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

Modeling and visualizing uncertainty in gene expression clusters using Dirichlet process mixtures

Although the use of clustering methods has rapidly become one of the standard computational approaches in the literature of microarray gene expression data, little attention has been paid to uncertainty in the results obtained. Dirichlet process mixture (DPM) models provide a nonparametric Bayesian alternative to the bootstrap approach to modeling uncertainty in gene expression clustering. Most previously published applications of Bayesian model-based clustering methods have been to short time series data. In this paper, we present a case study of the application of nonparametric Bayesian clustering methods to the clustering of high-dimensional nontime series gene expression data using full Gaussian covariances. We use the probability that two genes belong to the same cluster in a DPM model as a measure of the similarity of these gene expression profiles. Conversely, this probability can be used to define a dissimilarity measure, which, for the purposes of visualization, can be input to one of the standard linkage algorithms used for hierarchical clustering. Biologically plausible results are obtained from the Rosetta compendium of expression profiles which extend previously published cluster analyses of this data

Joint Clustering and Registration of Functional Data

Curve registration and clustering are fundamental tools in the analysis of functional data. While several methods have been developed and explored for either task individually, limited work has been done to infer functional clusters and register curves simultaneously. We propose a hierarchical model for joint curve clustering and registration. Our proposal combines a Dirichlet process mixture model for clustering of common shapes, with a reproducing kernel representation of phase variability for registration. We show how inference can be carried out applying standard posterior simulation algorithms and compare our method to several alternatives in both engineered data and a benchmark analysis of the Berkeley growth data. We conclude our investigation with an application to time course gene expression

R/BHC: fast Bayesian hierarchical clustering for microarray data

BACKGROUND: Although the use of clustering methods has rapidly become one of the standard computational approaches in the literature of microarray gene expression data analysis, little attention has been paid to uncertainty in the results obtained. RESULTS: We present an R/Bioconductor port of a fast novel algorithm for Bayesian agglomerative hierarchical clustering and demonstrate its use in clustering gene expression microarray data. The method performs bottom-up hierarchical clustering, using a Dirichlet Process (infinite mixture) to model uncertainty in the data and Bayesian model selection to decide at each step which clusters to merge. CONCLUSION: Biologically plausible results are presented from a well studied data set: expression profiles of A. thaliana subjected to a variety of biotic and abiotic stresses. Our method avoids several limitations of traditional methods, for example how many clusters there should be and how to choose a principled distance metric

Discovering transcriptional modules by Bayesian data integration

Motivation: We present a method for directly inferring transcriptional modules (TMs) by integrating gene expression and transcription factor binding (ChIP-chip) data. Our model extends a hierarchical Dirichlet process mixture model to allow data fusion on a gene-by-gene basis. This encodes the intuition that co-expression and co-regulation are not necessarily equivalent and hence we do not expect all genes to group similarly in both datasets. In particular, it allows us to identify the subset of genes that share the same structure of transcriptional modules in both datasets. Results: We find that by working on a gene-by-gene basis, our model is able to extract clusters with greater functional coherence than existing methods. By combining gene expression and transcription factor binding (ChIP-chip) data in this way, we are better able to determine the groups of genes that are most likely to represent underlying TMs

Colouring and breaking sticks: random distributions and heterogeneous clustering

We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which clusters are of different `colours', with statistical characteristics that are constant within colours, but different between colours. Thus cluster identities are exchangeable only within colours. The basic form of our model is a variant on the familiar Dirichlet process, and we find that much of the standard modelling and computational machinery associated with the Dirichlet process may be readily adapted to our generalisation. The methodology is illustrated with an application to the partially-parametric clustering of gene expression profiles.Comment: 26 pages, 3 figures. Chapter 13 of "Probability and Mathematical Genetics: Papers in Honour of Sir John Kingman" (Editors N.H. Bingham and C.M. Goldie), Cambridge University Press, 201

Bayesian correlated clustering to integrate multiple datasets

Motivation: The integration of multiple datasets remains a key challenge in systems biology and genomic medicine. Modern high-throughput technologies generate a broad array of different data types, providing distinct – but often complementary – information. We present a Bayesian method for the unsupervised integrative modelling of multiple datasets, which we refer to as MDI (Multiple Dataset Integration). MDI can integrate information from a wide range of different datasets and data types simultaneously (including the ability to model time series data explicitly using Gaussian processes). Each dataset is modelled using a Dirichlet-multinomial allocation (DMA) mixture model, with dependencies between these models captured via parameters that describe the agreement among the datasets. Results: Using a set of 6 artificially constructed time series datasets, we show that MDI is able to integrate a significant number of datasets simultaneously, and that it successfully captures the underlying structural similarity between the datasets. We also analyse a variety of real S. cerevisiae datasets. In the 2-dataset case, we show that MDI’s performance is comparable to the present state of the art. We then move beyond the capabilities of current approaches and integrate gene expression, ChIP-chip and protein-protein interaction data, to identify a set of protein complexes for which genes are co-regulated during the cell cycle. Comparisons to other unsupervised data integration techniques – as well as to non-integrative approaches – demonstrate that MDI is very competitive, while also providing information that would be difficult or impossible to extract using other methods