Hierarchical Dirichlet process model for gene expression clustering

Clustering is an important data processing tool for interpreting microarray data and genomic network inference. In this article, we propose a clustering algorithm based on the hierarchical Dirichlet processes (HDP). The HDP clustering introduces a hierarchical structure in the statistical model which captures the hierarchical features prevalent in biological data such as the gene express data. We develop a Gibbs sampling algorithm based on the Chinese restaurant metaphor for the HDP clustering. We apply the proposed HDP algorithm to both regulatory network segmentation and gene expression clustering. The HDP algorithm is shown to outperform several popular clustering algorithms by revealing the underlying hierarchical structure of the data. For the yeast cell cycle data, we compare the HDP result to the standard result and show that the HDP algorithm provides more information and reduces the unnecessary clustering fragments.     

Integrated analysis of multiple data sources reveals modular structure of biological networks

It has been a challenging task to integrate high-throughput data into investigations of the systematic and dynamic organization of biological networks. Here, we presented a simple hierarchical clustering algorithm that goes a long way to achieve this aim. Our method effectively reveals the modular structure of the yeast protein-protein interaction network and distinguishes protein complexes from functional modules by integrating high-throughput protein-protein interaction data with the added subcellular localization and expression profile data. Furthermore, we take advantage of the detected modules to provide a reliably functional context for the uncharacterized components within modules. On the other hand, the integration of various protein-protein association information makes our method robust to false-positives, especially for derived protein complexes. More importantly, this simple method can be extended naturally to other types of data fusion and provides a framework for the study of more comprehensive properties of the biological network and other forms of complex networks.     

Revisiting the variation of clustering coefficient of biological networks suggests new modular structure

ABSTRACT: A central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling). Although several studies have suggested other possible origins of this signature, it is still widely used nowadays to identify hierarchical modularity, especially in the analysis of biological networks. Therefore, a further and systematical investigation of this signature for different types of biological networks is necessary. RESULTS: We analyzed a variety of biological networks and found that the commonly used signature of hierarchical modularity is actually the reflection of spoke-like topology, suggesting a different view of network architecture. We proved that the existence of super-hubs is the origin that the clustering coefficient of a node follows a particular scaling law with degree k in metabolic networks. To study the modularity of biological networks, we systematically investigated the relationship between repulsion of hubs and variation of clustering coefficient. We provided direct evidences for repulsion between hubs being the underlying origin of the variation of clustering coefficient, and found that for biological networks having no anti-correlation between hubs, such as gene co-expression network, the clustering coefficient doesn't show dependence of degree. CONCLUSIONS: Here we have shown that the variation of clustering coefficient is neither sufficient nor exclusive for a network to be hierarchical. Our results suggest the existence of spoke-like modules as opposed to "deterministic model" of hierarchical modularity, and suggest the need to reconsider the organizational principle of biological hierarchy.     

与实验条件相关的基因功能模块聚类分析方法

针对细胞内基因功能模块化的现象,定义了“基因功能模块”和“特征功能模块”两个概念,并基于这两个概念提出一种“与实验条件相关的基因功能模块聚类算法”。该算法综合利用基因功能知识与基因表达谱信息,将基因聚类为与实验条件相关的基因功能模块。向基因表达谱中加入水平逐渐升高的数据噪音,根据基因功能模块对数据噪音的抵抗力,确定最稳定的基因功能模块,即特征功能模块。加噪音实验显示,在基因芯片技术可能发生的噪音范围内,该算法对噪音的稳健性优于层次聚类和模糊C均值聚类。将模块聚类算法应用在NCI60数据集上,发现了8个与实验条件高度相关的特征功能模块。     

A dynamically growing self-organizing tree (DGSOT) for hierarchical clustering gene expression profiles

MOTIVATION: The increasing use of microarray technologies is generating large amounts of data that must be processed in order to extract useful and rational fundamental patterns of gene expression. Hierarchical clustering technology is one method used to analyze gene expression data, but traditional hierarchical clustering algorithms suffer from several drawbacks (e.g. fixed topology structure; mis-clustered data which cannot be reevaluated). In this paper, we introduce a new hierarchical clustering algorithm that overcomes some of these drawbacks. RESULT: We propose a new tree-structure self-organizing neural network, called dynamically growing self-organizing tree (DGSOT) algorithm for hierarchical clustering. The DGSOT constructs a hierarchy from top to bottom by division. At each hierarchical level, the DGSOT optimizes the number of clusters, from which the proper hierarchical structure of the underlying dataset can be found. In addition, we propose a new cluster validation criterion based on the geometric property of the Voronoi partition of the dataset in order to find the proper number of clusters at each hierarchical level. This criterion uses the Minimum Spanning Tree (MST) concept of graph theory and is computationally inexpensive for large datasets. A K-level up distribution (KLD) mechanism, which increases the scope of data distribution in the hierarchy construction, was used to improve the clustering accuracy. The KLD mechanism allows the data misclustered in the early stages to be reevaluated at a later stage and increases the accuracy of the final clustering result. The clustering result of the DGSOT is easily displayed as a dendrogram for visualization. Based on a yeast cell cycle microarray expression dataset, we found that our algorithm extracts gene expression patterns at different levels. Furthermore, the biological functionality enrichment in the clusters is considerably high and the hierarchical structure of the clusters is more reasonable. AVAILABILITY: DGSOT is available upon request from the authors.     

Novel clustering algorithm for microarray expression data in a truncated SVD space

MOTIVATION: This paper introduces the application of a novel clustering method to microarray expression data. Its first stage involves compression of dimensions that can be achieved by applying SVD to the gene-sample matrix in microarray problems. Thus the data (samples or genes) can be represented by vectors in a truncated space of low dimensionality, 4 and 5 in the examples studied here. We find it preferable to project all vectors onto the unit sphere before applying a clustering algorithm. The clustering algorithm used here is the quantum clustering method that has one free scale parameter. Although the method is not hierarchical, it can be modified to allow hierarchy in terms of this scale parameter. RESULTS: We apply our method to three data sets. The results are very promising. On cancer cell data we obtain a dendrogram that reflects correct groupings of cells. In an AML/ALL data set we obtain very good clustering of samples into four classes of the data. Finally, in clustering of genes in yeast cell cycle data we obtain four groups in a problem that is estimated to contain five families. AVAILABILITY: Software is available as Matlab programs at http://neuron.tau.ac.il/~horn/QC.htm.     

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 estimation of cluster boundaries in gene expression profile data.

MOTIVATION: Gene expression profile data are rapidly accumulating due to advances in microarray techniques. The abundant data are analyzed by clustering procedures to extract the useful information about the genes inherent in the data. In the clustering analyses, the systematic determination of the boundaries of gene clusters, instead of by visual inspection and biological knowledge, still remains challenging. RESULTS: We propose a statistical procedure to estimate the number of clusters in the hierarchical clustering of the expression profiles. Following the hierarchical clustering, the statistical property of the profiles at the node in the dendrogram is evaluated by a statistics-based value: the variance inflation factor in the multiple regression analysis. The evaluation leads to an automatic determination of the cluster boundaries without any additional analyses and any biological knowledge of the measured genes. The performance of the present procedure is demonstrated on the profiles of 2467 yeast genes, with very promising results. AVAILABILITY: A set of programs will be electronically sent upon request. CONTACT: horimoto@post.saga-med.ac.jp; toh@beri.co.jp     

MCAM: multiple clustering analysis methodology for deriving hypotheses and insights from high-throughput proteomic datasets

Advances in proteomic technologies continue to substantially accelerate capability for generating experimental data on protein levels, states, and activities in biological samples. For example, studies on receptor tyrosine kinase signaling networks can now capture the phosphorylation state of hundreds to thousands of proteins across multiple conditions. However, little is known about the function of many of these protein modifications, or the enzymes responsible for modifying them. To address this challenge, we have developed an approach that enhances the power of clustering techniques to infer functional and regulatory meaning of protein states in cell signaling networks. We have created a new computational framework for applying clustering to biological data in order to overcome the typical dependence on specific a priori assumptions and expert knowledge concerning the technical aspects of clustering. Multiple clustering analysis methodology ('MCAM') employs an array of diverse data transformations, distance metrics, set sizes, and clustering algorithms, in a combinatorial fashion, to create a suite of clustering sets. These sets are then evaluated based on their ability to produce biological insights through statistical enrichment of metadata relating to knowledge concerning protein functions, kinase substrates, and sequence motifs. We applied MCAM to a set of dynamic phosphorylation measurements of the ERRB network to explore the relationships between algorithmic parameters and the biological meaning that could be inferred and report on interesting biological predictions. Further, we applied MCAM to multiple phosphoproteomic datasets for the ERBB network, which allowed us to compare independent and incomplete overlapping measurements of phosphorylation sites in the network. We report specific and global differences of the ERBB network stimulated with different ligands and with changes in HER2 expression. Overall, we offer MCAM as a broadly-applicable approach for analysis of proteomic data which may help increase the current understanding of molecular networks in a variety of biological problems.     

Context-specific infinite mixtures for clustering gene expression profiles across diverse microarray dataset

MOTIVATION: Identifying groups of co-regulated genes by monitoring their expression over various experimental conditions is complicated by the fact that such co-regulation is condition-specific. Ignoring the context-specific nature of co-regulation significantly reduces the ability of clustering procedures to detect co-expressed genes due to additional 'noise' introduced by non-informative measurements. RESULTS: We have developed a novel Bayesian hierarchical model and corresponding computational algorithms for clustering gene expression profiles across diverse experimental conditions and studies that accounts for context-specificity of gene expression patterns. The model is based on the Bayesian infinite mixtures framework and does not require a priori specification of the number of clusters. We demonstrate that explicit modeling of context-specificity results in increased accuracy of the cluster analysis by examining the specificity and sensitivity of clusters in microarray data. We also demonstrate that probabilities of co-expression derived from the posterior distribution of clusterings are valid estimates of statistical significance of created clusters. AVAILABILITY: The open-source package gimm is available at http://eh3.uc.edu/gimm.     

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.     

Gene ordering in partitive clustering using microarray expressions

A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering and ordering the genes using gene expression data into homogeneous groups was shown to be useful in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on gene ordering in hierarchical clustering framework for gene expression analysis, there is no work addressing and evaluating the importance of gene ordering in partitive clustering framework, to the best knowledge of the authors. Outside the framework of hierarchical clustering, different gene ordering algorithms are applied on the whole data set, and the domain of partitive clustering is still unexplored with gene ordering approaches. A new hybrid method is proposed for ordering genes in each of the clusters obtained from partitive clustering solution, using microarray gene expressions.Two existing algorithms for optimally ordering cities in travelling salesman problem (TSP), namely, FRAG_GALK and Concorde, are hybridized individually with self organizing MAP to show the importance of gene ordering in partitive clustering framework. We validated our hybrid approach using yeast and fibroblast data and showed that our approach improves the result quality of partitive clustering solution, by identifying subclusters within big clusters, grouping functionally correlated genes within clusters, minimization of summation of gene expression distances, and the maximization of biological gene ordering using MIPS categorization. Moreover, the new hybrid approach, finds comparable or sometimes superior biological gene order in less computation time than those obtained by optimal leaf ordering in hierarchical clustering solution.