A graph-based clustering method applied to protein sequences

The number of amino acid sequences is increasing very rapidly in the protein databases like Swiss-Prot, Uniprot, PIR and others, but the structure of only some amino acid sequences are found in the Protein Data Bank. Thus, an important problem in genomics is automatically clustering homologous protein sequences when only sequence information is available. Here, we use graph theoretic techniques for clustering amino acid sequences. A similarity graph is defined and clusters in that graph correspond to connected subgraphs. Cluster analysis seeks grouping of amino acid sequences into subsets based on distance or similarity score between pairs of sequences. Our goal is to find disjoint subsets, called clusters, such that two criteria are satisfied: homogeneity: sequences in the same cluster are highly similar to each other; and separation: sequences in different clusters have low similarity to each other. We tested our method on several subsets of SCOP (Structural Classification of proteins) database, a gold standard for protein structure classification. The results show that for a given set of proteins the number of clusters we obtained is close to the superfamilies in that set; there are fewer singeltons; and the method correctly groups most remote homologs.     

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.     

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.     

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/     

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.     

Ortholog clustering on a multipartite graph

We present a method for automatically extracting groups of orthologous genes from a large set of genomes by a new clustering algorithm on a weighted multipartite graph. The method assigns a score to an arbitrary subset of genes from multiple genomes to assess the orthologous relationships between genes in the subset. This score is computed using sequence similarities between the member genes and the phylogenetic relationship between the corresponding genomes. An ortholog cluster is found as the subset with the highest score, so ortholog clustering is formulated as a combinatorial optimization problem. The algorithm for finding an ortholog cluster runs in time O(|E| + |V| log |V|), where V and E are the sets of vertices and edges, respectively, in the graph. However, if we discretize the similarity scores into a constant number of bins, the runtime improves to O(|E| + |V|). The proposed method was applied to seven complete eukaryote genomes on which the manually curated database of eukaryotic ortholog clusters, KOG, is constructed. A comparison of our results with the manually curated ortholog clusters shows that our clusters are well correlated with the existing clusters     

Using Hierarchical Clustering and Dendrograms to Quantify the Clustering of Membrane Proteins

Cell biologists have developed methods to label membrane proteins with gold nanoparticles and then extract spatial point patterns of the gold particles from transmission electron microscopy images using image processing software. Previously, the resulting patterns were analyzed using the Hopkins statistic, which distinguishes nonclustered from modestly and highly clustered distributions, but is not designed to quantify the number or sizes of the clusters. Clusters were defined by the partitional clustering approach which required the choice of a distance. Two points from a pattern were put in the same cluster if they were closer than this distance. In this study, we present a new methodology based on hierarchical clustering to quantify clustering. An intrinsic distance is computed, which is the distance that produces the maximum number of clusters in the biological data, eliminating the need to choose a distance. To quantify the extent of clustering, we compare the clustering distance between the experimental data being analyzed with that from simulated random data. Results are then expressed as a dimensionless number, the clustering ratio that facilitates the comparison of clustering between experiments. Replacing the chosen cluster distance by the intrinsic clustering distance emphasizes densely packed clusters that are likely more important to downstream signaling events.     

Detecting clusters of different geometrical shapes in microarray gene expression data

MOTIVATION: Clustering has been used as a popular technique for finding groups of genes that show similar expression patterns under multiple experimental conditions. Many clustering methods have been proposed for clustering gene-expression data, including the hierarchical clustering, k-means clustering and self-organizing map (SOM). However, the conventional methods are limited to identify different shapes of clusters because they use a fixed distance norm when calculating the distance between genes. The fixed distance norm imposes a fixed geometrical shape on the clusters regardless of the actual data distribution. Thus, different distance norms are required for handling the different shapes of clusters. RESULTS: We present the Gustafson-Kessel (GK) clustering method for microarray gene-expression data. To detect clusters of different shapes in a dataset, we use an adaptive distance norm that is calculated by a fuzzy covariance matrix (F) of each cluster in which the eigenstructure of F is used as an indicator of the shape of the cluster. Moreover, the GK method is less prone to falling into local minima than the k-means and SOM because it makes decisions through the use of membership degrees of a gene to clusters. The algorithmic procedure is accomplished by the alternating optimization technique, which iteratively improves a sequence of sets of clusters until no further improvement is possible. To test the performance of the GK method, we applied the GK method and well-known conventional methods to three recently published yeast datasets, and compared the performance of each method using the Saccharomyces Genome Database annotations. The clustering results of the GK method are more significantly relevant to the biological annotations than those of the other methods, demonstrating its effectiveness and potential for clustering 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. SUPPLEMENTARY INFORMATION: Supplementary data are available at http://dragon.kaist.ac.kr/gk.     

Methods for comparative assessment of the results of cluster analysis of hydrobiocenoses structure (by the example of zooplankton communities of the Linda River,Nizhny Novgorod region)

In this paper we present modern approaches to the classification of hydrobiological samples based on various metrics of species-structure similarity—Euclidean distance, Renkonen index, and the cosine of the angle between the species abundances vectors. We use the cophenetic correlation coefficient, Gower distance, and Shepard-like plot for the justification of clustering method. For the choice of the optimal number of clusters, we apply approaches based on silhouette widths and binary matrices representing partitions. An analysis of the spatial structure of zooplankton communities in the small Linda River shows that average agglomerative clustering is an optimal algorithm for objects of this type. A comparative analysis of the results of cluster analysis on the basis of different similarity metrics shows that the most adequate classification can be obtained using the cosine of the angle between the species abundances vectors and the Renkonen index, whereas the classification based on the Euclidean distances is less successful from the biological point of view. Approaches outlined in this paper allow researchers to make quantitative decisions about key elements of classification, greatly reducing the subjectivity of the cluster analysis results.     

A generalized taxon concept

A generalized taxon concept (GTC) is proposed with a method for revealing and ranking difficult taxa at any level in the taxonomic hierarchy. The method is based on cluster quality, denned jointly by die compactness of a cluster's contents and its isolation from its informational neighbours. The cluster contents are individuals in die case of species and at higher levels, taxa from the rank below. A standard, quality threshold value is obtained from clustering accepted taxa in the informational region. If the quality value of a problem cluster lies at or above the threshold it is accepted as a taxon and ranked with others at the current level. If it lies below, and is likely to be informationally useful, it may be accepted as a sub-taxon such as a subgenus or subfamily. Provision is made for coarsely scored data. The clustering is mainly based on homogeneity, where possible with a rapid, fuzzily cladistic de-weighting of symplesiomorphies by self-graded factors. The strengms of inter-item reactions such as breeding and DNA-DNA hybridization may also be used. The method is agglomerative so that it can rapidly reveal polythetic groups which may be riddled with exceptional property states caused by long exposure to natural selective forces. All this fits the evolutionary oudook of the GTC, which sees taxa as fuzzy clusters of populations and lineages sharing much of a genetic memory, moulded by a unique history of evolution and extinction. Practical problems of memods based on mis and other taxon concepts are briefly compared. The GTC's approach offers important refinements that could be valuable in helping to speed up urgent surveys of biodiversity, especially in the moist tropics.     

CLUMPP: a cluster matching and permutation program for dealing with label switching and multimodality in analysis of population structure

MOTIVATION: Clustering of individuals into populations on the basis of multilocus genotypes is informative in a variety of settings. In population-genetic clustering algorithms, such as BAPS, STRUCTURE and TESS, individual multilocus genotypes are partitioned over a set of clusters, often using unsupervised approaches that involve stochastic simulation. As a result, replicate cluster analyses of the same data may produce several distinct solutions for estimated cluster membership coefficients, even though the same initial conditions were used. Major differences among clustering solutions have two main sources: (1) 'label switching' of clusters across replicates, caused by the arbitrary way in which clusters in an unsupervised analysis are labeled, and (2) 'genuine multimodality,' truly distinct solutions across replicates. RESULTS: To facilitate the interpretation of population-genetic clustering results, we describe three algorithms for aligning multiple replicate analyses of the same data set. We have implemented these algorithms in the computer program CLUMPP (CLUster Matching and Permutation Program). We illustrate the use of CLUMPP by aligning the cluster membership coefficients from 100 replicate cluster analyses of 600 chickens from 20 different breeds. AVAILABILITY: CLUMPP is freely available at http://rosenberglab.bioinformatics.med.umich.edu/clumpp.html.     

CHOP proteins into structural domain-like fragments

We developed a method CHOP dissecting proteins into domain-like fragments. The basic idea was to cut proteins beginning from very reliable experimental information (PDB), proceeding to expert annotations of domain-like regions (Pfam-A), and completing through cuts based on termini of known proteins. In this way, CHOP dissected more than two thirds of all proteins from 62 proteomes. Analysis of our structural domain-like fragments revealed four surprising results. First, >70% of all dissected proteins contained more than one fragment. Second, most domains spanned on average over approximately 100 residues. This average was similar for eukaryotic and prokaryotic proteins, and it is also valid-although previously not described-for all proteins in the PDB. Third, single-domain proteins were significant longer than most domains in multidomain proteins. Fourth, three fourths of all domains appeared shorter than 210 residues. We believe that our CHOP fragments constituted an important resource for functional and structural genomics. Nevertheless, our main motivation to develop CHOP was that the single-linkage clustering method failed to adequately group full-length proteins. In contrast, CLUP-the simple clustering scheme CLUP introduced here-succeeded largely to group the CHOP fragments from 62 proteomes such that all members of one cluster shared a basic structural core. CLUP found >63,000 multi- and >118,000 single-member clusters. Although most fragments were restricted to a particular cluster, approximately 24% of the fragments were duplicated in at least two clusters. Our thresholds for grouping two fragments into the same cluster were rather conservative. Nevertheless, our results suggested that structural genomics initiatives have to target >30,000 fragments to at least cover the multimember clusters in 62 proteomes.     

Autonomous learning of load and traffic patterns to improve cluster utilization

Adaptive clustering aims at improving cluster utilization for varying load and traffic patterns. Locality-based least-connection with replication (LBLCR) scheduling that comes with Linux is designed to help improve cluster utilization through adaptive clustering. A key issue with LBLCR, however, is that cluster performance depends much on a single threshold value that is used to determine adaptation. Once set, the threshold remains fixed, regardless of the load and traffic patterns. If a cluster of PCs is to adapt to different traffic patterns for high utilization, a good threshold has to be selected and used dynamically. We present in this paper an adaptive clustering framework that autonomously learns and adapts to different load and traffic patterns at runtime with no administrator intervention. The cluster is configured once and for all. As the patterns change, the cluster automatically expands/contracts to meet the changing demands. At the same time, the patterns are proactively learned so that when similar patterns emerge in the future, the cluster knows what to do to improve utilization. We have implemented this autonomous learning method and compared it with LBLCR using published Web traces. Experimental results indicate that our autonomous learning method produces high performance scalability and adaptability for different patterns. On the other hand LBLCR-based clustering suffers from performance scalability and adaptability for different traffic patterns since it is not designed to obtain good threshold values and use them at runtime.     

Accelerated Simplified Swarm Optimization with Exploitation Search Scheme for Data Clustering

Data clustering is commonly employed in many disciplines. The aim of clustering is to partition a set of data into clusters, in which objects within the same cluster are similar and dissimilar to other objects that belong to different clusters. Over the past decade, the evolutionary algorithm has been commonly used to solve clustering problems. This study presents a novel algorithm based on simplified swarm optimization, an emerging population-based stochastic optimization approach with the advantages of simplicity, efficiency, and flexibility. This approach combines variable vibrating search (VVS) and rapid centralized strategy (RCS) in dealing with clustering problem. VVS is an exploitation search scheme that can refine the quality of solutions by searching the extreme points nearby the global best position. RCS is developed to accelerate the convergence rate of the algorithm by using the arithmetic average. To empirically evaluate the performance of the proposed algorithm, experiments are examined using 12 benchmark datasets, and corresponding results are compared with recent works. Results of statistical analysis indicate that the proposed algorithm is competitive in terms of the quality of solutions.     

生物序列的聚类分析

通过不同的聚类方式,对公共数据库中生物序列数据进行生物信息的挖掘,以达到在更广泛和更深入的框架中了解它们之间的相互关系的目的。以帕金森病相关基因所对应的mRNA序列为例,使用双序列比对的得分值作为序列之间的距离定义。同时为解决不同聚类分析之间的差异,分别采用模糊聚类和层次聚类两种不同的方法进行聚类分析。并由不同聚类方法得到的一致分类聚类的结果为基因功能分类提供支持,为进一步揭示生物序列所蕴涵的生物学知识和生物学规律提供可参考的依据。     

Genetic diversity in sugarcane hybrids (Saccharum spp complex) grown in tropical India based on STMS markers

Understanding the pattern of diversity among the commercial sugarcane hybrids is highly useful to sugarcane breeders in planning and broadening the genetic base. Genetic analysis of 22 cultivated sugarcane hybrids representing all agro-eco climatic regions of tropical India was carried out using ten sequence tagged microsatellite sites (STMS) primers. A total of 127 markers were amplified, of which 78.74% were polymorphic with an average of 10 polymorphic products per STMS primer. Jaccard’s similarity coefficient value estimated between closely related hybrids was 0.889 while the lowest coefficient value of 0.574 was detected with distantly related hybrids. The average genetic similarity among the hybrids was ~84.8%. These results indicated the existence of low level of genetic diversity among the commercial hybrids under cultivation. Unweighted pair group method with arithmetic averages (UPGMA) cluster analysis detected five major clusters. Cluster II consisted of four varieties which had Co 775 as one of the parents. Variety CoC 671 and its somaclone Co 94012 were grouped into cluster IIa. Varieties grouped in the cluster III had either CoC 671 or Co 775 in their genealogy indicating the influence of parental genome contribution to clustering. Varieties developed for east coast zone were grouped in the clusters IIb, IIIb, IIIc and IVe which indicated the influence of adaptation of varieties to particular agro-climatic condition. The study also identified 12 unique markers which can be useful in varietal identification and rouging in seed plot.     

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     

A multicriteria decision making approach for estimating the number of clusters in a data set

Determining the number of clusters in a data set is an essential yet difficult step in cluster analysis. Since this task involves more than one criterion, it can be modeled as a multiple criteria decision making (MCDM) problem. This paper proposes a multiple criteria decision making (MCDM)-based approach to estimate the number of clusters for a given data set. In this approach, MCDM methods consider different numbers of clusters as alternatives and the outputs of any clustering algorithm on validity measures as criteria. The proposed method is examined by an experimental study using three MCDM methods, the well-known clustering algorithm-k-means, ten relative measures, and fifteen public-domain UCI machine learning data sets. The results show that MCDM methods work fairly well in estimating the number of clusters in the data and outperform the ten relative measures considered in the study.