Including probe-level uncertainty in model-based gene expression clustering.

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. 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. 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

Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful approaches in cluster analysis. The mixture density estimation is generally performed by maximizing the observed-data log-likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the EM algorithm initialization is crucial. In addition, the standard EM algorithm requires the number of clusters to be known a priori. Some solutions have been provided in [31], [12] for model-based clustering with Gaussian mixture models for multivariate data. In this paper we focus on model-based curve clustering approaches, when the data are curves rather than vectorial data, based on regression mixtures. We propose a new robust EM algorithm for clustering curves. We extend the model-based clustering approach presented in [31] for Gaussian mixture models, to the case of curve clustering by regression mixtures, including polynomial regression mixtures as well as spline or B-spline regressions mixtures. Our approach both handles the problem of initialization and the one of choosing the optimal number of clusters as the EM learning proceeds, rather than in a twofold scheme. This is achieved by optimizing a penalized log-likelihood criterion. A simulation study confirms the potential benefit of the proposed algorithm in terms of robustness regarding initialization and funding the actual number of clusters.

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. 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. MCLUST is available at http://www.stat.washington.edu/fraley/mclust. The software for the diagonal model is under development. kayee@cs.washington.edu. http://www.cs.washington.edu/homes/kayee/model.

Clustering is one of the most important techniques, which group genes of similar expression pattern into a small number of meaningful homogeneous groups or clusters. Gene expression data has certain special characteristics and is a challenging research problem. There are many applications for clustering gene expression data. Clustering can be applied for genes called gene clustering. Hard clustering allows a gene to get placed in exactly one cluster and converges in local optima. Soft clustering approach allows gene to get placed in all the clusters with some membership values. As the hard clustering approach converges in local optimum, an evolutionary computation technique like swarm clustering is required to find the global optimum solution. This chapter studies swarm clustering techniques such as Particle Swarm Clustering K-Means, Cuckoo Search Clustering, Cuckoo Search Clustering with levy flight, harmony search, Fuzzy PSO and Ant Colony Optimization based Clustering for clustering gene expression data. Evaluation measures for clustering gene expression data are also discussed.

Model-based clustering is a popular approach for clustering multivariate data which has seen applications in numerous fields. Nowadays, high-dimensional data are more and more common and the model-based clustering approach has adapted to deal with the increasing dimensionality. In particular, the development of variable selection techniques has received a lot of attention and research effort in recent years. Even for small size problems, variable selection has been advocated to facilitate the interpretation of the clustering results. This review provides a summary of the methods developed for variable selection in model-based clustering. Existing R packages implementing the different methods are indicated and illustrated in application to two data analysis examples.

Clustering gene expression data are an important problem in bioinformatics because understanding which genes behave similarly can lead to the discovery of important biological information. Many clustering methods have been used in the field of gene clustering. This paper proposed a new method for gene expression data clustering based on an improved expectation maximization(EM) method of multivariate Gaussian mixture models. To solve the problem of over-reliance on the initialization, we propose a remove and add initialization for the classical EM, and make a random perturbation on the solution before continuing EM iterations. The number of clusters is estimated with the Quasi Akaike’s information criterion in this paper. The improved EM method is tested and compared with some other clustering methods; the performance of our clustering algorithm has been extensively compared over several simulated and real gene expression data sets. Our results indicated that improved EM clustering method is superior than other clustering algorithms and can be widely used for gene clustering.

DNA microarray technology monitors gene activity in real-time in living organisms. It creates a large amount of data that helps scientists learn about how genes work. Clustering this data helps understand gene interactions and uncover important biological processes. However, the traditional clustering techniques have difficulties due to the enormous dimensionality of gene expression data and the intricacy of biological networks. Although ensemble clustering is a viable strategy, such high-dimensional data may not lend itself well to traditional approaches. This study introduces a novel technique for gene expression data clustering called incremental ensemble clustering for gene expression data (IECG). There are two steps in the IECG. A technique for grouping gene expression data into windows is presented in the first step, producing a tree of clusters. This procedure is carried out again for succeeding windows that have distinct feature sets. The base clusterings of two consecutive windows are ensembled using a new goal function to form a new clustering solution. By repeating this step-by-step method for further windows, reliable patterns that are beneficial for medical applications can be extracted. The results from both biological and non-biological data demonstrate that the proposed algorithm outperformed the state-of-the-art algorithms. Additionally, the running time of the proposed algorithm has been examined.

Based on the previously proposed Quantum-behaved Particle Swarm Optimization (QPSO) algorithm, in this paper, we focus on the application of QPSO in gene expression data clustering which can be reduced to an optimization problem. The proposed clustering algorithm partitions the N patterns of the gene expression dataset into user-defined K categories to minimize the fitness function of Total Within-Cluster Variation. Thus a partition with high performance is obtained. The experiment results on four gene expression data sets show that our QPSO-based clustering algorithm will be an effective and promising tool for gene expression data analysis.

Massive amounts of gene expression data are generated using microarrays for functional studies of genes and gene expression data clustering is a useful tool for studying the functional relationship among genes in a biological process. We have developed a computer package EXCAVATOR for clustering gene expression profiles based on our new framework for representing gene expression data as a minimum spanning tree. EXCAVATOR uses a number of rigorous and efficient clustering algorithms. This program has a number of unique features, including capabilities for: (i) data- constrained clustering; (ii) identification of genes with similar expression profiles to pre-specified seed genes; (iii) cluster identification from a noisy background; (iv) computational comparison between different clustering results of the same data set. EXCAVATOR can be run from a Unix/Linux/DOS shell, from a Java interface or from a Web server. The clustering results can be visualized as colored figures and 2-dimensional plots. Moreover, EXCAVATOR provides a wide range of options for data formats, distance measures, objective functions, clustering algorithms, methods to choose number of clusters, etc. The effectiveness of EXCAVATOR has been demonstrated on several experimental data sets. Its performance compares favorably against the popular K-means clustering method in terms of clustering quality and computing time.

Support Vector Domain Description (SVDD) is a kind of classification method based on Support Vector Machine. This paper discussed its application in gene expression data clustering. The training samples are mapped into a high dimension feature space through kernel function, at the same time, the non- objective samples are introduced in training to increase the refusing ability. After obtaining the support vectors to form the initial boundary by setting the kernel's parameter, the boundary energy function is constructed, so the real classified boundary can be approximated through finding the minimum energy function. The experimental results in Yeast Cell gene expression data show it could obtain a tighter hyper sphere and better clustering.

An often overlooked pitfall of model-based clustering is that it typically results in the same number of clusters per margin, an assumption that may not be natural in practice. We develop a clustering method that takes advantage of the sturdiness of model-based clustering, while attempting to mitigate this issue. The proposed approach allows each margin to have a varying number of clusters and employs a strategy game-inspired algorithm, named ‘Reign-and-Conquer’, to cluster the data. Since the proposed clustering approach only specifies a model for the margins, but leaves the joint unspecified, it has the advantage of being partially parallelizable; hence, the proposed approach is computationally appealing as well as more tractable for moderate to high dimensions than a ‘full’ (joint) model-based clustering approach. A battery of numerical experiments on simulated data indicates an overall good performance of the proposed methods in a variety of scenarios, and real datasets are used to showcase their usefulness in practice.

We present the use of KICA to perform clustering of gene expression data. Comparison experiments between KICA and two other methods, PCA and ICA, are performed. Three clustering algorithms, including weighted graph partitioning, k-means and agglomerative hierarchical clustering, and two similarity measures, including Euclidean and Pearson correlation, are also evaluated. The results indicate that KICA is an efficient feature extraction approach for gene expression data clustering. Our empirical study showed that clustering with the components instead of the original variables does improve cluster quality. In particular, the first few components by KICA capture most of the cluster structure. We also showed that clustering with components has different impact on different algorithms and different similarity metrics. Overall, we would recommend KICA before clustering gene expression data.

The combined interpretation of gene expression data and gene sequences offers a valuable approach to investigate the intricate relationships involving gene transcriptional regulation. The highly interactive expression data produced by microarray hybridization experiments allow us to find the clusters of coexpressed genes. By analyzing the upstream regions of the identified coexpressed genes, we can discover the regulatory patterns characterized by transcription factor binding sites, which govern the process of transcriptional regulation. This paper presents a generic clustering algorithm that uses a Hybrid GA approach to discover clusters in gene expression data. The advantage of this method is that large search space can be effectively explored by utilizing the evolutionary algorithm techniques. Moreover, it is able to discover underlying patterns in noisy gene expression data for meaningful data groupings, and also statistically significant patterns hidden in each cluster can be extracted at the same time. Since the proposed method can handle both continuous-and discrete-valued data, it can be used with different microarray and biomedical data. To test its effectiveness, we have used it on real expression data. The experimental results reveal meaningful groupings and uncover many known transcription factor binding sites.

The real-time system of the JT-60 has a cascade structure with the major and the minor control loops. The multi-variable feedback control is adopted in the major control loop in order to adjust non-linear effects which will appear in the high-/beta/region. By applying the concept of 'phase shift control' to the control program of the major control loop, a flexible tokamak discharge control is expected to be performed with taking account of machine protection.

The increasing application of microarray technology is generating large amounts of high dimensional gene expression data. Genes participating in the same biological process tend to have similar expression patterns, and clustering is one of the most useful and efficient methods for identifying these patterns. Due to the complexity of microarray profiles, there are some limitations in directly applying traditional clustering techniques to the microarray data. Recently, researchers have proposed clustering algorithms custom tailored to overcome their limitations for microarray analysis. In this chapter, we first introduce the microarray technique. Next, we review seven representative clustering algorithms: K-means, quality-based clustering, hierarchical agglomerative clustering, self-organizing neural network-based clustering, graph-theory-based clustering, model-based clustering, and subspace clustering. All these algorithms have shown their applicability to the microarray profiles.We also survey several criteria for evaluating clustering results. Biology plays an important role in the evaluation of clustering results. We discuss possible research directions to equip clustering techniques with underlying biological interpretations for better microarray profile analysis.