kind of data such as hierarchical clustering and K-means. The clustering performance suggests that the new similarity measure is an alternative to the traditional correlation/distance measures typically used in clustering algorithms.     

Model-based clustering and data transformations for gene expression data.

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.     

Complementary hierarchical clustering

When applying hierarchical clustering algorithms to cluster patient samples from microarray data, the clustering patterns generated by most algorithms tend to be dominated by groups of highly differentially expressed genes that have closely related expression patterns. Sometimes, these genes may not be relevant to the biological process under study or their functions may already be known. The problem is that these genes can potentially drown out the effects of other genes that are relevant or have novel functions. We propose a procedure called complementary hierarchical clustering that is designed to uncover the structures arising from these novel genes that are not as highly expressed. Simulation studies show that the procedure is effective when applied to a variety of examples. We also define a concept called relative gene importance that can be used to identify the influential genes in a given clustering. Finally, we analyze a microarray data set from 295 breast cancer patients, using clustering with the correlation-based distance measure. The complementary clustering reveals a grouping of the patients which is uncorrelated with a number of known prognostic signatures and significantly differing distant metastasis-free probabilities.     

A web-based tool for principal component and significance analysis of microarray data

We have developed a program for microarray data analysis, which features the false discovery rate for testing statistical significance and the principal component analysis using the singular value decomposition method for detecting the global trends of gene-expression patterns. Additional features include analysis of variance with multiple methods for error variance adjustment, correction of cross-channel correlation for two-color microarrays, identification of genes specific to each cluster of tissue samples, biplot of tissues and corresponding tissue-specific genes, clustering of genes that are correlated with each principal component (PC), three-dimensional graphics based on virtual reality modeling language and sharing of PC between different experiments. The software also supports parameter adjustment, gene search and graphical output of results. The software is implemented as a web tool and thus the speed of analysis does not depend on the power of a client computer. AVAILABILITY: The tool can be used on-line or downloaded at http://lgsun.grc.nia.nih.gov/ANOVA/     

GEPIS--quantitative gene expression profiling in normal and cancer tissues

MOTIVATION: Expression profiling in diverse tissues is fundamental to understanding gene function as well as therapeutic target identification. The vast collection of expressed sequence tags (ESTs) and the associated tissue source information provides an attractive opportunity for studying gene expression. RESULTS: To facilitate EST-based expression analysis, we developed GEPIS (gene expression profiling in silico), a tool that integrates EST and tissue source information to compute gene expression patterns in a large panel of normal and tumor samples. We found EST-based expression patterns to be consistent with published papers as well as our own experimental results. We also built a GEPIS Regional Atlas that depicts expression characteristics of all genes in a selected genomic region. This program can be adapted for large-scale screening for genes with desirable expression patterns, as illustrated by our large-scale mining for tissue- and tumor-specific genes. AVAILABILITY: The email server version of the GEPIS application is freely available at http://share.gene.com/share/gepis. An interactive version of GEPIS will soon be freely available at http://www.cgl.ucsf.edu/Research/genentech/gepis/. The source code, modules, data and gene lists can be downloaded at http://share.gene.com/share/gepis.