An improved algorithm for clustering gene expression data

MOTIVATION: Recent advancements in microarray technology allows simultaneous monitoring of the expression levels of a large number of genes over different time points. Clustering is an important tool for analyzing such microarray data, typical properties of which are its inherent uncertainty, noise and imprecision. In this article, a two-stage clustering algorithm, which employs a recently proposed variable string length genetic scheme and a multiobjective genetic clustering algorithm, is proposed. It is based on the novel concept of points having significant membership to multiple classes. An iterated version of the well-known Fuzzy C-Means is also utilized for clustering. RESULTS: The significant superiority of the proposed two-stage clustering algorithm as compared to the average linkage method, Self Organizing Map (SOM) and a recently developed weighted Chinese restaurant-based clustering method (CRC), widely used methods for clustering gene expression data, is established on a variety of artificial and publicly available real life data sets. The biological relevance of the clustering solutions are also analyzed.     

Principal component analysis for clustering gene expression data

MOTIVATION: There is a great need to develop analytical methodology to analyze and to exploit the information contained in gene expression data. Because of the large number of genes and the complexity of biological networks, clustering is a useful exploratory technique for analysis of gene expression data. Other classical techniques, such as principal component analysis (PCA), have also been applied to analyze gene expression data. Using different data analysis techniques and different clustering algorithms to analyze the same data set can lead to very different conclusions. Our goal is to study the effectiveness of principal components (PCs) in capturing cluster structure. Specifically, using both real and synthetic gene expression data sets, we compared the quality of clusters obtained from the original data to the quality of clusters obtained after projecting onto subsets of the principal component axes. RESULTS: Our empirical study showed that clustering with the PCs instead of the original variables does not necessarily improve, and often degrades, cluster quality. In particular, the first few PCs (which contain most of the variation in the data) do not necessarily capture most of the cluster structure. We also showed that clustering with PCs has different impact on different algorithms and different similarity metrics. Overall, we would not recommend PCA before clustering except in special circumstances.     

Dynamic model-based clustering for time-course gene expression data

Microarray technology has produced a huge body of time-course gene expression data. Such gene expression data has proved useful in genomic disease diagnosis and genomic drug design. The challenge is how to uncover useful information in such data. Cluster analysis has played an important role in analyzing gene expression data. Many distance/correlation- and static model-based clustering techniques have been applied to time-course expression data. However, these techniques are unable to account for the dynamics of such data. It is the dynamics that characterize the data and that should be considered in cluster analysis so as to obtain high quality clustering. This paper proposes a dynamic model-based clustering method for time-course gene expression data. The proposed method regards a time-course gene expression dataset as a set of time series, generated by a number of stochastic processes. Each stochastic process defines a cluster and is described by an autoregressive model. A relocation-iteration algorithm is proposed to identity the model parameters and posterior probabilities are employed to assign each gene to an appropriate cluster. A bootstrapping method and an average adjusted Rand index (AARI) are employed to measure the quality of clustering. Computational experiments are performed on a synthetic and three real time-course gene expression datasets to investigate the proposed method. The results show that our method allows the better quality clustering than other clustering methods (e.g. k-means) for time-course gene expression data, and thus it is a useful and powerful tool for analyzing time-course gene expression data.     

Model-based clustering and data transformations for gene expression data.

MOTIVATION: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a 'good' clustering method and determining the 'correct' number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications. RESULTS: We benchmarked the performance of model-based clustering on several synthetic and real gene expression data sets for which external evaluation criteria were available. The model-based approach has superior performance on our synthetic data sets, consistently selecting the correct model and the number of clusters. On real expression data, the model-based approach produced clusters of quality comparable to a leading heuristic clustering algorithm, but with the key advantage of suggesting the number of clusters and an appropriate model. We also explored the validity of the Gaussian mixture assumption on different transformations of real data. We also assessed the degree to which these real gene expression data sets fit multivariate Gaussian distributions both before and after subjecting them to commonly used data transformations. Suitably chosen transformations seem to result in reasonable fits. AVAILABILITY: MCLUST is available at http://www.stat.washington.edu/fraley/mclust. The software for the diagonal model is under development. CONTACT: kayee@cs.washington.edu. SUPPLEMENTARY INFORMATION: http://www.cs.washington.edu/homes/kayee/model.     

Gene-Ontology-based clustering of gene expression data

The expected correlation between genetic co-regulation and affiliation to a common biological process is not necessarily the case when numerical cluster algorithms are applied to gene expression data. GO-Cluster uses the tree structure of the Gene Ontology database as a framework for numerical clustering, and thus allowing a simple visualization of gene expression data at various levels of the ontology tree. AVAILABILITY: The 32-bit Windows application is freely available at http://www.mpibpc.mpg.de/go-cluster/     

Statistical inference for simultaneous clustering of gene expression data

Current methods for analysis of gene expression data are mostly based on clustering and classification of either genes or samples. We offer support for the idea that more complex patterns can be identified in the data if genes and samples are considered simultaneously. We formalize the approach and propose a statistical framework for two-way clustering. A simultaneous clustering parameter is defined as a function theta=Phi(P) of the true data generating distribution P, and an estimate is obtained by applying this function to the empirical distribution P(n). We illustrate that a wide range of clustering procedures, including generalized hierarchical methods, can be defined as parameters which are compositions of individual mappings for clustering patients and genes. This framework allows one to assess classical properties of clustering methods, such as consistency, and to formally study statistical inference regarding the clustering parameter. We present results of simulations designed to assess the asymptotic validity of different bootstrap methods for estimating the distribution of Phi(P(n)). The method is illustrated on a publicly available data set.     

Modes and clustering for time-warped gene expression profile data

MOTIVATION: The study of the dynamics of regulatory processes has led to increased interest for the analysis of temporal gene expression level data. To address the dynamics of regulation, expression data are collected repeatedly over time. It is difficult to statistically represent the resulting high-dimensional data. When regulatory processes determine gene expression, time-warping is likely to be present, i.e. the sample of gene expression trajectories reflects variation not only in terms of the expression amplitudes, but also in terms of the temporal structure of gene expression. RESULTS: A non-parametric time-synchronized iterative mean updating technique is proposed to find an overall representation that corresponds to a mode of a sample of expression profiles, viewed as a random sample in function space. The proposed algorithm explores the application of previous work of Hall and Heckman to genome-wide expression data and provides an extension that includes random time-warping with the aim to synchronize timescales across genes. The proposed algorithm is universally applicable for the construction of modes for functional data with time-warping. We demonstrate the construction of mode functions for a sample of Drosophila gene expression data. The algorithm can be applied to define clusters among the observed trajectories of gene expression, without any kind of prior non-time-warped clustering, as illustrated in the numerical example.     

Comparisons of graph-structure clustering methods for gene expression data

Although many numerical clustering algorithms have been applied to gene expression dataanalysis,the essential step is still biological interpretation by manual inspection.The correlation betweengenetic co-regulation and affiliation to a common biological process is what biologists expect.Here,weintroduce some clustering algorithms that are based on graph structure constituted by biological knowledge.After applying a widely used dataset,we compared the result clusters of two of these algorithms in terms ofthe homogeneity of clusters and coherence of annotation and matching ratio.The results show that theclusters of knowledge-guided analysis are the kernel parts of the clusters of Gene Ontology (GO)-Clustersoftware,which contains the genes that are most expression correlative and most consistent with biologicalfunctions.Moreover,knowledge-guided analysis seems much more applicable than GO-Cluster in a largerdataset.     

K-ary clustering with optimal leaf ordering for gene expression data

MOTIVATION: A major challenge in gene expression analysis is effective data organization and visualization. One of the most popular tools for this task is hierarchical clustering. Hierarchical clustering allows a user to view relationships in scales ranging from single genes to large sets of genes, while at the same time providing a global view of the expression data. However, hierarchical clustering is very sensitive to noise, it usually lacks of a method to actually identify distinct clusters, and produces a large number of possible leaf orderings of the hierarchical clustering tree. In this paper we propose a new hierarchical clustering algorithm which reduces susceptibility to noise, permits up to k siblings to be directly related, and provides a single optimal order for the resulting tree. RESULTS: We present an algorithm that efficiently constructs a k-ary tree, where each node can have up to k children, and then optimally orders the leaves of that tree. By combining k clusters at each step our algorithm becomes more robust against noise and missing values. By optimally ordering the leaves of the resulting tree we maintain the pairwise relationships that appear in the original method, without sacrificing the robustness. Our k-ary construction algorithm runs in O(n(3)) regardless of k and our ordering algorithm runs in O(4(k)n(3)). We present several examples that show that our k-ary clustering algorithm achieves results that are superior to the binary tree results in both global presentation and cluster identification. AVAILABILITY: We have implemented the above algorithms in C++ on the Linux operating system.     

A data-driven clustering method for time course gene expression data

Gene expression over time is, biologically, a continuous process and can thus be represented by a continuous function, i.e. a curve. Individual genes often share similar expression patterns (functional forms). However, the shape of each function, the number of such functions, and the genes that share similar functional forms are typically unknown. Here we introduce an approach that allows direct discovery of related patterns of gene expression and their underlying functions (curves) from data without a priori specification of either cluster number or functional form. Smoothing spline clustering (SSC) models natural properties of gene expression over time, taking into account natural differences in gene expression within a cluster of similarly expressed genes, the effects of experimental measurement error, and missing data. Furthermore, SSC provides a visual summary of each cluster's gene expression function and goodness-of-fit by way of a 'mean curve' construct and its associated confidence bands. We apply this method to gene expression data over the life-cycle of Drosophila melanogaster and Caenorhabditis elegans to discover 17 and 16 unique patterns of gene expression in each species, respectively. New and previously described expression patterns in both species are discovered, the majority of which are biologically meaningful and exhibit statistically significant gene function enrichment. Software and source code implementing the algorithm, SSClust, is freely available (http://genemerge.bioteam.net/SSClust.html).     

GenClust: A genetic algorithm for clustering gene expression data

Background  

Clustering is a key step in the analysis of gene expression data, and in fact, many classical clustering algorithms are used, or more innovative ones have been designed and validated for the task. Despite the widespread use of artificial intelligence techniques in bioinformatics and, more generally, data analysis, there are very few clustering algorithms based on the genetic paradigm, yet that paradigm has great potential in finding good heuristic solutions to a difficult optimization problem such as clustering.     

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.     

Genetic algorithms applied to multi-class clustering for gene expression data

A hybrid GA (genetic algorithm)-based clustering (HGACLUS) schema, combining merits of the Simulated Annealing, was described for finding an optimal or near-optimal set of medoids. This schema maximized the clustering success by achieving internal cluster cohesion and external cluster isolation. The performance     

Noise-robust soft clustering of gene expression time-course data

Clustering is an important tool in microarray data analysis. This unsupervised learning technique is commonly used to reveal structures hidden in large gene expression data sets. The vast majority of clustering algorithms applied so far produce hard partitions of the data, i.e. each gene is assigned exactly to one cluster. Hard clustering is favourable if clusters are well separated. However, this is generally not the case for microarray time-course data, where gene clusters frequently overlap. Additionally, hard clustering algorithms are often highly sensitive to noise. To overcome the limitations of hard clustering, we applied soft clustering which offers several advantages for researchers. First, it generates accessible internal cluster structures, i.e. it indicates how well corresponding clusters represent genes. This can be used for the more targeted search for regulatory elements. Second, the overall relation between clusters, and thus a global clustering structure, can be defined. Additionally, soft clustering is more noise robust and a priori pre-filtering of genes can be avoided. This prevents the exclusion of biologically relevant genes from the data analysis. Soft clustering was implemented here using the fuzzy c-means algorithm. Procedures to find optimal clustering parameters were developed. A software package for soft clustering has been developed based on the open-source statistical language R. The package called Mfuzz is freely available.     

Kernel hierarchical gene clustering from microarray expression data

MOTIVATION: Unsupervised analysis of microarray gene expression data attempts to find biologically significant patterns within a given collection of expression measurements. For example, hierarchical clustering can be applied to expression profiles of genes across multiple experiments, identifying groups of genes that share similar expression profiles. Previous work using the support vector machine supervised learning algorithm with microarray data suggests that higher-order features, such as pairwise and tertiary correlations across multiple experiments, may provide significant benefit in learning to recognize classes of co-expressed genes. RESULTS: We describe a generalization of the hierarchical clustering algorithm that efficiently incorporates these higher-order features by using a kernel function to map the data into a high-dimensional feature space. We then evaluate the utility of the kernel hierarchical clustering algorithm using both internal and external validation. The experiments demonstrate that the kernel representation itself is insufficient to provide improved clustering performance. We conclude that mapping gene expression data into a high-dimensional feature space is only a good idea when combined with a learning algorithm, such as the support vector machine that does not suffer from the curse of dimensionality. AVAILABILITY: Supplementary data at www.cs.columbia.edu/compbio/hiclust. Software source code available by request.     

Computing gene expression data with a knowledge-based gene clustering approach

Computational analysis methods for gene expression data gathered in microarray experiments can be used to identify the functions of previously unstudied genes. While obtaining the expression data is not a difficult task, interpreting and extracting the information from the datasets is challenging. In this study, a knowledge-based approach which identifies and saves important functional genes before filtering based on variability and fold change differences was utilized to study light regulation. Two clustering methods were used to cluster the filtered datasets, and clusters containing a key light regulatory gene were located. The common genes to both of these clusters were identified, and the genes in the common cluster were ranked based on their coexpression to the key gene. This process was repeated for 11 key genes in 3 treatment combinations. The initial filtering method reduced the dataset size from 22,814 probes to an average of 1134 genes, and the resulting common cluster lists contained an average of only 14 genes. These common cluster lists scored higher gene enrichment scores than two individual clustering methods. In addition, the filtering method increased the proportion of light responsive genes in the dataset from 1.8% to 15.2%, and the cluster lists increased this proportion to 18.4%. The relatively short length of these common cluster lists compared to gene groups generated through typical clustering methods or coexpression networks narrows the search for novel functional genes while increasing the likelihood that they are biologically relevant.