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.     

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/     

Evaluation and optimization of clustering in gene expression data analysis

MOTIVATION: A measurement of cluster quality is needed to choose potential clusters of genes that contain biologically relevant patterns of gene expression. This is strongly desirable when a large number of gene expression profiles have to be analyzed and proper clusters of genes need to be identified for further analysis, such as the search for meaningful patterns, identification of gene functions or gene response analysis. RESULTS: We propose a new cluster quality method, called stability, by which unsupervised learning of gene expression data can be performed efficiently. The method takes into account a cluster's stability on partition. We evaluate this method and demonstrate its performance using four independent, real gene expression and three simulated datasets. We demonstrate that our method outperforms other techniques listed in the literature. The method has applications in evaluating clustering validity as well as identifying stable clusters. AVAILABILITY: Please contact the first author.     

Validating clustering for gene expression data

MOTIVATION: Many clustering algorithms have been proposed for the analysis of gene expression data, but little guidance is available to help choose among them. We provide a systematic framework for assessing the results of clustering algorithms. Clustering algorithms attempt to partition the genes into groups exhibiting similar patterns of variation in expression level. Our methodology is to apply a clustering algorithm to the data from all but one experimental condition. The remaining condition is used to assess the predictive power of the resulting clusters-meaningful clusters should exhibit less variation in the remaining condition than clusters formed by chance. RESULTS: We successfully applied our methodology to compare six clustering algorithms on four gene expression data sets. We found our quantitative measures of cluster quality to be positively correlated with external standards of cluster quality.     

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     

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.     

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.     

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.     

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.     

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.     

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.     

Coupled two-way clustering analysis of breast cancer and colon cancer gene expression data

We present and review coupled two-way clustering, a method designed to mine gene expression data. The method identifies submatrices of the total expression matrix, whose clustering analysis reveals partitions of samples (and genes) into biologically relevant classes. We demonstrate, on data from colon and breast cancer, that we are able to identify partitions that elude standard clustering analysis. AVAILABILITY: Free, at http://ctwc.weizmann.ac.il.. SUPPLEMENTARY INFORMATION: http://www.weizmann.ac.il/physics/complex/compphys/bioinfo2/     

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.     

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.     

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.     

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.