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     

Clustering millions of tandem mass spectra

Tandem mass spectrometry (MS/MS) experiments often generate redundant data sets containing multiple spectra of the same peptides. Clustering of MS/MS spectra takes advantage of this redundancy by identifying multiple spectra of the same peptide and replacing them with a single representative spectrum. Analyzing only representative spectra results in significant speed-up of MS/MS database searches. We present an efficient clustering approach for analyzing large MS/MS data sets (over 10 million spectra) with a capability to reduce the number of spectra submitted to further analysis by an order of magnitude. The MS/MS database search of clustered spectra results in fewer spurious hits to the database and increases number of peptide identifications as compared to regular nonclustered searches. Our open source software MS-Clustering is available for download at http://peptide.ucsd.edu or can be run online at http://proteomics.bioprojects.org/MassSpec.     

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     

Towards clustering of incomplete microarray data without the use of imputation

MOTIVATION: Clustering technique is used to find groups of genes that show similar expression patterns under multiple experimental conditions. Nonetheless, the results obtained by cluster analysis are influenced by the existence of missing values that commonly arise in microarray experiments. Because a clustering method requires a complete data matrix as an input, previous studies have estimated the missing values using an imputation method in the preprocessing step of clustering. However, a common limitation of these conventional approaches is that once the estimates of missing values are fixed in the preprocessing step, they are not changed during subsequent processes of clustering; badly estimated missing values obtained in data preprocessing are likely to deteriorate the quality and reliability of clustering results. Thus, a new clustering method is required for improving missing values during iterative clustering process. RESULTS: We present a method for Clustering Incomplete data using Alternating Optimization (CIAO) in which a prior imputation method is not required. To reduce the influence of imputation in preprocessing, we take an alternative optimization approach to find better estimates during iterative clustering process. This method improves the estimates of missing values by exploiting the cluster information such as cluster centroids and all available non-missing values in each iteration. To test the performance of the CIAO, we applied the CIAO and conventional imputation-based clustering methods, e.g. k-means based on KNNimpute, for clustering two yeast incomplete data sets, and compared the clustering result of each method using the Saccharomyces Genome Database annotations. The clustering results of the CIAO method are more significantly relevant to the biological gene annotations than those of other methods, indicating its effectiveness and potential for clustering incomplete gene expression data. AVAILABILITY: The software was developed using Java language, and can be executed on the platforms that JVM (Java Virtual Machine) is running. It is available from the authors upon request.     

Two-stage clustering (TSC): a pipeline for selecting operational taxonomic units for the high-throughput sequencing of PCR amplicons

Clustering 16S/18S rRNA amplicon sequences into operational taxonomic units (OTUs) is a critical step for the bioinformatic analysis of microbial diversity. Here, we report a pipeline for selecting OTUs with a relatively low computational demand and a high degree of accuracy. This pipeline is referred to as two-stage clustering (TSC) because it divides tags into two groups according to their abundance and clusters them sequentially. The more abundant group is clustered using a hierarchical algorithm similar to that in ESPRIT, which has a high degree of accuracy but is computationally costly for large datasets. The rarer group, which includes the majority of tags, is then heuristically clustered to improve efficiency. To further improve the computational efficiency and accuracy, two preclustering steps are implemented. To maintain clustering accuracy, all tags are grouped into an OTU depending on their pairwise Needleman-Wunsch distance. This method not only improved the computational efficiency but also mitigated the spurious OTU estimation from 'noise' sequences. In addition, OTUs clustered using TSC showed comparable or improved performance in beta-diversity comparisons compared to existing OTU selection methods. This study suggests that the distribution of sequencing datasets is a useful property for improving the computational efficiency and increasing the clustering accuracy of the high-throughput sequencing of PCR amplicons. The software and user guide are freely available at http://hwzhoulab.smu.edu.cn/paperdata/.     

Combining gene annotations and gene expression data in model-based clustering: weighted method

It has been increasingly recognized that incorporating prior knowledge into cluster analysis can result in more reliable and meaningful clusters. In contrast to the standard modelbased clustering with a global mixture model, which does not use any prior information, a stratified mixture model was recently proposed to incorporate gene functions or biological pathways as priors in model-based clustering of gene expression profiles: various gene functional groups form the strata in a stratified mixture model. Albeit useful, the stratified method may be less efficient than the global analysis if the strata are non-informative to clustering. We propose a weighted method that aims to strike a balance between a stratified analysis and a global analysis: it weights between the clustering results of the stratified analysis and that of the global analysis; the weight is determined by data. More generally, the weighted method can take advantage of the hierarchical structure of most existing gene functional annotation systems, such as MIPS and Gene Ontology (GO), and facilitate choosing appropriate gene functional groups as priors. We use simulated data and real data to demonstrate the feasibility and advantages of the proposed method.     

UniCarb-DB: a database resource for glycomic discovery

Glycosylation is one of the most important post-translational modifications of proteins, known to be involved in pathogen recognition, innate immune response and protection of epithelial membranes. However, when compared to the tools and databases available for the processing of high-throughput proteomic data, the glycomic domain is severely lacking. While tools to assist the analysis of mass spectrometry (MS) and HPLC are continuously improving, there are few resources available to support liquid chromatography (LC)-MS/MS techniques for glycan structure profiling. Here, we present a platform for presenting oligosaccharide structures and fragment data characterized by LC-MS/MS strategies. The database is annotated with high-quality datasets and is designed to extend and reinforce those standards and ontologies developed by existing glycomics databases. AVAILABILITY: http://www.unicarb-db.org     

基于聚类分析方法的酒后人脑状态研究

目的:本文对酒精引起的人脑状态变化进行讨论。通过对客观记录的受试者摄入酒精事件的脑电图数据进行系统聚类分析,从而分析摄入酒精事件与21导联电极分类的关系,进而为有关人脑的其它研究提供实验和理论根据。方法:选取4名习惯用右手、健康的人进行实验,采用标准21个脑电极的10-20导联系统,获取受试者在安静闭眼和摄入一定量啤酒的2个事件的脑电图数据。然后进行数据分析。数据分析的方法是系统聚类分析方法。程序实现采用独立设计的脑电图分析工具箱和聚类分析程序。结果:对脑电图数据聚类分析后发现,未喝酒时脑电活动大致按前额部和中央、后头部、两侧得到3个聚类簇;摄入200毫升啤酒后,受试者P1和P2的大部分额部电极、中央部电极以及后头部电极聚类为一个簇,个别颞部、后头部电极聚类为一个簇,或单个电极独立为一簇,形成孤立点;摄入400毫升啤酒后,受试者P3和P4的大部分额极电极、额部电极、中央部电极以及后头部电极聚类为一个簇,个别额部、中央部、颞部单个电极独立为一簇,形成孤立点。结论:脑电活动对摄入酒精有显著反应。由于人在安静闭眼状态下,后头部记录到的α波较为显著,所以未喝酒时前后头部脑电信号相关性较弱,受试者前后头部的电极基本不在一个聚类簇中;摄入酒精后,受试者大部分额部、中央部和后头部电极聚类为一簇,即前后头部脑电信号的相关性增强,这说明在酒精的作用下,前头部α波增加,α波呈现扩大和增强的趋势。     

Clustering 100,000 protein structure decoys in minutes

Ab initio protein structure prediction methods first generate large sets of structural conformations as candidates (called decoys), and then select the most representative decoys through clustering techniques. Classical clustering methods are inefficient due to the pairwise distance calculation, and thus become infeasible when the number of decoys is large. In addition, the existing clustering approaches suffer from the arbitrariness in determining a distance threshold for proteins within a cluster: a small distance threshold leads to many small clusters, while a large distance threshold results in the merging of several independent clusters into one cluster. In this paper, we propose an efficient clustering method through fast estimating cluster centroids and efficient pruning rotation spaces. The number of clusters is automatically detected by information distance criteria. A package named ONION, which can be downloaded freely, is implemented accordingly. Experimental results on benchmark data sets suggest that ONION is 14 times faster than existing tools, and ONION obtains better selections for 31 targets, and worse selection for 19 targets compared to SPICKER’s selections. On an average PC, ONION can cluster 100,000 decoys in around 12 minutes.     

Binary tree-structured vector quantization approach to clustering and visualizing microarray data

MOTIVATION: With the increasing number of gene expression databases, the need for more powerful analysis and visualization tools is growing. Many techniques have successfully been applied to unravel latent similarities among genes and/or experiments. Most of the current systems for microarray data analysis use statistical methods, hierarchical clustering, self-organizing maps, support vector machines, or k-means clustering to organize genes or experiments into 'meaningful' groups. Without prior explicit bias almost all of these clustering methods applied to gene expression data not only produce different results, but may also produce clusters with little or no biological relevance. Of these methods, agglomerative hierarchical clustering has been the most widely applied, although many limitations have been identified. RESULTS: Starting with a systematic comparison of the underlying theories behind clustering approaches, we have devised a technique that combines tree-structured vector quantization and partitive k-means clustering (BTSVQ). This hybrid technique has revealed clinically relevant clusters in three large publicly available data sets. In contrast to existing systems, our approach is less sensitive to data preprocessing and data normalization. In addition, the clustering results produced by the technique have strong similarities to those of self-organizing maps (SOMs). We discuss the advantages and the mathematical reasoning behind our approach.     

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     

UniRef: comprehensive and non-redundant UniProt reference clusters

MOTIVATION: Redundant protein sequences in biological databases hinder sequence similarity searches and make interpretation of search results difficult. Clustering of protein sequence space based on sequence similarity helps organize all sequences into manageable datasets and reduces sampling bias and overrepresentation of sequences. RESULTS: The UniRef (UniProt Reference Clusters) provide clustered sets of sequences from the UniProt Knowledgebase (UniProtKB) and selected UniProt Archive records to obtain complete coverage of sequence space at several resolutions while hiding redundant sequences. Currently covering >4 million source sequences, the UniRef100 database combines identical sequences and subfragments from any source organism into a single UniRef entry. UniRef90 and UniRef50 are built by clustering UniRef100 sequences at the 90 or 50% sequence identity levels. UniRef100, UniRef90 and UniRef50 yield a database size reduction of approximately 10, 40 and 70%, respectively, from the source sequence set. The reduced redundancy increases the speed of similarity searches and improves detection of distant relationships. UniRef entries contain summary cluster and membership information, including the sequence of a representative protein, member count and common taxonomy of the cluster, the accession numbers of all the merged entries and links to rich functional annotation in UniProtKB to facilitate biological discovery. UniRef has already been applied to broad research areas ranging from genome annotation to proteomics data analysis. AVAILABILITY: UniRef is updated biweekly and is available for online search and retrieval at http://www.uniprot.org, as well as for download at ftp://ftp.uniprot.org/pub/databases/uniprot/uniref. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Evaluation and comparison of gene clustering methods in microarray analysis

MOTIVATION: Microarray technology has been widely applied in biological and clinical studies for simultaneous monitoring of gene expression in thousands of genes. Gene clustering analysis is found useful for discovering groups of correlated genes potentially co-regulated or associated to the disease or conditions under investigation. Many clustering methods including hierarchical clustering, K-means, PAM, SOM, mixture model-based clustering and tight clustering have been widely used in the literature. Yet no comprehensive comparative study has been performed to evaluate the effectiveness of these methods. RESULTS: In this paper, six gene clustering methods are evaluated by simulated data from a hierarchical log-normal model with various degrees of perturbation as well as four real datasets. A weighted Rand index is proposed for measuring similarity of two clustering results with possible scattered genes (i.e. a set of noise genes not being clustered). Performance of the methods in the real data is assessed by a predictive accuracy analysis through verified gene annotations. Our results show that tight clustering and model-based clustering consistently outperform other clustering methods both in simulated and real data while hierarchical clustering and SOM perform among the worst. Our analysis provides deep insight to the complicated gene clustering problem of expression profile and serves as a practical guideline for routine microarray cluster analysis.     

A data-mining scheme for identifying peptide structural motifs responsible for different MS/MS fragmentation intensity patterns

Although tandem mass spectrometry (MS/MS) has become an integral part of proteomics, intensity patterns in MS/MS spectra are rarely weighted heavily in most widely used algorithms because they are not yet fully understood. Here a knowledge mining approach is demonstrated to discover fragmentation intensity patterns and elucidate the chemical factors behind such patterns. Fragmentation intensity information from 28 330 ion trap peptide MS/MS spectra of different charge states and sequences went through unsupervised clustering using a penalized K-means algorithm. Without any prior chemistry assumptions, four clusters with distinctive fragmentation patterns were obtained. A decision tree was generated to investigate peptide sequence motif and charge state status that caused these fragmentation patterns. This data-mining scheme is generally applicable for any large data sets. It bypasses the common prior knowledge constraints and reports on the overall peptide fragmentation behavior. It improves the understanding of gas-phase peptide dissociation and provides a foundation for new or improved protein identification algorithms.     

A comprehensive set of protein complexes in yeast: mining large scale protein-protein interaction screens

MOTIVATION: The analysis of protein-protein interactions allows for detailed exploration of the cellular machinery. The biochemical purification of protein complexes followed by identification of components by mass spectrometry is currently the method, which delivers the most reliable information--albeit that the data sets are still difficult to interpret. Consolidating individual experiments into protein complexes, especially for high-throughput screens, is complicated by many contaminants, the occurrence of proteins in otherwise dissimilar purifications due to functional re-use and technical limitations in the detection. A non-redundant collection of protein complexes from experimental data would be useful for biological interpretation, but manual assembly is tedious and often inconsistent. RESULTS: Here, we introduce a measure to define similarity within collections of purifications and generate a set of minimally redundant, comprehensive complexes using unsupervised clustering. AVAILABILITY: Programs and results are freely available from http://www.bork.embl-heidelberg.de/Docu/purclust/     

Inference from clustering with application to gene-expression microarrays.

There are many algorithms to cluster sample data points based on nearness or a similarity measure. Often the implication is that points in different clusters come from different underlying classes, whereas those in the same cluster come from the same class. Stochastically, the underlying classes represent different random processes. The inference is that clusters represent a partition of the sample points according to which process they belong. This paper discusses a model-based clustering toolbox that evaluates cluster accuracy. Each random process is modeled as its mean plus independent noise, sample points are generated, the points are clustered, and the clustering error is the number of points clustered incorrectly according to the generating random processes. Various clustering algorithms are evaluated based on process variance and the key issue of the rate at which algorithmic performance improves with increasing numbers of experimental replications. The model means can be selected by hand to test the separability of expected types of biological expression patterns. Alternatively, the model can be seeded by real data to test the expected precision of that output or the extent of improvement in precision that replication could provide. In the latter case, a clustering algorithm is used to form clusters, and the model is seeded with the means and variances of these clusters. Other algorithms are then tested relative to the seeding algorithm. Results are averaged over various seeds. Output includes error tables and graphs, confusion matrices, principal-component plots, and validation measures. Five algorithms are studied in detail: K-means, fuzzy C-means, self-organizing maps, hierarchical Euclidean-distance-based and correlation-based clustering. The toolbox is applied to gene-expression clustering based on cDNA microarrays using real data. Expression profile graphics are generated and error analysis is displayed within the context of these profile graphics. A large amount of generated output is available over the web.     

Protein and peptide identification algorithms using MS for use in high-throughput, automated pipelines

Current proteomics experiments can generate vast quantities of data very quickly, but this has not been matched by data analysis capabilities. Although there have been a number of recent reviews covering various aspects of peptide and protein identification methods using MS, comparisons of which methods are either the most appropriate for, or the most effective at, their proposed tasks are not readily available. As the need for high-throughput, automated peptide and protein identification systems increases, the creators of such pipelines need to be able to choose algorithms that are going to perform well both in terms of accuracy and computational efficiency. This article therefore provides a review of the currently available core algorithms for PMF, database searching using MS/MS, sequence tag searches and de novo sequencing. We also assess the relative performances of a number of these algorithms. As there is limited reporting of such information in the literature, we conclude that there is a need for the adoption of a system of standardised reporting on the performance of new peptide and protein identification algorithms, based upon freely available datasets. We go on to present our initial suggestions for the format and content of these datasets.     

Semi-supervised adaptive-height snipping of the hierarchical clustering tree

Background

In genomics, hierarchical clustering (HC) is a popular method for grouping similar samples based on a distance measure. HC algorithms do not actually create clusters, but compute a hierarchical representation of the data set. Usually, a fixed height on the HC tree is used, and each contiguous branch of samples below that height is considered a separate cluster. Due to the fixed-height cutting, those clusters may not unravel significant functional coherence hidden deeper in the tree. Besides that, most existing approaches do not make use of available clinical information to guide cluster extraction from the HC. Thus, the identified subgroups may be difficult to interpret in relation to that information.

Results

We develop a novel framework for decomposing the HC tree into clusters by semi-supervised piecewise snipping. The framework, called guided piecewise snipping, utilizes both molecular data and clinical information to decompose the HC tree into clusters. It cuts the given HC tree at variable heights to find a partition (a set of non-overlapping clusters) which does not only represent a structure deemed to underlie the data from which HC tree is derived, but is also maximally consistent with the supplied clinical data. Moreover, the approach does not require the user to specify the number of clusters prior to the analysis. Extensive results on simulated and multiple medical data sets show that our approach consistently produces more meaningful clusters than the standard fixed-height cut and/or non-guided approaches.

Conclusions

The guided piecewise snipping approach features several novelties and advantages over existing approaches. The proposed algorithm is generic, and can be combined with other algorithms that operate on detected clusters. This approach represents an advancement in several regards: (1) a piecewise tree snipping framework that efficiently extracts clusters by snipping the HC tree possibly at variable heights while preserving the HC tree structure; (2) a flexible implementation allowing a variety of data types for both building and snipping the HC tree, including patient follow-up data like survival as auxiliary information.The data sets and R code are provided as supplementary files. The proposed method is available from Bioconductor as the R-package HCsnip.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0448-1) contains supplementary material, which is available to authorized users.     

Fuzzy C-means method for clustering microarray data

MOTIVATION: Clustering analysis of data from DNA microarray hybridization studies is essential for identifying biologically relevant groups of genes. Partitional clustering methods such as K-means or self-organizing maps assign each gene to a single cluster. However, these methods do not provide information about the influence of a given gene for the overall shape of clusters. Here we apply a fuzzy partitioning method, Fuzzy C-means (FCM), to attribute cluster membership values to genes. RESULTS: A major problem in applying the FCM method for clustering microarray data is the choice of the fuzziness parameter m. We show that the commonly used value m = 2 is not appropriate for some data sets, and that optimal values for m vary widely from one data set to another. We propose an empirical method, based on the distribution of distances between genes in a given data set, to determine an adequate value for m. By setting threshold levels for the membership values, genes which are tigthly associated to a given cluster can be selected. Using a yeast cell cycle data set as an example, we show that this selection increases the overall biological significance of the genes within the cluster. AVAILABILITY: Supplementary text and Matlab functions are available at http://www-igbmc.u-strasbg.fr/fcm/