Graph-based consensus clustering for class discovery from gene expression data

MOTIVATION: Consensus clustering, also known as cluster ensemble, is one of the important techniques for microarray data analysis, and is particularly useful for class discovery from microarray data. Compared with traditional clustering algorithms, consensus clustering approaches have the ability to integrate multiple partitions from different cluster solutions to improve the robustness, stability, scalability and parallelization of the clustering algorithms. By consensus clustering, one can discover the underlying classes of the samples in gene expression data. RESULTS: In addition to exploring a graph-based consensus clustering (GCC) algorithm to estimate the underlying classes of the samples in microarray data, we also design a new validation index to determine the number of classes in microarray data. To our knowledge, this is the first time in which GCC is applied to class discovery for microarray data. Given a pre specified maximum number of classes (denoted as K(max) in this article), our algorithm can discover the true number of classes for the samples in microarray data according to a new cluster validation index called the Modified Rand Index. Experiments on gene expression data indicate that our new algorithm can (i) outperform most of the existing algorithms, (ii) identify the number of classes correctly in real cancer datasets, and (iii) discover the classes of samples with biological meaning. AVAILABILITY: Matlab source code for the GCC algorithm is available upon request from Zhiwen Yu.     

Gene expression data analysis using multiobjective clustering improved with SVM based ensemble

Microarray technology facilitates the monitoring of the expression levels of thousands of genes over different experimental conditions simultaneously. Clustering is a popular data mining tool which can be applied to microarray gene expression data to identify co-expressed genes. Most of the traditional clustering methods optimize a single clustering goodness criterion and thus may not be capable of performing well on all kinds of datasets. Motivated by this, in this article, a multiobjective clustering technique that optimizes cluster compactness and separation simultaneously, has been improved through a novel support vector machine classification based cluster ensemble method. The superiority of MOCSVMEN (MultiObjective Clustering with Support Vector Machine based ENsemble) has been established by comparing its performance with that of several well known existing microarray data clustering algorithms. Two real-life benchmark gene expression datasets have been used for testing the comparative performances of different algorithms. A recently developed metric, called Biological Homogeneity Index (BHI), which computes the clustering goodness with respect to functional annotation, has been used for the comparison purpose.     

SHIPS: Spectral Hierarchical Clustering for the Inference of Population Structure in Genetic Studies

Inferring the structure of populations has many applications for genetic research. In addition to providing information for evolutionary studies, it can be used to account for the bias induced by population stratification in association studies. To this end, many algorithms have been proposed to cluster individuals into genetically homogeneous sub-populations. The parametric algorithms, such as Structure, are very popular but their underlying complexity and their high computational cost led to the development of faster parametric alternatives such as Admixture. Alternatives to these methods are the non-parametric approaches. Among this category, AWclust has proven efficient but fails to properly identify population structure for complex datasets. We present in this article a new clustering algorithm called Spectral Hierarchical clustering for the Inference of Population Structure (SHIPS), based on a divisive hierarchical clustering strategy, allowing a progressive investigation of population structure. This method takes genetic data as input to cluster individuals into homogeneous sub-populations and with the use of the gap statistic estimates the optimal number of such sub-populations. SHIPS was applied to a set of simulated discrete and admixed datasets and to real SNP datasets, that are data from the HapMap and Pan-Asian SNP consortium. The programs Structure, Admixture, AWclust and PCAclust were also investigated in a comparison study. SHIPS and the parametric approach Structure were the most accurate when applied to simulated datasets both in terms of individual assignments and estimation of the correct number of clusters. The analysis of the results on the real datasets highlighted that the clusterings of SHIPS were the more consistent with the population labels or those produced by the Admixture program. The performances of SHIPS when applied to SNP data, along with its relatively low computational cost and its ease of use make this method a promising solution to infer fine-scale genetic patterns.     

A multi-stage approach to clustering and imputation of gene expression profiles

MOTIVATION: Microarray experiments have revolutionized the study of gene expression with their ability to generate large amounts of data. This article describes an alternative to existing approaches to clustering of gene expression profiles; the key idea is to cluster in stages using a hierarchy of distance measures. This method is motivated by the way in which the human mind sorts and so groups many items. The distance measures arise from the orthogonal breakup of Euclidean distance, giving us a set of independent measures of different attributes of the gene expression profile. Interpretation of these distances is closely related to the statistical design of the microarray experiment. This clustering method not only accommodates missing data but also leads to an associated imputation method. RESULTS: The performance of the clustering and imputation methods was tested on a simulated dataset, a yeast cell cycle dataset and a central nervous system development dataset. Based on the Rand and adjusted Rand indices, the clustering method is more consistent with the biological classification of the data than commonly used clustering methods. The imputation method, at varying levels of missingness, outperforms most imputation methods, based on root mean squared error (RMSE). AVAILABILITY: Code in R is available on request from the authors.     

A Comparison Study on Similarity and Dissimilarity Measures in Clustering Continuous Data

Similarity or distance measures are core components used by distance-based clustering algorithms to cluster similar data points into the same clusters, while dissimilar or distant data points are placed into different clusters. The performance of similarity measures is mostly addressed in two or three-dimensional spaces, beyond which, to the best of our knowledge, there is no empirical study that has revealed the behavior of similarity measures when dealing with high-dimensional datasets. To fill this gap, a technical framework is proposed in this study to analyze, compare and benchmark the influence of different similarity measures on the results of distance-based clustering algorithms. For reproducibility purposes, fifteen publicly available datasets were used for this study, and consequently, future distance measures can be evaluated and compared with the results of the measures discussed in this work. These datasets were classified as low and high-dimensional categories to study the performance of each measure against each category. This research should help the research community to identify suitable distance measures for datasets and also to facilitate a comparison and evaluation of the newly proposed similarity or distance measures with traditional ones.     

A comparison of clustering methods for river benthic community analysis

Four commonly used clustering methods (UPGMA, Ward Linkage,Complete Linkage and TWINSPAN) were compared in their abilitytorecognise the structure of three river macroinvertebratesdatasetswhich were pre-determined based on habitat and biologicalcharacteristics or chemical water quality of sampling sites.DCA,NMDS and ANOSIM were applied to the same datasets to providefurther information about data structure, and nonparametrictestswere also undertaken on major chemical variables to justifythepredeterminations. The modified Rand Index was used to measuretheagreement between a particular solution and the pre-determinedclassification. The results showed that Ward Linkage performedbestwhen its use was broadened and used with the CY DissimilarityMeasure, followed by TWINSPAN and Complete Linkage with UPGMAbeingleast successful. There was evidence to suggest that theeffectiveness of some clustering methods (e.g. UPGMA) may varyatdifferent clustering levels, and simulation techniques whichhavebeen used to assess clustering methods could leave somepropertiesof clustering methods unexamined.     

Reducing the Time Requirement of k-Means Algorithm

Traditional k-means and most k-means variants are still computationally expensive for large datasets, such as microarray data, which have large datasets with large dimension size d. In k-means clustering, we are given a set of n data points in d-dimensional space R^d and an integer k. The problem is to determine a set of k points in R^d, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this work, we develop a novel k-means algorithm, which is simple but more efficient than the traditional k-means and the recent enhanced k-means. Our new algorithm is based on the recently established relationship between principal component analysis and the k-means clustering. We provided the correctness proof for this algorithm. Results obtained from testing the algorithm on three biological data and six non-biological data (three of these data are real, while the other three are simulated) also indicate that our algorithm is empirically faster than other known k-means algorithms. We assessed the quality of our algorithm clusters against the clusters of a known structure using the Hubert-Arabie Adjusted Rand index (ARI_HA). We found that when k is close to d, the quality is good (ARI_HA>0.8) and when k is not close to d, the quality of our new k-means algorithm is excellent (ARI_HA>0.9). In this paper, emphases are on the reduction of the time requirement of the k-means algorithm and its application to microarray data due to the desire to create a tool for clustering and malaria research. However, the new clustering algorithm can be used for other clustering needs as long as an appropriate measure of distance between the centroids and the members is used. This has been demonstrated in this work on six non-biological data.     

SMART: Unique Splitting-While-Merging Framework for Gene Clustering

Successful clustering algorithms are highly dependent on parameter settings. The clustering performance degrades significantly unless parameters are properly set, and yet, it is difficult to set these parameters a priori. To address this issue, in this paper, we propose a unique splitting-while-merging clustering framework, named “splitting merging awareness tactics” (SMART), which does not require any a priori knowledge of either the number of clusters or even the possible range of this number. Unlike existing self-splitting algorithms, which over-cluster the dataset to a large number of clusters and then merge some similar clusters, our framework has the ability to split and merge clusters automatically during the process and produces the the most reliable clustering results, by intrinsically integrating many clustering techniques and tasks. The SMART framework is implemented with two distinct clustering paradigms in two algorithms: competitive learning and finite mixture model. Nevertheless, within the proposed SMART framework, many other algorithms can be derived for different clustering paradigms. The minimum message length algorithm is integrated into the framework as the clustering selection criterion. The usefulness of the SMART framework and its algorithms is tested in demonstration datasets and simulated gene expression datasets. Moreover, two real microarray gene expression datasets are studied using this approach. Based on the performance of many metrics, all numerical results show that SMART is superior to compared existing self-splitting algorithms and traditional algorithms. Three main properties of the proposed SMART framework are summarized as: (1) needing no parameters dependent on the respective dataset or a priori knowledge about the datasets, (2) extendible to many different applications, (3) offering superior performance compared with counterpart algorithms.     

Misty Mountain clustering: application to fast unsupervised flow cytometry gating

Background  

There are many important clustering questions in computational biology for which no satisfactory method exists. Automated clustering algorithms, when applied to large, multidimensional datasets, such as flow cytometry data, prove unsatisfactory in terms of speed, problems with local minima or cluster shape bias. Model-based approaches are restricted by the assumptions of the fitting functions. Furthermore, model based clustering requires serial clustering for all cluster numbers within a user defined interval. The final cluster number is then selected by various criteria. These supervised serial clustering methods are time consuming and frequently different criteria result in different optimal cluster numbers. Various unsupervised heuristic approaches that have been developed such as affinity propagation are too expensive to be applied to datasets on the order of 10⁶ points that are often generated by high throughput experiments.     

A multiple kernel density clustering algorithm for incomplete datasets in bioinformatics

Background

While there are a large number of bioinformatics datasets for clustering, many of them are incomplete, i.e., missing attribute values in some data samples needed by clustering algorithms. A variety of clustering algorithms have been proposed in the past years, but they usually are limited to cluster on the complete dataset. Besides, conventional clustering algorithms cannot obtain a trade-off between accuracy and efficiency of the clustering process since many essential parameters are determined by the human user’s experience.

Results

The paper proposes a Multiple Kernel Density Clustering algorithm for Incomplete datasets called MKDCI. The MKDCI algorithm consists of recovering missing attribute values of input data samples, learning an optimally combined kernel for clustering the input dataset, reducing dimensionality with the optimal kernel based on multiple basis kernels, detecting cluster centroids with the Isolation Forests method, assigning clusters with arbitrary shape and visualizing the results.

Conclusions

Extensive experiments on several well-known clustering datasets in bioinformatics field demonstrate the effectiveness of the proposed MKDCI algorithm. Compared with existing density clustering algorithms and parameter-free clustering algorithms, the proposed MKDCI algorithm tends to automatically produce clusters of better quality on the incomplete dataset in bioinformatics.

     

蛋白质结构确定领域中的几种矩阵填充算法的对比评估

目的 目前,如何从核磁共振(nuclear magnetic resonance,NMR)光谱实验中准确地确定蛋白质的三维结构是生物物理学中的一个热门课题,因为蛋白质是生物体的重要组成成分,了解蛋白质的空间结构对研究其功能至关重要,然而由于实验数据的严重缺乏使其成为一个很大的挑战。方法 在本文中,通过恢复距离矩阵的矩阵填充(matrix completion,MC)算法来解决蛋白质结构确定问题。首先,初始距离矩阵模型被建立,由于实验数据的缺乏,此时的初始距离矩阵为不完整矩阵,随后通过MC算法恢复初始距离矩阵的缺失数据,从而获得整个蛋白质三维结构。为了进一步测试算法的性能,本文选取了4种不同拓扑结构的蛋白质和6种现有的MC算法进行了测试,探究了算法在不同的采样率以及不同程度噪声的情况下算法的恢复效果。结果 通过分析均方根偏差(root-mean-square deviation,RMSD)和计算时间这两个重要指标的平均值及标准差评估了算法的性能,结果显示当采样率和噪声因子控制在一定范围内时,RMSD值和标准差都能达到很小的值。另外本文更加具体地比较了不同算法的特点和优势,在精确采样情况下...     

Performance assessment of kernel density clustering for gene expression profile data

Kernel density smoothing techniques have been used in classification or supervised learning of gene expression profile (GEP) data, but their applications to clustering or unsupervised learning of those data have not been explored and assessed. Here we report a kernel density clustering method for analysing GEP data and compare its performance with the three most widely-used clustering methods: hierarchical clustering, K-means clustering, and multivariate mixture model-based clustering. Using several methods to measure agreement, between-cluster isolation, and withincluster coherence, such as the Adjusted Rand Index, the Pseudo F test, the r(2) test, and the profile plot, we have assessed the effectiveness of kernel density clustering for recovering clusters, and its robustness against noise on clustering both simulated and real GEP data. Our results show that the kernel density clustering method has excellent performance in recovering clusters from simulated data and in grouping large real expression profile data sets into compact and well-isolated clusters, and that it is the most robust clustering method for analysing noisy expression profile data compared to the other three methods assessed.     

Medoid-based clustering using ant colony optimization

The application of ACO-based algorithms in data mining has been growing over the last few years, and several supervised and unsupervised learning algorithms have been developed using this bio-inspired approach. Most recent works about unsupervised learning have focused on clustering, showing the potential of ACO-based techniques. However, there are still clustering areas that are almost unexplored using these techniques, such as medoid-based clustering. Medoid-based clustering methods are helpful—compared to classical centroid-based techniques—when centroids cannot be easily defined. This paper proposes two medoid-based ACO clustering algorithms, where the only information needed is the distance between data: one algorithm that uses an ACO procedure to determine an optimal medoid set (METACOC algorithm) and another algorithm that uses an automatic selection of the number of clusters (METACOC-K algorithm). The proposed algorithms are compared against classical clustering approaches using synthetic and real-world datasets.     

Reproducible Clusters from Microarray Research: Whither?

Motivation

In cluster analysis, the validity of specific solutions, algorithms, and procedures present significant challenges because there is no null hypothesis to test and no 'right answer'. It has been noted that a replicable classification is not necessarily a useful one, but a useful one that characterizes some aspect of the population must be replicable. By replicable we mean reproducible across multiple samplings from the same population. Methodologists have suggested that the validity of clustering methods should be based on classifications that yield reproducible findings beyond chance levels. We used this approach to determine the performance of commonly used clustering algorithms and the degree of replicability achieved using several microarray datasets.

Methods

We considered four commonly used iterative partitioning algorithms (Self Organizing Maps (SOM), K-means, Clutsering LARge Applications (CLARA), and Fuzzy C-means) and evaluated their performances on 37 microarray datasets, with sample sizes ranging from 12 to 172. We assessed reproducibility of the clustering algorithm by measuring the strength of relationship between clustering outputs of subsamples of 37 datasets. Cluster stability was quantified using Cramer's v ² from a kXk table. Cramer's v ² is equivalent to the squared canonical correlation coefficient between two sets of nominal variables. Potential scores range from 0 to 1, with 1 denoting perfect reproducibility.

Results

All four clustering routines show increased stability with larger sample sizes. K-means and SOM showed a gradual increase in stability with increasing sample size. CLARA and Fuzzy C-means, however, yielded low stability scores until sample sizes approached 30 and then gradually increased thereafter. Average stability never exceeded 0.55 for the four clustering routines, even at a sample size of 50. These findings suggest several plausible scenarios: (1) microarray datasets lack natural clustering structure thereby producing low stability scores on all four methods; (2) the algorithms studied do not produce reliable results and/or (3) sample sizes typically used in microarray research may be too small to support derivation of reliable clustering results. Further research should be directed towards evaluating stability performances of more clustering algorithms on more datasets specially having larger sample sizes with larger numbers of clusters considered.

     

Consensus framework for exploring microarray data using multiple clustering methods

The large variety of clustering algorithms and their variants can be daunting to researchers wishing to explore patterns within their microarray datasets. Furthermore, each clustering method has distinct biases in finding patterns within the data, and clusterings may not be reproducible across different algorithms. A consensus approach utilizing multiple algorithms can show where the various methods agree and expose robust patterns within the data. In this paper, we present a software package - Consense, written for R/Bioconductor - that utilizes such an approach to explore microarray datasets. Consense produces clustering results for each of the clustering methods and produces a report of metrics comparing the individual clusterings. A feature of Consense is identification of genes that cluster consistently with an index gene across methods. Utilizing simulated microarray data, sensitivity of the metrics to the biases of the different clustering algorithms is explored. The framework is easily extensible, allowing this tool to be used by other functional genomic data types, as well as other high-throughput OMICS data types generated from metabolomic and proteomic experiments. It also provides a flexible environment to benchmark new clustering algorithms. Consense is currently available as an installable R/Bioconductor package (http://www.ohsucancer.com/isrdev/consense/).     

Performance comparison of gene family clustering methods with expert curated gene family data set in <Emphasis Type="Italic">Arabidopsis thaliana</Emphasis>

With the exponential growth of genomics data, the demand for reliable clustering methods is increasing every day. Despite the wide usage of many clustering algorithms, the accuracy of these algorithms has been evaluated mostly on simulated data sets and seldom on real biological data for which a "correct answer" is available. In order to address this issue, we use the manually curated high-quality Arabidopsis thaliana gene family database as a "gold standard" to conduct a comprehensive comparison of the accuracies of four widely used clustering methods including K-means, TribeMCL, single-linkage clustering and complete-linkage clustering. We compare the results from running different clustering methods on two matrices: the E-value matrix and the k-tuple distance matrix. The E-value matrix is computed based on BLAST E-values. The k-tuple distance matrix is computed based on the difference in tuple frequencies. The TribeMCL with the E-value matrix performed best, with the Inflation parameter (=1.15) tuned considerably lower than what has been suggested previously (=2). The single-linkage clustering method with the E-value matrix was second best. Single-linkage clustering, K-means clustering, complete-linkage clustering, and TribeMCL with a k-tuple distance matrix performed reasonably well. Complete-linkage clustering with the k-tuple distance matrix performed the worst.     

Ant clustering with locally weighted ant perception and diversified memory

Ant clustering algorithms are a robust and flexible tool for clustering data that have produced some promising results. This paper introduces two improvements that can be incorporated into any ant clustering algorithm: kernel function similarity weights and a similarity memory model replacement scheme. A kernel function weights objects within an ant’s neighborhood according to the object distance and provides an alternate interpretation of the similarity of objects in an ant’s neighborhood. Ants can hill-climb the kernel gradients as they look for a suitable place to drop a carried object. The similarity memory model equips ants with a small memory consisting of a sampling of the current clustering space. We test several kernel functions and memory replacement schemes on the Iris, Wisconsin Breast Cancer, and Lincoln Lab network intrusion datasets. Compared to a basic ant clustering algorithm, we show that kernel functions and the similarity memory model increase clustering speed and cluster quality, especially for datasets with an unbalanced class distribution, such as network intrusion.