Towards a consensus for calculating dendrogram-based functional diversity indices

The widely used FD index of functional diversity is based on the construction of a dendrogram. This index has been the subject of a strong debate concerning the choice of the distance and the clustering method to be used, since the method chosen may greatly affect the FD values obtained. Much of this debate has been centred around which method of dendrogram construction gives a faithful representation of species distribution in multidimensional functional trait space. From artificially generated datasets varying in species richness and correlations between traits, we test whether any single combination of clustering method(s) and distance consistently produces a dendrogram that most closely corresponds to the matrix of functional distances between pairs of species studied. We also test the ability of consensus trees, which incorporate features common to a range of different dendrograms, to summarize distance matrices. Our results show that no combination of clustering method(s) and distance constantly outperforms the others due to the complexity of interactions between correlations of traits, species richness, distance measures and clustering methods. Furthermore, the construction of a consensus tree from a range of dendrograms is often the best solution. Consequently, we recommend testing all combinations of distances and clustering methods (including consensus trees), then selecting the most reliable tree (with the lowest dissimilarity) to estimate FD value. Furthermore we suggest that any index that requires the construction of functional dendrograms potentially benefits from this new approach.     

A new unsupervised feature ranking method for gene expression data based on consensus affinity

Feature selection is widely established as one of the fundamental computational techniques in mining microarray data. Due to the lack of categorized information in practice, unsupervised feature selection is more practically important but correspondingly more difficult. Motivated by the cluster ensemble techniques, which combine multiple clustering solutions into a consensus solution of higher accuracy and stability, recent efforts in unsupervised feature selection proposed to use these consensus solutions as oracles. However,these methods are dependent on both the particular cluster ensemble algorithm used and the knowledge of the true cluster number. These methods will be unsuitable when the true cluster number is not available, which is common in practice. In view of the above problems, a new unsupervised feature ranking method is proposed to evaluate the importance of the features based on consensus affinity. Different from previous works, our method compares the corresponding affinity of each feature between a pair of instances based on the consensus matrix of clustering solutions. As a result, our method alleviates the need to know the true number of clusters and the dependence on particular cluster ensemble approaches as in previous works. Experiments on real gene expression data sets demonstrate significant improvement of the feature ranking results when compared to several state-of-the-art techniques.     

Robust consensus clustering for identification of expressed genes linked to malignancy of human colorectal carcinoma

Previous studies have been conducted in gene expression profiling to identify groups of genes that characterize the colorectal carcinoma disease. Despite the success of previous attempts to identify groups of genes in the progression of the colorectal carcinoma disease, their methods either require subjective interpretation of the number of clusters, or lack stability during different runs of the algorithms. All of which limits the usefulness of these methods. In this study, we propose an enhanced algorithm that provides stability and robustness in identifying differentially expressed genes in an expression profile analysis. Our proposed algorithm uses multiple clustering algorithms under the consensus clustering framework. The results of the experiment show that the robustness of our method provides a consistent structure of clusters, similar to the structure found in the previous study. Furthermore, our algorithm outperforms any single clustering algorithms in terms of the cluster quality score.     

Family relationships: should consensus reign?--consensus clustering for protein families

MOTIVATION: Reliable identification of protein families is key to phylogenetic analysis, functional annotation and the exploration of protein function diversity in a given phylogenetic branch. As more and more complete genomes are sequenced, there is a need for powerful and reliable algorithms facilitating protein families construction. RESULTS: We have formulated the problem of protein families construction as an instance of consensus clustering, for which we designed a novel algorithm that is computationally efficient in practice and produces high quality results. Our algorithm uses an election method to construct consensus families from competing clustering computations. Our consensus clustering algorithm is tailored to serve the specific needs of comparative genomics projects. First, it provides a robust means to incorporate results from different and complementary clustering methods, thus avoiding the need for an a priori choice that may introduce computational bias in the results. Second, it is suited to large-scale projects due to the practical efficiency. And third, it produces high quality results where families tend to represent groupings by biological function. AVAILABILITY: This method has been used for Génolevures project to compute protein families of Hemiascomycetous yeasts. The data are available online at http://cbi.labri.fr/Genolevures/fam/     

Consensus clustering and functional interpretation of gene-expression data

Microarray analysis using clustering algorithms can suffer from lack of inter-method consistency in assigning related gene-expression profiles to clusters. Obtaining a consensus set of clusters from a number of clustering methods should improve confidence in gene-expression analysis. Here we introduce consensus clustering, which provides such an advantage. When coupled with a statistically based gene functional analysis, our method allowed the identification of novel genes regulated by NFκB and the unfolded protein response in certain B-cell lymphomas.     

Assessing reliability of gene clusters from gene expression data

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

An ensemble framework for clustering protein-protein interaction networks

MOTIVATION: Protein-Protein Interaction (PPI) networks are believed to be important sources of information related to biological processes and complex metabolic functions of the cell. The presence of biologically relevant functional modules in these networks has been theorized by many researchers. However, the application of traditional clustering algorithms for extracting these modules has not been successful, largely due to the presence of noisy false positive interactions as well as specific topological challenges in the network. RESULTS: In this article, we propose an ensemble clustering framework to address this problem. For base clustering, we introduce two topology-based distance metrics to counteract the effects of noise. We develop a PCA-based consensus clustering technique, designed to reduce the dimensionality of the consensus problem and yield informative clusters. We also develop a soft consensus clustering variant to assign multifaceted proteins to multiple functional groups. We conduct an empirical evaluation of different consensus techniques using topology-based, information theoretic and domain-specific validation metrics and show that our approaches can provide significant benefits over other state-of-the-art approaches. Our analysis of the consensus clusters obtained demonstrates that ensemble clustering can (a) produce improved biologically significant functional groupings; and (b) facilitate soft clustering by discovering multiple functional associations for proteins. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

ArrayMining: a modular web-application for microarray analysis combining ensemble and consensus methods with cross-study normalization

Background  

Statistical analysis of DNA microarray data provides a valuable diagnostic tool for the investigation of genetic components of diseases. To take advantage of the multitude of available data sets and analysis methods, it is desirable to combine both different algorithms and data from different studies. Applying ensemble learning, consensus clustering and cross-study normalization methods for this purpose in an almost fully automated process and linking different analysis modules together under a single interface would simplify many microarray analysis tasks.     

PCA and Clustering Reveal Alternate mtDNA Phylogeny of N and M Clades

Phylogenetic trees based on mtDNA polymorphisms are often used to infer the history of recent human migrations. However, there is no consensus on which method to use. Most methods make strong assumptions which may bias the choice of polymorphisms and result in computational complexity which limits the analysis to a few samples/polymorphisms. For example, parsimony minimizes the number of mutations, which biases the results to minimizing homoplasy events. Such biases may miss the global structure of the polymorphisms altogether, with the risk of identifying a "common" polymorphism as ancient without an internal check on whether it either is homoplasic or is identified as ancient because of sampling bias (from oversampling the population with the polymorphism). A signature of this problem is that different methods applied to the same data or the same method applied to different datasets results in different tree topologies. When the results of such analyses are combined, the consensus trees have a low internal branch consensus. We determine human mtDNA phylogeny from 1737 complete sequences using a new, direct method based on principal component analysis (PCA) and unsupervised consensus ensemble clustering. PCA identifies polymorphisms representing robust variations in the data and consensus ensemble clustering creates stable haplogroup clusters. The tree is obtained from the bifurcating network obtained when the data are split into k = 2,3,4,...,kmax clusters, with equal sampling from each haplogroup. Our method assumes only that the data can be clustered into groups based on mutations, is fast, is stable to sample perturbation, uses all significant polymorphisms in the data, works for arbitrary sample sizes, and avoids sample choice and haplogroup size bias. The internal branches of our tree have a 90% consensus accuracy. In conclusion, our tree recreates the standard phylogeny of the N, M, L0/L1, L2, and L3 clades, confirming the African origin of modern humans and showing that the M and N clades arose in almost coincident migrations. However, the N clade haplogroups split along an East-West geographic divide, with a "European R clade" containing the haplogroups H, V, H/V, J, T, and U and a "Eurasian N subclade" including haplogroups B, R5, F, A, N9, I, W, and X. The haplogroup pairs (N9a, N9b) and (M7a, M7b) within N and M are placed in nonnearest locations in agreement with their expected large TMRCA from studies of their migrations into Japan. For comparison, we also construct consensus maximum likelihood, parsimony, neighbor joining, and UPGMA-based trees using the same polymorphisms and show that these methods give consistent results only for the clade tree. For recent branches, the consensus accuracy for these methods is in the range of 1-20%. From a comparison of our haplogroups to two chimp and one bonobo sequences, and assuming a chimp-human coalescent time of 5 million years before present, we find a human mtDNA TMRCA of 206,000 +/- 14,000 years before present.     

Reference materials for cellular therapeutics

The development of cellular therapeutics (CTP) takes place over many years, and, where successful, the developer will anticipate the product to be in clinical use for decades. Successful demonstration of manufacturing and quality consistency is dependent on the use of complex analytical methods; thus, the risk of process and method drift over time is high. The use of reference materials (RM) is an established scientific principle and as such also a regulatory requirement. The various uses of RM in the context of CTP manufacturing and quality are discussed, along with why they are needed for living cell products and the analytical methods applied to them. Relatively few consensus RM exist that are suitable for even common methods used by CTP developers, such as flow cytometry. Others have also identified this need and made proposals; however, great care will be needed to ensure any consensus RM that result are fit for purpose. Such consensus RM probably will need to be applied to specific standardized methods, and the idea that a single RM can have wide applicability is challenged. Written standards, including standardized methods, together with appropriate measurement RM are probably the most appropriate way to define specific starting cell types. The characteristics of a specific CTP will to some degree deviate from those of the starting cells; consequently, a product RM remains the best solution where feasible. Each CTP developer must consider how and what types of RM should be used to ensure the reliability of their own analytical measurements.     

Statistically based postprocessing of phylogenetic analysis by clustering

MOTIVATION: Phylogenetic analyses often produce thousands of candidate trees. Biologists resolve the conflict by computing the consensus of these trees. Single-tree consensus as postprocessing methods can be unsatisfactory due to their inherent limitations. RESULTS: In this paper we present an alternative approach by using clustering algorithms on the set of candidate trees. We propose bicriterion problems, in particular using the concept of information loss, and new consensus trees called characteristic trees that minimize the information loss. Our empirical study using four biological datasets shows that our approach provides a significant improvement in the information content, while adding only a small amount of complexity. Furthermore, the consensus trees we obtain for each of our large clusters are more resolved than the single-tree consensus trees. We also provide some initial progress on theoretical questions that arise in this context.     

Faithful consensus methods for n-trees

A class of new consensus methods for n-trees (hierarchical clusterings) is proposed. These methods apply systematically to an arbitrary collection of given classifications of a fixed set of taxa, and produce a single consensus classification. They are motivated by the desire that the consensus classification retain as much information as possible from the given classifications, even in the case of only approximate agreement among them. A focus of the paper is the concept of faithfulness of consensus methods; this concept explicates the informal notion of adequate retention of information referred to above, and is proposed as a desirable requirement for consensus methods in general. The new methods are all faithful; they have the additional property that they take hierarchical level into account. Other general properties of consensus methods are investigated, especially with reference to their relation with faithfulness. The most important of these properties is neutrality; loosely speaking a consensus method is neutral if all nontrivial clusters are treated equally in the conditions on the given classifications required to guarantee the appearance of a cluster in the consensus. A central result of the paper is an analogue of the classical impossibility theorem of K. Arrow: with trivial exceptions it is impossible to have a consensus method that is simultaneously faithful and neutral. Thus two intuitively very appealing general properties of consensus methods are seen to be incompatible.     

Rapid membrane protein topology prediction

State-of-the-art methods for topology of α-helical membrane proteins are based on the use of time-consuming multiple sequence alignments obtained from PSI-BLAST or other sources. Here, we examine if it is possible to use the consensus of topology prediction methods that are based on single sequences to obtain a similar accuracy as the more accurate multiple sequence-based methods. Here, we show that TOPCONS-single performs better than any of the other topology prediction methods tested here, but ~6% worse than the best method that is utilizing multiple sequence alignments. AVAILABILITY AND IMPLEMENTATION: TOPCONS-single is available as a web server from http://single.topcons.net/ and is also included for local installation from the web site. In addition, consensus-based topology predictions for the entire international protein index (IPI) is available from the web server and will be updated at regular intervals.     

Optimal search space for clustering gene expression data via consensus.

Ensemble clustering methods have become increasingly important to ease the task of choosing the most appropriate cluster algorithm for a particular data analysis problem. The consensus clustering (CC) algorithm is a recognized ensemble clustering method that uses an artificial intelligence technique to optimize a fitness function. We formally prove the existence of a subspace of the search space for CC, which contains all solutions of maximal fitness and suggests two greedy algorithms to search this subspace. We evaluate the algorithms on two gene expression data sets and one synthetic data set, and compare the result with the results of other ensemble clustering approaches.     

Linkage and heritability analysis of migraine symptom groupings: a comparison of three different clustering methods on twin data

Migraine is a painful disorder for which the etiology remains obscure. Diagnosis is largely based on International Headache Society criteria. However, no feature occurs in all patients who meet these criteria, and no single symptom is required for diagnosis. Consequently, this definition may not accurately reflect the phenotypic heterogeneity or genetic basis of the disorder. Such phenotypic uncertainty is typical for complex genetic disorders and has encouraged interest in multivariate statistical methods for classifying disease phenotypes. We applied three popular statistical phenotyping methods—latent class analysis, grade of membership and grade of membership “fuzzy” clustering (Fanny)—to migraine symptom data, and compared heritability and genome-wide linkage results obtained using each approach. Our results demonstrate that different methodologies produce different clustering structures and non-negligible differences in subsequent analyses. We therefore urge caution in the use of any single approach and suggest that multiple phenotyping methods be used.     

Clumpak: a program for identifying clustering modes and packaging population structure inferences across K

The identification of the genetic structure of populations from multilocus genotype data has become a central component of modern population‐genetic data analysis. Application of model‐based clustering programs often entails a number of steps, in which the user considers different modelling assumptions, compares results across different predetermined values of the number of assumed clusters (a parameter typically denoted K), examines multiple independent runs for each fixed value of K, and distinguishes among runs belonging to substantially distinct clustering solutions. Here, we present Clumpak (Cluster Markov Packager Across K), a method that automates the postprocessing of results of model‐based population structure analyses. For analysing multiple independent runs at a single K value, Clumpak identifies sets of highly similar runs, separating distinct groups of runs that represent distinct modes in the space of possible solutions. This procedure, which generates a consensus solution for each distinct mode, is performed by the use of a Markov clustering algorithm that relies on a similarity matrix between replicate runs, as computed by the software Clumpp . Next, Clumpak identifies an optimal alignment of inferred clusters across different values of K, extending a similar approach implemented for a fixed K in Clumpp and simplifying the comparison of clustering results across different K values. Clumpak incorporates additional features, such as implementations of methods for choosing K and comparing solutions obtained by different programs, models, or data subsets. Clumpak , available at http://clumpak.tau.ac.il , simplifies the use of model‐based analyses of population structure in population genetics and molecular ecology.