Analysis of a Gibbs sampler method for model-based clustering of gene expression data

BackgroundClustering is an important analysis performed on microarray gene expression data since it groups genes which have similar expression patterns and enables the exploration of unknown gene functions. Microarray experiments are associated with many sources of experimental and biological variation and the resulting gene expression data are therefore very noisy. Many heuristic and model-based clustering approaches have been developed to cluster this noisy data. However, few of them include consideration of probe-level measurement error which provides rich information about technical variability.ResultsWe augment a standard model-based clustering method to incorporate probe-level measurement error. Using probe-level measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we include the probe-level measurement error directly into the standard Gaussian mixture model. Our augmented model is shown to provide improved clustering performance on simulated datasets and a real mouse time-course dataset.ConclusionThe performance of model-based clustering of gene expression data is improved by including probe-level measurement error and more biologically meaningful clustering results are obtained.

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 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.

Clustering of gene expression data simplifies subsequent data analyses and forms the basis of numerous approaches for biomarker identification, prediction of clinical outcome, and personalized therapeutic strategies. The most popular clustering methods such as K-means and hierarchical clustering are intuitive and easy to use, but they require arbitrary choices on their various parameters (number of clusters for K-means, and a threshold to cut the tree for hierarchical clustering). Human disease gene expression data are in general more difficult to cluster efficiently due to background (genotype) heterogeneity, disease stage and progression differences and disease subtyping; all of which cause gene expression datasets to be more heterogeneous. Spectral clustering has been recently introduced in many fields as a promising alternative to standard clustering methods. The idea is that pairwise comparisons can help reveal global features through the eigen techniques. In this paper, we developed a new recursive K-means spectral clustering method (ReKS) for disease gene expression data. We benchmarked ReKS on three large-scale cancer datasets and we compared it to different clustering methods with respect to execution time, background models and external biological knowledge. We found ReKS to be superior to the hierarchical methods and equally good to K-means, but much faster than them and without the requirement for a priori knowledge of K. Overall, ReKS offers an attractive alternative for efficient clustering of human disease data.

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.

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.

Motivation: Gene set enrichment has become a critical tool for interpreting the results of high-throughput genomic experiments. Inconsistent annotation quality and lack of annotation specificity, however, limit the statistical power of enrichment methods and make it difficult to replicate enrichment results across biologically similar datasets.Results: We propose a novel algorithm for optimizing gene set annotations to best match the structure of specific empirical data sources. Our proposed method, entropy minimization over variable clusters (EMVC), filters the annotations for each gene set to minimize a measure of entropy across disjoint gene clusters computed for a range of cluster sizes over multiple bootstrap resampled datasets. As shown using simulated gene sets with simulated data and Molecular Signatures Database collections with microarray gene expression data, the EMVC algorithm accurately filters annotations unrelated to the experimental outcome resulting in increased gene set enrichment power and better replication of enrichment results.Availability and implementation:http://cran.r-project.org/web/packages/EMVC/index.html.Contact:jason.h.moore@dartmouth.eduSupplementary information:Supplementary data are available at Bioinformatics online.

Motivation: The results of initial analyses for many high-throughput technologies commonly take the form of gene or protein sets, and one of the ensuing tasks is to evaluate the functional coherence of these sets. The study of gene set function most commonly makes use of controlled vocabulary in the form of ontology annotations. For a given gene set, the statistical significance of observing these annotations or ‘enrichment’ may be tested using a number of methods. Instead of testing for significance of individual terms, this study is concerned with the task of assessing the global functional coherence of gene sets, for which novel metrics and statistical methods have been devised.Results: The metrics of this study are based on the topological properties of graphs comprised of genes and their Gene Ontology annotations. A novel aspect of these methods is that both the enrichment of annotations and the relationships among annotations are considered when determining the significance of functional coherence. We applied our methods to perform analyses on an existing database and on microarray experimental results. Here, we demonstrated that our approach is highly discriminative in terms of differentiating coherent gene sets from random ones and that it provides biologically sensible evaluations in microarray analysis. We further used examples to show the utility of graph visualization as a tool for studying the functional coherence of gene sets.Availability: The implementation is provided as a freely accessible web application at: http://projects.dbbe.musc.edu/gosteiner. Additionally, the source code written in the Python programming language, is available under the General Public License of the Free Software Foundation.Contact: lux@musc.eduSupplementary information: Supplementary data are available at Bioinformatics online.

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.

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.

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.

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.

Breast cancer is classified into five intrinsic subtypes, with differing treatment methods and prognoses. Therefore, accurate identification of subtypes from patient transcriptome data is essential. Many gene signatures, including PAM50, have been developed to classify breast cancer subtypes. However, existing gene selection methods do not utilize biological pathways. Gene signature selection using biological pathways can explain signature genes in terms of biological functions. Thus, we propose a probabilistic model for pathway-guided gene set selection using gene expression data. First, we defined gene and pathway factors based on gene expression and pathway activation levels, and calculated the posterior probability. Second, we adopted the prediction strength to guide gene set selection. Third, the gene set was selected using the posterior probability and prediction strength values. Finally, on evaluating the selected gene set, it was experimentally confirmed that our gene set performed better on classification tasks than the PAM50 gene set, a gene set produced by the XGBoost classifier, and a random gene set. Among the genes selected by our method, it was confirmed that the genes included in the cell cycle and circadian rhythm pathways showed different expression patterns for each breast cancer subtype. Our selected gene set exhibited biological significance in terms of pathway activation.