Fuzzy J-Means and VNS methods for clustering genes from microarray data

MOTIVATION: In the interpretation of gene expression data from a group of microarray experiments that include samples from either different patients or conditions, special consideration must be given to the pleiotropic and epistatic roles of genes, as observed in the variation of gene coexpression patterns. Crisp clustering methods assign each gene to one cluster, thereby omitting information about the multiple roles of genes. RESULTS: Here, we present the application of a local search heuristic, Fuzzy J-Means, embedded into the variable neighborhood search metaheuristic for the clustering of microarray gene expression data. We show that for all the datasets studied this algorithm outperforms the standard Fuzzy C-Means heuristic. Different methods for the utilization of cluster membership information in determining gene coregulation are presented. The clustering and data analyses were performed on simulated datasets as well as experimental cDNA microarray data for breast cancer and human blood from the Stanford Microarray Database. AVAILABILITY: The source code of the clustering software (C programming language) is freely available from Nabil.Belacel@nrc-cnrc.gc.ca     

Incorporating gene functions as priors in model-based clustering of microarray gene expression data

MOTIVATION: Cluster analysis of gene expression profiles has been widely applied to clustering genes for gene function discovery. Many approaches have been proposed. The rationale is that the genes with the same biological function or involved in the same biological process are more likely to co-express, hence they are more likely to form a cluster with similar gene expression patterns. However, most existing methods, including model-based clustering, ignore known gene functions in clustering. RESULTS: To take advantage of accumulating gene functional annotations, we propose incorporating known gene functions as prior probabilities in model-based clustering. In contrast to a global mixture model applicable to all the genes in the standard model-based clustering, we use a stratified mixture model: one stratum corresponds to the genes of unknown function while each of the other ones corresponding to the genes sharing the same biological function or pathway; the genes from the same stratum are assumed to have the same prior probability of coming from a cluster while those from different strata are allowed to have different prior probabilities of coming from the same cluster. We derive a simple EM algorithm that can be used to fit the stratified model. A simulation study and an application to gene function prediction demonstrate the advantage of our proposal over the standard method. CONTACT: weip@biostat.umn.edu     

Modeling and Visualizing Uncertainty in Gene Expression Clusters Using Dirichlet Process Mixtures

Although the use of clustering methods has rapidly become one of the standard computational approaches in the literature of microarray gene expression data, little attention has been paid to uncertainty in the results obtained. Dirichlet process mixture (DPM) models provide a nonparametric Bayesian alternative to the bootstrap approach to modeling uncertainty in gene expression clustering. Most previously published applications of Bayesian model-based clustering methods have been to short time series data. In this paper, we present a case study of the application of nonparametric Bayesian clustering methods to the clustering of high-dimensional nontime series gene expression data using full Gaussian covariances. We use the probability that two genes belong to the same cluster in a DPM model as a measure of the similarity of these gene expression profiles. Conversely, this probability can be used to define a dissimilarity measure, which, for the purposes of visualization, can be input to one of the standard linkage algorithms used for hierarchical clustering. Biologically plausible results are obtained from the Rosetta compendium of expression profiles which extend previously published cluster analyses of this data.     

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     

Incorporating biological knowledge into distance-based clustering analysis of microarray gene expression data

MOTIVATION: Because co-expressed genes are likely to share the same biological function, cluster analysis of gene expression profiles has been applied for gene function discovery. Most existing clustering methods ignore known gene functions in the process of clustering. RESULTS: To take advantage of accumulating gene functional annotations, we propose incorporating known gene functions into a new distance metric, which shrinks a gene expression-based distance towards 0 if and only if the two genes share a common gene function. A two-step procedure is used. First, the shrinkage distance metric is used in any distance-based clustering method, e.g. K-medoids or hierarchical clustering, to cluster the genes with known functions. Second, while keeping the clustering results from the first step for the genes with known functions, the expression-based distance metric is used to cluster the remaining genes of unknown function, assigning each of them to either one of the clusters obtained in the first step or some new clusters. A simulation study and an application to gene function prediction for the yeast demonstrate the advantage of our proposal over the standard method.     

CLICK and EXPANDER: a system for clustering and visualizing gene expression data

MOTIVATION: Microarrays have become a central tool in biological research. Their applications range from functional annotation to tissue classification and genetic network inference. A key step in the analysis of gene expression data is the identification of groups of genes that manifest similar expression patterns. This translates to the algorithmic problem of clustering genes based on their expression patterns. RESULTS: We present a novel clustering algorithm, called CLICK, and its applications to gene expression analysis. The algorithm utilizes graph-theoretic and statistical techniques to identify tight groups (kernels) of highly similar elements, which are likely to belong to the same true cluster. Several heuristic procedures are then used to expand the kernels into the full clusters. We report on the application of CLICK to a variety of gene expression data sets. In all those applications it outperformed extant algorithms according to several common figures of merit. We also point out that CLICK can be successfully used for the identification of common regulatory motifs in the upstream regions of co-regulated genes. Furthermore, we demonstrate how CLICK can be used to accurately classify tissue samples into disease types, based on their expression profiles. Finally, we present a new java-based graphical tool, called EXPANDER, for gene expression analysis and visualization, which incorporates CLICK and several other popular clustering algorithms. AVAILABILITY: http://www.cs.tau.ac.il/~rshamir/expander/expander.html     

A tripartite clustering analysis on microrna, gene and disease model

Alteration of gene expression in response to regulatory molecules or mutations could lead to different diseases. MicroRNAs (miRNAs) have been discovered to be involved in regulation of gene expression and a wide variety of diseases. In a tripartite biological network of human miRNAs, their predicted target genes and the diseases caused by altered expressions of these genes, valuable knowledge about the pathogenicity of miRNAs, involved genes and related disease classes can be revealed by co-clustering miRNAs, target genes and diseases simultaneously. Tripartite co-clustering can lead to more informative results than traditional co-clustering with only two kinds of members and pass the hidden relational information along the relation chain by considering multi-type members. Here we report a spectral co-clustering algorithm for k-partite graph to find clusters with heterogeneous members. We use the method to explore the potential relationships among miRNAs, genes and diseases. The clusters obtained from the algorithm have significantly higher density than randomly selected clusters, which means members in the same cluster are more likely to have common connections. Results also show that miRNAs in the same family based on the hairpin sequences tend to belong to the same cluster. We also validate the clustering results by checking the correlation of enriched gene functions and disease classes in the same cluster. Finally, widely studied miR-17-92 and its paralogs are analyzed as a case study to reveal that genes and diseases co-clustered with the miRNAs are in accordance with current research findings.     

'Gene shaving' as a method for identifying distinct sets of genes with similar expression patterns

Background  

Large gene expression studies, such as those conducted using DNA arrays, often provide millions of different pieces of data. To address the problem of analyzing such data, we describe a statistical method, which we have called 'gene shaving'. The method identifies subsets of genes with coherent expression patterns and large variation across conditions. Gene shaving differs from hierarchical clustering and other widely used methods for analyzing gene expression studies in that genes may belong to more than one cluster, and the clustering may be supervised by an outcome measure. The technique can be 'unsupervised', that is, the genes and samples are treated as unlabeled, or partially or fully supervised by using known properties of the genes or samples to assist in finding meaningful groupings.     

Paradigm of Tunable Clustering Using Binarization of Consensus Partition Matrices (Bi-CoPaM) for Gene Discovery

Clustering analysis has a growing role in the study of co-expressed genes for gene discovery. Conventional binary and fuzzy clustering do not embrace the biological reality that some genes may be irrelevant for a problem and not be assigned to a cluster, while other genes may participate in several biological functions and should simultaneously belong to multiple clusters. Also, these algorithms cannot generate tight clusters that focus on their cores or wide clusters that overlap and contain all possibly relevant genes. In this paper, a new clustering paradigm is proposed. In this paradigm, all three eventualities of a gene being exclusively assigned to a single cluster, being assigned to multiple clusters, and being not assigned to any cluster are possible. These possibilities are realised through the primary novelty of the introduction of tunable binarization techniques. Results from multiple clustering experiments are aggregated to generate one fuzzy consensus partition matrix (CoPaM), which is then binarized to obtain the final binary partitions. This is referred to as Binarization of Consensus Partition Matrices (Bi-CoPaM). The method has been tested with a set of synthetic datasets and a set of five real yeast cell-cycle datasets. The results demonstrate its validity in generating relevant tight, wide, and complementary clusters that can meet requirements of different gene discovery studies.     

Clustering threshold gradient descent regularization: with applications to microarray studies

MOTIVATION: An important goal of microarray studies is to discover genes that are associated with clinical outcomes, such as disease status and patient survival. While a typical experiment surveys gene expressions on a global scale, there may be only a small number of genes that have significant influence on a clinical outcome. Moreover, expression data have cluster structures and the genes within a cluster have correlated expressions and coordinated functions, but the effects of individual genes in the same cluster may be different. Accordingly, we seek to build statistical models with the following properties. First, the model is sparse in the sense that only a subset of the parameter vector is non-zero. Second, the cluster structures of gene expressions are properly accounted for. RESULTS: For gene expression data without pathway information, we divide genes into clusters using commonly used methods, such as K-means or hierarchical approaches. The optimal number of clusters is determined using the Gap statistic. We propose a clustering threshold gradient descent regularization (CTGDR) method, for simultaneous cluster selection and within cluster gene selection. We apply this method to binary classification and censored survival analysis. Compared to the standard TGDR and other regularization methods, the CTGDR takes into account the cluster structure and carries out feature selection at both the cluster level and within-cluster gene level. We demonstrate the CTGDR on two studies of cancer classification and two studies correlating survival of lymphoma patients with microarray expressions. AVAILABILITY: R code is available upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Adaptive quality-based clustering of gene expression profiles

MOTIVATION: Microarray experiments generate a considerable amount of data, which analyzed properly help us gain a huge amount of biologically relevant information about the global cellular behaviour. Clustering (grouping genes with similar expression profiles) is one of the first steps in data analysis of high-throughput expression measurements. A number of clustering algorithms have proved useful to make sense of such data. These classical algorithms, though useful, suffer from several drawbacks (e.g. they require the predefinition of arbitrary parameters like the number of clusters; they force every gene into a cluster despite a low correlation with other cluster members). In the following we describe a novel adaptive quality-based clustering algorithm that tackles some of these drawbacks. RESULTS: We propose a heuristic iterative two-step algorithm: First, we find in the high-dimensional representation of the data a sphere where the "density" of expression profiles is locally maximal (based on a preliminary estimate of the radius of the cluster-quality-based approach). In a second step, we derive an optimal radius of the cluster (adaptive approach) so that only the significantly coexpressed genes are included in the cluster. This estimation is achieved by fitting a model to the data using an EM-algorithm. By inferring the radius from the data itself, the biologist is freed from finding an optimal value for this radius by trial-and-error. The computational complexity of this method is approximately linear in the number of gene expression profiles in the data set. Finally, our method is successfully validated using existing data sets. AVAILABILITY: http://www.esat.kuleuven.ac.be/~thijs/Work/Clustering.html     

Bayesian infinite mixture model based clustering of gene expression profiles

MOTIVATION: The biologic significance of results obtained through cluster analyses of gene expression data generated in microarray experiments have been demonstrated in many studies. In this article we focus on the development of a clustering procedure based on the concept of Bayesian model-averaging and a precise statistical model of expression data. RESULTS: We developed a clustering procedure based on the Bayesian infinite mixture model and applied it to clustering gene expression profiles. Clusters of genes with similar expression patterns are identified from the posterior distribution of clusterings defined implicitly by the stochastic data-generation model. The posterior distribution of clusterings is estimated by a Gibbs sampler. We summarized the posterior distribution of clusterings by calculating posterior pairwise probabilities of co-expression and used the complete linkage principle to create clusters. This approach has several advantages over usual clustering procedures. The analysis allows for incorporation of a reasonable probabilistic model for generating data. The method does not require specifying the number of clusters and resulting optimal clustering is obtained by averaging over models with all possible numbers of clusters. Expression profiles that are not similar to any other profile are automatically detected, the method incorporates experimental replicates, and it can be extended to accommodate missing data. This approach represents a qualitative shift in the model-based cluster analysis of expression data because it allows for incorporation of uncertainties involved in the model selection in the final assessment of confidence in similarities of expression profiles. We also demonstrated the importance of incorporating the information on experimental variability into the clustering model. AVAILABILITY: The MS Windows(TM) based program implementing the Gibbs sampler and supplemental material is available at http://homepages.uc.edu/~medvedm/BioinformaticsSupplement.htm CONTACT: medvedm@email.uc.edu     

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.     

Constrained clusters of gene expression profiles with pathological features

MOTIVATION: Gene expression profiles should be useful in distinguishing variations in disease, since they reflect accurately the status of cells. The primary clustering of gene expression reveals the genotypes that are responsible for the proximity of members within each cluster, while further clustering elucidates the pathological features of the individual members of each cluster. However, since the first clustering process and the second classification step, in which the features are associated with clusters, are performed independently, the initial set of clusters may omit genes that are associated with pathologically meaningful features. Therefore, it is important to devise a way of identifying gene expression clusters that are associated with pathological features. RESULTS: We present the novel technique of 'itemset constrained clustering' (IC-Clustering), which computes the optimal cluster that maximizes the interclass variance of gene expression between groups, which are divided according to the restriction that only divisions that can be expressed using common features are allowed. This constraint automatically labels each cluster with a set of pathological features which characterize that cluster. When applied to liver cancer datasets, IC-Clustering revealed informative gene expression clusters, which could be annotated with various pathological features, such as 'tumor' and 'man', or 'except tumor' and 'normal liver function'. In contrast, the k-means method overlooked these clusters.     

A mixture model with random-effects components for clustering correlated gene-expression profiles

MOTIVATION: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. RESULTS: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation)and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too. AVAILABILITY: A Fortran program blue called EMMIX-WIRE (EM-based MIXture analysis WIth Random Effects) is available on request from the corresponding author.     

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.     

昆虫谷胱甘肽S-转移酶的基因结构及其表达调控

谷胱甘肽S-转移酶（glutathione S-transferases, GSTs）属于一个超家族,目前已从20多种昆虫中克隆得到了近百个GSTs基因序列。这些基因分属于至少3个类别,Ⅰ（Delta）类,Ⅱ类和Ⅲ（Epsilon）类,其中Ⅰ类和Ⅲ类是昆虫特异性的类别。昆虫Ⅰ类GSTs基因通常由多基因家族编码,基因多态性在不同昆虫种类中差异很大。Ⅱ类基因的种类较少,基因的结构较简单,通常是单拷贝基因。Ⅲ类基因是最近才鉴定出来的新类别,目前仅在黑腹果蝇和冈比亚按蚊中明确了其在染色体上的定位。基因簇、可变剪接和基因融合等机制是导致昆虫GSTs基因多态性的主要原因。在抗性昆虫种群中,GSTs表达量的增加有mRNA水平的提高和基因扩增两种机制,但后一种机制的报道很少。GSTs活性的增加是由于属于一类或多类的多个同工酶的增量调控,也有少数是由于单个同工酶的增量调控。GSTs的表达受反式调控元件和顺式调控元件的调控。目前仅有少数含有调节基因的染色体大致位点和可能的调控元件得到鉴定。     

Microarray time course experiments: finding profiles

Time course studies with microarray techniques and experimental replicates are very useful in biomedical research. We present, in replicate experiments, an alternative approach to select and cluster genes according to a new measure for association between genes. First, the procedure normalizes and standardizes the expression profile of each gene, and then, identifies scaling parameters that will further minimize the distance between replicates of the same gene. Then, the procedure filters out genes with a flat profile, detects differences between replicates, and separates genes without significant differences from the rest. For this last group of genes, we define a mean profile for each gene and use it to compute the distance between two genes. Next, a hierarchical clustering procedure is proposed, a statistic is computed for each cluster to determine its compactness, and the total number of classes is determined. For the rest of the genes, those with significant differences between replicates, the procedure detects where the differences between replicates lie, and assigns each gene to the best fitting previously identified profile or defines a new profile. We illustrate this new procedure using simulated data and a representative data set arising from a microarray experiment with replication, and report interesting results.