Clusternomics: Integrative context-dependent clustering for heterogeneous datasets.

Integrative clustering is used to identify groups of samples by jointly analysing multiple datasets describing the same set of biological samples, such as gene expression, copy number, methylation etc. Most existing algorithms for integrative clustering assume that there is a shared consistent set of clusters across all datasets, and most of the data samples follow this structure. However in practice, the structure across heterogeneous datasets can be more varied, with clusters being joined in some datasets and separated in others. In this paper, we present a probabilistic clustering method to identify groups across datasets that do not share the same cluster structure. The proposed algorithm, Clusternomics, identifies groups of samples that share their global behaviour across heterogeneous datasets. The algorithm models clusters on the level of individual datasets, while also extracting global structure that arises from the local cluster assignments. Clusters on both the local and the global level are modelled using a hierarchical Dirichlet mixture model to identify structure on both levels. We evaluated the model both on simulated and on real-world datasets. The simulated data exemplifies datasets with varying degrees of common structure. In such a setting Clusternomics outperforms existing algorithms for integrative and consensus clustering. In a real-world application, we used the algorithm for cancer subtyping, identifying subtypes of cancer from heterogeneous datasets. We applied the algorithm to TCGA breast cancer dataset, integrating gene expression, miRNA expression, DNA methylation and proteomics. The algorithm extracted clinically meaningful clusters with significantly different survival probabilities. We also evaluated the algorithm on lung and kidney cancer TCGA datasets with high dimensionality, again showing clinically significant results and scalability of the algorithm

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Survival curves for global clusters in the breast cancer dataset from TCGA, using the model with 3 context-specific clusters and up to 18 global clusters.

<p>The differences between the survival curves are significant with <i>p</i> = 0.0382 using the log-rank test.</p

Consistency between global clustering results for different number of local context-specific clusters, as measured by the ARI.

<p>The compared models were trained with 18 global clusters and 3 to 5 context-specific clusters.</p

Average number of occupied clusters across different numbers of global clusters.

<p>The number of clusters is the average of the posterior number of global clusters that have any samples assigned to them across the MCMC iterations. The figure shows both the total number of occupied clusters and the number of clusters that have more than 5 samples assigned to them.</p

Example of the simulated data for <i>p</i> = 0 and <i>p</i> = 0.5, which show different degrees of dependence.

<p>The <i>x</i> axis corresponds to the data in the first dataset (context), the <i>y</i> axis represents the data in the second dataset (context). The two subfigures show the two extreme situations: (a) For <i>p</i> = 0, we get two global clusters. Cluster membership is fully dependent on each other in both datasets. (b) For <i>p</i> = 0.5, we get four global clusters, where cluster membership in one dataset is fully independent on cluster membership in the second dataset.</p

ARI comparing global clustering of simulated datasets for varying values of <i>p</i> (see Fig 2).

<p>Each point corresponds to the corresponding algorithm applied to one dataset, the plot shows also the loess curve for each method. Higher values correspond to better agreement between the estimated cluster assignments and the true cluster membership.</p

Consistency between local clustering results for different number of global clusters with 3 context-specific clusters, as measured by the ARI.

<p>The ARI values show several local optima. (a) Gene expression context. (b) DNA methylation context. (c) miRNA context. (d) RPPA context.</p

Consistency between global clustering results for different number of global clusters with 3 context-specific clusters, as measured by the ARI.

<p>Consistency between global clustering results for different number of global clusters with 3 context-specific clusters, as measured by the ARI.</p