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.     

AGGRESCAN: a server for the prediction and evaluation of "hot spots" of aggregation in polypeptides

Background

A tremendous amount of efforts have been devoted to identifying genes for diagnosis and prognosis of diseases using microarray gene expression data. It has been demonstrated that gene expression data have cluster structure, where the clusters consist of co-regulated genes which tend to have coordinated functions. However, most available statistical methods for gene selection do not take into consideration the cluster structure.

Results

We propose a supervised group Lasso approach that takes into account the cluster structure in gene expression data for gene selection and predictive model building. For gene expression data without biological cluster information, we first divide genes into clusters using the K-means approach and determine the optimal number of clusters using the Gap method. The supervised group Lasso consists of two steps. In the first step, we identify important genes within each cluster using the Lasso method. In the second step, we select important clusters using the group Lasso. Tuning parameters are determined using V-fold cross validation at both steps to allow for further flexibility. Prediction performance is evaluated using leave-one-out cross validation. We apply the proposed method to disease classification and survival analysis with microarray data.

Conclusion

We analyze four microarray data sets using the proposed approach: two cancer data sets with binary cancer occurrence as outcomes and two lymphoma data sets with survival outcomes. The results show that the proposed approach is capable of identifying a small number of influential gene clusters and important genes within those clusters, and has better prediction performance than existing methods.     

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     

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.     

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.     

Dimension reduction methods for microarrays with application to censored survival data

MOTIVATION: Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles. RESULTS: We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis. AVAILABILITY: R programs are available upon request from the authors. SUPPLEMENTARY INFORMATION: http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.     

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/.     

Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data

MOTIVATION: An important application of microarray technology is to relate gene expression profiles to various clinical phenotypes of patients. Success has been demonstrated in molecular classification of cancer in which the gene expression data serve as predictors and different types of cancer serve as a categorical outcome variable. However, there has been less research in linking gene expression profiles to the censored survival data such as patients' overall survival time or time to cancer relapse. It would be desirable to have models with good prediction accuracy and parsimony property. RESULTS: We propose to use the L(1) penalized estimation for the Cox model to select genes that are relevant to patients' survival and to build a predictive model for future prediction. The computational difficulty associated with the estimation in the high-dimensional and low-sample size settings can be efficiently solved by using the recently developed least-angle regression (LARS) method. Our simulation studies and application to real datasets on predicting survival after chemotherapy for patients with diffuse large B-cell lymphoma demonstrate that the proposed procedure, which we call the LARS-Cox procedure, can be used for identifying important genes that are related to time to death due to cancer and for building a parsimonious model for predicting the survival of future patients. The LARS-Cox regression gives better predictive performance than the L(2) penalized regression and a few other dimension-reduction based methods. CONCLUSIONS: We conclude that the proposed LARS-Cox procedure can be very useful in identifying genes relevant to survival phenotypes and in building a parsimonious predictive model that can be used for classifying future patients into clinically relevant high- and low-risk groups based on the gene expression profile and survival times of previous patients.     

Multi-class clustering of cancer subtypes through SVM based ensemble of pareto-optimal solutions for gene marker identification

With the advancement of microarray technology, it is now possible to study the expression profiles of thousands of genes across different experimental conditions or tissue samples simultaneously. Microarray cancer datasets, organized as samples versus genes fashion, are being used for classification of tissue samples into benign and malignant or their subtypes. They are also useful for identifying potential gene markers for each cancer subtype, which helps in successful diagnosis of particular cancer types. In this article, we have presented an unsupervised cancer classification technique based on multiobjective genetic clustering of the tissue samples. In this regard, a real-coded encoding of the cluster centers is used and cluster compactness and separation are simultaneously optimized. The resultant set of near-Pareto-optimal solutions contains a number of non-dominated solutions. A novel approach to combine the clustering information possessed by the non-dominated solutions through Support Vector Machine (SVM) classifier has been proposed. Final clustering is obtained by consensus among the clusterings yielded by different kernel functions. The performance of the proposed multiobjective clustering method has been compared with that of several other microarray clustering algorithms for three publicly available benchmark cancer datasets. Moreover, statistical significance tests have been conducted to establish the statistical superiority of the proposed clustering method. Furthermore, relevant gene markers have been identified using the clustering result produced by the proposed clustering method and demonstrated visually. Biological relationships among the gene markers are also studied based on gene ontology. The results obtained are found to be promising and can possibly have important impact in the area of unsupervised cancer classification as well as gene marker identification for multiple cancer subtypes.     

Analysis of breast cancer progression using principal component analysis and clustering

We develop a new technique to analyse microarray data which uses a combination of principal components analysis and consensus ensemble k-clustering to find robust clusters and gene markers in the data. We apply our method to a public microarray breast cancer dataset which has expression levels of genes in normal samples as well as in three pathological stages of disease; namely, atypical ductal hyperplasia or ADH, ductal carcinoma in situ or DCIS and invasive ductal carcinoma or IDC. Our method averages over clustering techniques and data perturbation to find stable, robust clusters and gene markers. We identify the clusters and their pathways with distinct subtypes of breast cancer (Luminal,Basal and Her2+). We confirm that the cancer phenotype develops early (in early hyperplasia or ADH stage) and find from our analysis that each subtype progresses from ADH to DCIS to IDC along its own specific pathway, as if each was a distinct disease.     

Network constrained clustering for gene microarray data

Many bioinformatics problems can be tackled from a fresh angle offered by the network perspective. Directly inspired by metabolic network structural studies, we propose an improved gene clustering approach for inferring gene signaling pathways from gene microarray data. Based on the construction of co-expression networks that consists of both significantly linear and non-linear gene associations together with controlled biological and statistical significance, our approach tends to group functionally related genes into tight clusters despite their expression dissimilarities. We illustrate our approach and compare it to the traditional clustering approaches on a yeast galactose metabolism dataset and a retinal gene expression dataset. Our approach greatly outperforms the traditional approach in rediscovering the relatively well known galactose metabolism pathway in yeast and in clustering genes of the photoreceptor differentiation pathway. AVAILABILITY: The clustering method has been implemented in an R package "GeneNT" that is freely available from: http://www.cran.org.     

The impact on high‐grade serous ovarian cancer of obesity and lipid metabolism‐related gene expression patterns: the underestimated driving force affecting prognosis

To investigate whether specific obesity/metabolism‐related gene expression patterns affect the survival of patients with ovarian cancer. Clinical and genomic data of 590 samples from the high‐grade ovarian serous carcinoma (HGOSC) study of The Cancer Genome Atlas (TCGA) and 91 samples from the Australian Ovarian Cancer Study were downloaded from the International Cancer Genome Consortium (ICGC) portal. Clustering of mRNA microarray and reverse‐phase protein array (RPPA) data was performed with 83 consensus driver genes and 144 obesity and lipid metabolism‐related genes. Association between different clusters and survival was analyzed with the Kaplan–Meier method and a Cox regression. Mutually exclusive, co‐occurrence and network analyses were also carried out. Using RNA and RPPA data, it was possible to identify two subsets of HGOSCs with similar clinical characteristics and cancer driver mutation profiles (e.g. TP53), but with different outcome. These differences depend more on up‐regulation of specific obesity and lipid metabolism‐related genes than on the number of gene mutations or copy number alterations. It was also found that CD36 and TGF‐ß are highly up‐regulated at the protein levels in the cluster with the poorer outcome. In contrast, BSCL2 is highly up‐regulated in the cluster with better progression‐free and overall survival. Different obesity/metabolism‐related gene expression patterns constitute a risk factor for prognosis independent of the therapy results in the Cox regression. Prognoses were conditioned by the differential expression of obesity and lipid metabolism‐related genes in HGOSCs with similar cancer driver mutation profiles, independent of the initial therapeutic response.     

Discriminant analysis to evaluate clustering of gene expression data

In this work we present a procedure that combines classical statistical methods to assess the confidence of gene clusters identified by hierarchical clustering of expression data. This approach was applied to a publicly released Drosophila metamorphosis data set [White et al., Science 286 (1999) 2179-2184]. We have been able to produce reliable classifications of gene groups and genes within the groups by applying unsupervised (cluster analysis), dimension reduction (principal component analysis) and supervised methods (linear discriminant analysis) in a sequential form. This procedure provides a means to select relevant information from microarray data, reducing the number of genes and clusters that require further biological analysis.     

Testing association of a pathway with survival using gene expression data

MOTIVATION: A recent surge of interest in survival as the primary clinical endpoint of microarray studies has called for an extension of the Global Test methodology to survival. RESULTS: We present a score test for association of the expression profile of one or more groups of genes with a (possibly censored) survival time. Groups of genes may be pathways, areas of the genome, clusters from a cluster analysis or all genes on a chip. The test allows one to test hypotheses about the influence of these groups of genes on survival directly, without the intermediary of single gene testing. The test is based on the Cox proportional hazards model and is calculated using martingale residuals. It is possible to adjust the test for the presence of covariates. We also present a diagnostic graph to assist in the interpretation of the test result, visualizing the influence of genes. The test is applied to a tumor dataset, revealing pathways from the gene ontology database that are associated with survival of patients. AVAILABILITY: The Global Test for survival has been incorporated into the R-package globaltest (version 3.0), available at http://www.bioconductor.org     

Mixture modelling of gene expression data from microarray experiments

MOTIVATION: Hierarchical clustering is one of the major analytical tools for gene expression data from microarray experiments. A major problem in the interpretation of the output from these procedures is assessing the reliability of the clustering results. We address this issue by developing a mixture model-based approach for the analysis of microarray data. Within this framework, we present novel algorithms for clustering genes and samples. One of the byproducts of our method is a probabilistic measure for the number of true clusters in the data. RESULTS: The proposed methods are illustrated by application to microarray datasets from two cancer studies; one in which malignant melanoma is profiled (Bittner et al., Nature, 406, 536-540, 2000), and the other in which prostate cancer is profiled (Dhanasekaran et al., 2001, submitted).     

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.     

Tight clustering: a resampling-based approach for identifying stable and tight patterns in data

In this article, we propose a method for clustering that produces tight and stable clusters without forcing all points into clusters. The methodology is general but was initially motivated from cluster analysis of microarray experiments. Most current algorithms aim to assign all genes into clusters. For many biological studies, however, we are mainly interested in identifying the most informative, tight, and stable clusters of sizes, say, 20-60 genes for further investigation. We want to avoid the contamination of tightly regulated expression patterns of biologically relevant genes due to other genes whose expressions are only loosely compatible with these patterns. "Tight clustering" has been developed specifically to address this problem. It applies K-means clustering as an intermediate clustering engine. Early truncation of a hierarchical clustering tree is used to overcome the local minimum problem in K-means clustering. The tightest and most stable clusters are identified in a sequential manner through an analysis of the tendency of genes to be grouped together under repeated resampling. We validated this method in a simulated example and applied it to analyze a set of expression profiles in the study of embryonic stem cells.