Generalized gene co-expression analysis via subspace clustering using low-rank representation

BACKGROUND: Gene Co-expression Network Analysis (GCNA) helps identify gene modules with potential biological functions and has become a popular method in bioinformatics and biomedical research. However, most current GCNA algorithms use correlation to build gene co-expression networks and identify modules with highly correlated genes. There is a need to look beyond correlation and identify gene modules using other similarity measures for finding novel biologically meaningful modules. RESULTS: We propose a new generalized gene co-expression analysis algorithm via subspace clustering that can identify biologically meaningful gene co-expression modules with genes that are not all highly correlated. We use low-rank representation to construct gene co-expression networks and local maximal quasi-clique merger to identify gene co-expression modules. We applied our method on three large microarray datasets and a single-cell RNA sequencing dataset. We demonstrate that our method can identify gene modules with different biological functions than current GCNA methods and find gene modules with prognostic values. CONCLUSIONS: The presented method takes advantage of subspace clustering to generate gene co-expression networks rather than using correlation as the similarity measure between genes. Our generalized GCNA method can provide new insights from gene expression datasets and serve as a complement to current GCNA algorithms

Sample Size Evaluation and Comparison of K-Means Clusterings of RNA-Seq Gene Expression Data

The process by which DNA is transformed into gene products, such as RNA and proteins, is called gene expression. Gene expression profiling quantifies the expression of genes (amount of RNA) in a particular tissue at a particular time. Two commonly used high-throughput techniques for gene expression analysis are DNA microarrays and RNA-Seq, with RNA-Seq being the newer technique based on high-throughput sequencing. Statistical analysis is needed to deal with complex datasets — one commonly used statistical tool is clustering. Clustering comparison is an existing area dedicated to comparing multiple clusterings from one or more clustering algorithms. However, there has been limited application of cluster comparisons to clusterings of RNA-Seq gene expression data. In particular, cluster comparisons are useful in order to test the differences between clusterings obtained using a single algorithm when using different samples for clustering. Here we use a metric for cluster comparisons that is a variation of existing metrics. The metric is simply the minimal number of genes that need to be moved from one cluster to another in one given clustering to produce another given clustering. As the metric only has genes (or elements) as units, it is easy to interpret for RNA-Seq analysis. Moreover, three different algorithmic techniques — brute force, branch-and-bound, and maximal bipartite matching — for computing the proposed metric exactly are compared in terms of time to compute, with bipartite matching being significantly more time efficient. This metric is then applied to the important issue of understanding the effect of increasing the number of RNA-Seq samples to clusterings. Three datasets were used where a large number of samples were available: mouse embryonic stem cell tissue data, Drosophila melanogaster data from multiple tissues and micro-climates, and a mouse multi-tissue dataset. For each, a reference clustering was computed from all of the samples, and then it was compared to clusterings created from smaller subsets of the samples. All clusterings were created using a standard heuristic K-means clustering algorithm, while also systematically varying the numbers of clusters, and also using both Euclidean distance and Manhattan distance. The clustering comparisons suggest that for the three large datasets tested, there seems to be a limited impact of adding more RNA-Seq samples on K-means clusterings using both Euclidean distance and Manhattan distance (Manhattan distance gives a higher variation) beyond some small number of samples. That is, the clusterings compiled based on a limited number of samples were all either quite similar to the reference clustering or did not improve as additional samples were added. These findings were the same for different numbers of clusters. The methods developed could also be applied to other clustering comparison problems

Network-based stratification of tumor mutations.

Many forms of cancer have multiple subtypes with different causes and clinical outcomes. Somatic tumor genome sequences provide a rich new source of data for uncovering these subtypes but have proven difficult to compare, as two tumors rarely share the same mutations. Here we introduce network-based stratification (NBS), a method to integrate somatic tumor genomes with gene networks. This approach allows for stratification of cancer into informative subtypes by clustering together patients with mutations in similar network regions. We demonstrate NBS in ovarian, uterine and lung cancer cohorts from The Cancer Genome Atlas. For each tissue, NBS identifies subtypes that are predictive of clinical outcomes such as patient survival, response to therapy or tumor histology. We identify network regions characteristic of each subtype and show how mutation-derived subtypes can be used to train an mRNA expression signature, which provides similar information in the absence of DNA sequence

Clustering by soft-constraint affinity propagation: Applications to gene-expression data

Motivation: Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis. Recently, a powerful new algorithm called Affinity Propagation (AP) based on message-passing techniques was proposed by Frey and Dueck \cite{Frey07}. In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to, and exemplars have to refer to themselves. Albeit its proved power, AP in its present form suffers from a number of drawbacks. The hard constraint of having exactly one exemplar per cluster restricts AP to classes of regularly shaped clusters, and leads to suboptimal performance, {\it e.g.}, in analyzing gene expression data. Results: This limitation can be overcome by relaxing the AP hard constraints. A new parameter controls the importance of the constraints compared to the aim of maximizing the overall similarity, and allows to interpolate between the simple case where each data point selects its closest neighbor as an exemplar and the original AP. The resulting soft-constraint affinity propagation (SCAP) becomes more informative, accurate and leads to more stable clustering. Even though a new {\it a priori} free-parameter is introduced, the overall dependence of the algorithm on external tuning is reduced, as robustness is increased and an optimal strategy for parameter selection emerges more naturally. SCAP is tested on biological benchmark data, including in particular microarray data related to various cancer types. We show that the algorithm efficiently unveils the hierarchical cluster structure present in the data sets. Further on, it allows to extract sparse gene expression signatures for each cluster.Comment: 11 pages, supplementary material: http://isiosf.isi.it/~weigt/scap_supplement.pd

The Iterative Signature Algorithm for the analysis of large scale gene expression data

We present a new approach for the analysis of genome-wide expression data. Our method is designed to overcome the limitations of traditional techniques, when applied to large-scale data. Rather than alloting each gene to a single cluster, we assign both genes and conditions to context-dependent and potentially overlapping transcription modules. We provide a rigorous definition of a transcription module as the object to be retrieved from the expression data. An efficient algorithm, that searches for the modules encoded in the data by iteratively refining sets of genes and conditions until they match this definition, is established. Each iteration involves a linear map, induced by the normalized expression matrix, followed by the application of a threshold function. We argue that our method is in fact a generalization of Singular Value Decomposition, which corresponds to the special case where no threshold is applied. We show analytically that for noisy expression data our approach leads to better classification due to the implementation of the threshold. This result is confirmed by numerical analyses based on in-silico expression data. We discuss briefly results obtained by applying our algorithm to expression data from the yeast S. cerevisiae.Comment: Latex, 36 pages, 8 figure

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

Mapping genomic and transcriptomic alterations spatially in epithelial cells adjacent to human breast carcinoma.

Almost all genomic studies of breast cancer have focused on well-established tumours because it is technically challenging to study the earliest mutational events occurring in human breast epithelial cells. To address this we created a unique dataset of epithelial samples ductoscopically obtained from ducts leading to breast carcinomas and matched samples from ducts on the opposite side of the nipple. Here, we demonstrate that perturbations in mRNA abundance, with increasing proximity to tumour, cannot be explained by copy number aberrations. Rather, we find a possibility of field cancerization surrounding the primary tumour by constructing a classifier that evaluates where epithelial samples were obtained relative to a tumour (cross-validated micro-averaged AUC = 0.74). We implement a spectral co-clustering algorithm to define biclusters. Relating to over-represented bicluster pathways, we further validate two genes with tissue microarrays and in vitro experiments. We highlight evidence suggesting that bicluster perturbation occurs early in tumour development