Mfuzz: a software package for soft clustering of microarray data

For the analysis of microarray data, clustering techniques are frequently used. Most of such methods are based on hard clustering of data wherein one gene (or sample) is assigned to exactly one cluster. Hard clustering, however, suffers from several drawbacks such as sensitivity to noise and information loss. In contrast, soft clustering methods can assign a gene to several clusters. They can overcome shortcomings of conventional hard clustering techniques and offer further advantages. Thus, we constructed an R package termed Mfuzz implementing soft clustering tools for microarray data analysis. The additional package Mfuzzgui provides a convenient TclTk based graphical user interface. AVAILABILITY: The R package Mfuzz and Mfuzzgui are available at http://itb1.biologie.hu-berlin.de/~futschik/software/R/Mfuzz/index.html. Their distribution is subject to GPL version 2 license.     

Analysis of a Gibbs sampler method for model-based clustering of gene expression data

MOTIVATION: Over the last decade, a large variety of clustering algorithms have been developed to detect coregulatory relationships among genes from microarray gene expression data. Model-based clustering approaches have emerged as statistically well-grounded methods, but the properties of these algorithms when applied to large-scale data sets are not always well understood. An in-depth analysis can reveal important insights about the performance of the algorithm, the expected quality of the output clusters, and the possibilities for extracting more relevant information out of a particular data set. RESULTS: We have extended an existing algorithm for model-based clustering of genes to simultaneously cluster genes and conditions, and used three large compendia of gene expression data for Saccharomyces cerevisiae to analyze its properties. The algorithm uses a Bayesian approach and a Gibbs sampling procedure to iteratively update the cluster assignment of each gene and condition. For large-scale data sets, the posterior distribution is strongly peaked on a limited number of equiprobable clusterings. A GO annotation analysis shows that these local maxima are all biologically equally significant, and that simultaneously clustering genes and conditions performs better than only clustering genes and assuming independent conditions. A collection of distinct equivalent clusterings can be summarized as a weighted graph on the set of genes, from which we extract fuzzy, overlapping clusters using a graph spectral method. The cores of these fuzzy clusters contain tight sets of strongly coexpressed genes, while the overlaps exhibit relations between genes showing only partial coexpression. AVAILABILITY: GaneSh, a Java package for coclustering, is available under the terms of the GNU General Public License from our website at http://bioinformatics.psb.ugent.be/software     

Microarray learning with ABC

Standard clustering algorithms when applied to DNA microarray data often tend to produce erroneous clusters. A major contributor to this divergence is the feature characteristic of microarray data sets that the number of predictors (genes) in such data far exceeds the number of samples by many orders of magnitude, with only a small percentage of predictors being truly informative with regards to the clustering while the rest merely add noise. An additional complication is that the predictors exhibit an unknown complex correlational configuration embedded in a small subspace of the entire predictor space. Under these conditions, standard clustering algorithms fail to find the true clusters even when applied in tandem with some sort of gene filtering or dimension reduction to reduce the number of predictors. We propose, as an alternative, a novel method for unsupervised classification of DNA microarray data. The method, which is based on the idea of aggregating results obtained from an ensemble of randomly resampled data (where both samples and genes are resampled), introduces a way of tilting the procedure so that the ensemble includes minimal representation from less important areas of the gene predictor space. The method produces a measure of dissimilarity between each pair of samples that can be used in conjunction with (a) a method like Ward's procedure to generate a cluster analysis and (b) multidimensional scaling to generate useful visualizations of the data. We call the dissimilarity measures ABC dissimilarities since they are obtained by aggregating bundles of clusters. An extensive comparison of several clustering methods using actual DNA microarray data convincingly demonstrates that classification using ABC dissimilarities offers significantly superior performance.     

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.     

Text mining biomedical literature for discovering gene-to-gene relationships: a comparative study of algorithms

Partitioning closely related genes into clusters has become an important element of practically all statistical analyses of microarray data. A number of computer algorithms have been developed for this task. Although these algorithms have demonstrated their usefulness for gene clustering, some basic problems remain. This paper describes our work on extracting functional keywords from MEDLINE for a set of genes that are isolated for further study from microarray experiments based on their differential expression patterns. The sharing of functional keywords among genes is used as a basis for clustering in a new approach called BEA-PARTITION in this paper. Functional keywords associated with genes were extracted from MEDLINE abstracts. We modified the Bond Energy Algorithm (BEA), which is widely accepted in psychology and database design but is virtually unknown in bioinformatics, to cluster genes by functional keyword associations. The results showed that BEA-PARTITION and hierarchical clustering algorithm outperformed k-means clustering and self-organizing map by correctly assigning 25 of 26 genes in a test set of four known gene groups. To evaluate the effectiveness of BEA-PARTITION for clustering genes identified by microarray profiles, 44 yeast genes that are differentially expressed during the cell cycle and have been widely studied in the literature were used as a second test set. Using established measures of cluster quality, the results produced by BEA-PARTITION had higher purity, lower entropy, and higher mutual information than those produced by k-means and self-organizing map. Whereas BEA-PARTITION and the hierarchical clustering produced similar quality of clusters, BEA-PARTITION provides clear cluster boundaries compared to the hierarchical clustering. BEA-PARTITION is simple to implement and provides a powerful approach to clustering genes or to any clustering problem where starting matrices are available from experimental observations.     

Context-specific infinite mixtures for clustering gene expression profiles across diverse microarray dataset

MOTIVATION: Identifying groups of co-regulated genes by monitoring their expression over various experimental conditions is complicated by the fact that such co-regulation is condition-specific. Ignoring the context-specific nature of co-regulation significantly reduces the ability of clustering procedures to detect co-expressed genes due to additional 'noise' introduced by non-informative measurements. RESULTS: We have developed a novel Bayesian hierarchical model and corresponding computational algorithms for clustering gene expression profiles across diverse experimental conditions and studies that accounts for context-specificity of gene expression patterns. The model is based on the Bayesian infinite mixtures framework and does not require a priori specification of the number of clusters. We demonstrate that explicit modeling of context-specificity results in increased accuracy of the cluster analysis by examining the specificity and sensitivity of clusters in microarray data. We also demonstrate that probabilities of co-expression derived from the posterior distribution of clusterings are valid estimates of statistical significance of created clusters. AVAILABILITY: The open-source package gimm is available at http://eh3.uc.edu/gimm.     

Clustering microarray gene expression data using weighted Chinese restaurant process

MOTIVATION: Clustering microarray gene expression data is a powerful tool for elucidating co-regulatory relationships among genes. Many different clustering techniques have been successfully applied and the results are promising. However, substantial fluctuation contained in microarray data, lack of knowledge on the number of clusters and complex regulatory mechanisms underlying biological systems make the clustering problems tremendously challenging. RESULTS: We devised an improved model-based Bayesian approach to cluster microarray gene expression data. Cluster assignment is carried out by an iterative weighted Chinese restaurant seating scheme such that the optimal number of clusters can be determined simultaneously with cluster assignment. The predictive updating technique was applied to improve the efficiency of the Gibbs sampler. An additional step is added during reassignment to allow genes that display complex correlation relationships such as time-shifted and/or inverted to be clustered together. Analysis done on a real dataset showed that as much as 30% of significant genes clustered in the same group display complex relationships with the consensus pattern of the cluster. Other notable features including automatic handling of missing data, quantitative measures of cluster strength and assignment confidence. Synthetic and real microarray gene expression datasets were analyzed to demonstrate its performance. AVAILABILITY: A computer program named Chinese restaurant cluster (CRC) has been developed based on this algorithm. The program can be downloaded at http://www.sph.umich.edu/csg/qin/CRC/.     

An unsupervised hierarchical dynamic self-organizing approach to cancer class discovery and marker gene identification in microarray data

MOTIVATION: Current Self-Organizing Maps (SOMs) approaches to gene expression pattern clustering require the user to predefine the number of clusters likely to be expected. Hierarchical clustering methods used in this area do not provide unique partitioning of data. We describe an unsupervised dynamic hierarchical self-organizing approach, which suggests an appropriate number of clusters, to perform class discovery and marker gene identification in microarray data. In the process of class discovery, the proposed algorithm identifies corresponding sets of predictor genes that best distinguish one class from other classes. The approach integrates merits of hierarchical clustering with robustness against noise known from self-organizing approaches. RESULTS: The proposed algorithm applied to DNA microarray data sets of two types of cancers has demonstrated its ability to produce the most suitable number of clusters. Further, the corresponding marker genes identified through the unsupervised algorithm also have a strong biological relationship to the specific cancer class. The algorithm tested on leukemia microarray data, which contains three leukemia types, was able to determine three major and one minor cluster. Prediction models built for the four clusters indicate that the prediction strength for the smaller cluster is generally low, therefore labelled as uncertain cluster. Further analysis shows that the uncertain cluster can be subdivided further, and the subdivisions are related to two of the original clusters. Another test performed using colon cancer microarray data has automatically derived two clusters, which is consistent with the number of classes in data (cancerous and normal). AVAILABILITY: JAVA software of dynamic SOM tree algorithm is available upon request for academic use. SUPPLEMENTARY INFORMATION: A comparison of rectangular and hexagonal topologies for GSOM is available from http://www.mame.mu.oz.au/mechatronics/journalinfo/Hsu2003supp.pdf     

Consensus framework for exploring microarray data using multiple clustering methods

The large variety of clustering algorithms and their variants can be daunting to researchers wishing to explore patterns within their microarray datasets. Furthermore, each clustering method has distinct biases in finding patterns within the data, and clusterings may not be reproducible across different algorithms. A consensus approach utilizing multiple algorithms can show where the various methods agree and expose robust patterns within the data. In this paper, we present a software package - Consense, written for R/Bioconductor - that utilizes such an approach to explore microarray datasets. Consense produces clustering results for each of the clustering methods and produces a report of metrics comparing the individual clusterings. A feature of Consense is identification of genes that cluster consistently with an index gene across methods. Utilizing simulated microarray data, sensitivity of the metrics to the biases of the different clustering algorithms is explored. The framework is easily extensible, allowing this tool to be used by other functional genomic data types, as well as other high-throughput OMICS data types generated from metabolomic and proteomic experiments. It also provides a flexible environment to benchmark new clustering algorithms. Consense is currently available as an installable R/Bioconductor package (http://www.ohsucancer.com/isrdev/consense/).     

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.     

Gene expression data analysis using multiobjective clustering improved with SVM based ensemble

Microarray technology facilitates the monitoring of the expression levels of thousands of genes over different experimental conditions simultaneously. Clustering is a popular data mining tool which can be applied to microarray gene expression data to identify co-expressed genes. Most of the traditional clustering methods optimize a single clustering goodness criterion and thus may not be capable of performing well on all kinds of datasets. Motivated by this, in this article, a multiobjective clustering technique that optimizes cluster compactness and separation simultaneously, has been improved through a novel support vector machine classification based cluster ensemble method. The superiority of MOCSVMEN (MultiObjective Clustering with Support Vector Machine based ENsemble) has been established by comparing its performance with that of several well known existing microarray data clustering algorithms. Two real-life benchmark gene expression datasets have been used for testing the comparative performances of different algorithms. A recently developed metric, called Biological Homogeneity Index (BHI), which computes the clustering goodness with respect to functional annotation, has been used for the comparison purpose.     

Graph-based consensus clustering for class discovery from gene expression data

MOTIVATION: Consensus clustering, also known as cluster ensemble, is one of the important techniques for microarray data analysis, and is particularly useful for class discovery from microarray data. Compared with traditional clustering algorithms, consensus clustering approaches have the ability to integrate multiple partitions from different cluster solutions to improve the robustness, stability, scalability and parallelization of the clustering algorithms. By consensus clustering, one can discover the underlying classes of the samples in gene expression data. RESULTS: In addition to exploring a graph-based consensus clustering (GCC) algorithm to estimate the underlying classes of the samples in microarray data, we also design a new validation index to determine the number of classes in microarray data. To our knowledge, this is the first time in which GCC is applied to class discovery for microarray data. Given a pre specified maximum number of classes (denoted as K(max) in this article), our algorithm can discover the true number of classes for the samples in microarray data according to a new cluster validation index called the Modified Rand Index. Experiments on gene expression data indicate that our new algorithm can (i) outperform most of the existing algorithms, (ii) identify the number of classes correctly in real cancer datasets, and (iii) discover the classes of samples with biological meaning. AVAILABILITY: Matlab source code for the GCC algorithm is available upon request from Zhiwen Yu.     

Mining gene expression data using a novel approach based on hidden Markov models

In this work we have developed a new framework for microarray gene expression data analysis. This framework is based on hidden Markov models. We have benchmarked the performance of this probability model-based clustering algorithm on several gene expression datasets for which external evaluation criteria were available. The results showed that this approach could produce clusters of quality comparable to two prevalent clustering algorithms, but with the major advantage of determining the number of clusters. We have also applied this algorithm to analyze published data of yeast cell cycle gene expression and found it able to successfully dig out biologically meaningful gene groups. In addition, this algorithm can also find correlation between different functional groups and distinguish between function genes and regulation genes, which is helpful to construct a network describing particular biological associations. Currently, this method is limited to time series data. Supplementary materials are available at http://www.bioinfo.tsinghua.edu.cn/~rich/hmmgep_supp/.     

Inferential Clustering Approach for Microarray Experiments with Replicated Measurements

Cluster analysis has proven to be a useful tool for investigating the association structure among genes in a microarray data set. There is a rich literature on cluster analysis and various techniques have been developed. Such analyses heavily depend on an appropriate (dis)similarity measure. In this paper, we introduce a general clustering approach based on the confidence interval inferential methodology, which is applied to gene expression data of microarray experiments. Emphasis is placed on data with low replication (three or five replicates). The proposed method makes more efficient use of the measured data and avoids the subjective choice of a dissimilarity measure. This new methodology, when applied to real data, provides an easy-to-use bioinformatics solution for the cluster analysis of microarray experiments with replicates (see the Appendix). Even though the method is presented under the framework of microarray experiments, it is a general algorithm that can be used to identify clusters in any situation. The method's performance is evaluated using simulated and publicly available data set. Our results also clearly show that our method is not an extension of the conventional clustering method based on correlation or euclidean distance.     

Assessing reliability of gene clusters from gene expression data

The rapid development of microarray technologies has raised many challenging problems in experiment design and data analysis. Although many numerical algorithms have been successfully applied to analyze gene expression data, the effects of variations and uncertainties in measured gene expression levels across samples and experiments have been largely ignored in the literature. In this article, in the context of hierarchical clustering algorithms, we introduce a statistical resampling method to assess the reliability of gene clusters identified from any hierarchical clustering method. Using the clustering trees constructed from the resampled data, we can evaluate the confidence value for each node in the observed clustering tree. A majority-rule consensus tree can be obtained, showing clusters that only occur in a majority of the resampled trees. We illustrate our proposed methods with applications to two published data sets. Although the methods are discussed in the context of hierarchical clustering methods, they can be applied with other cluster-identification methods for gene expression data to assess the reliability of any gene cluster of interest. Electronic Publication     

How well do we understand the clusters found in microarray data?

We wished to quantify the state-of-the-art of our understanding of clusters in microarray data. To do this we systematically compared the clusters produced on sets of microarray data using a representative set of clustering algorithms (hierarchical, k-means, and a modified version of QT_CLUST) with the annotation schemes MIPS, GeneOntology and GenProtEC. We assumed that if a cluster reflected known biology its members would share related ontological annotations. This assumption is the basis of "guilt-by-association" and is commonly used to assign the putative function of proteins. To statistically measure the relationship between cluster and annotation we developed a new predictive discriminatory measure. We found that the clusters found in microarray data do not in general agree with functional annotation classes. Although many statistically significant relationships can be found, the majority of clusters are not related to known biology (as described in annotation ontologies). This implies that use of guilt-by-association is not supported by annotation ontologies. Depending on the estimate of the amount of noise in the data, our results suggest that bioinformatics has only codified a small proportion of the biological knowledge required to understand microarray data.     

Reordering hierarchical tree based on bilateral symmetric distance

Background

In microarray data analysis, hierarchical clustering (HC) is often used to group samples or genes according to their gene expression profiles to study their associations. In a typical HC, nested clustering structures can be quickly identified in a tree. The relationship between objects is lost, however, because clusters rather than individual objects are compared. This results in a tree that is hard to interpret.

Methodology/Principal Findings

This study proposes an ordering method, HC-SYM, which minimizes bilateral symmetric distance of two adjacent clusters in a tree so that similar objects in the clusters are located in the cluster boundaries. The performance of HC-SYM was evaluated by both supervised and unsupervised approaches and compared favourably with other ordering methods.

Conclusions/Significance

The intuitive relationship between objects and flexibility of the HC-SYM method can be very helpful in the exploratory analysis of not only microarray data but also similar high-dimensional data.     

Identifying subset of genes that have influential impacts on cancer progression: a new approach to analyze cancer microarray data

Cancer is a complex genetic disease, resulting from defects of multiple genes. Development of microarray techniques makes it possible to survey the whole genome and detect genes that have influential impacts on the progression of cancer. Statistical analysis of cancer microarray data is challenging because of the high dimensionality and cluster nature of gene expressions. Here, clusters are composed of genes with coordinated pathological functions and/or correlated expressions. In this article, we consider cancer studies where censored survival endpoint is measured along with microarray gene expressions. We propose a hybrid clustering approach, which uses both pathological pathway information retrieved from KEGG and statistical correlations of gene expressions, to construct gene clusters. Cancer survival time is modeled as a linear function of gene expressions. We adopt the clustering threshold gradient directed regularization (CTGDR) method for simultaneous gene cluster selection, within-cluster gene selection, and predictive model building. Analysis of two lymphoma studies shows that the proposed approach - which is composed of the hybrid gene clustering, linear regression model for survival, and clustering regularized estimation with CTGDR - can effectively identify gene clusters and genes within selected clusters that have satisfactory predictive power for censored cancer survival outcomes.