Motivation: One of the most important research areas in personalized medicine is the discovery of disease sub-types with relevance in clinical applications. This is usually accomplished by exploring gene expression data with unsupervised clustering methodologies. Then, with the advent of multiple omics technologies, data integration methodologies have been further developed to obtain better performances in patient separability. However, these methods do not guarantee the survival separability of the patients in different clusters. Results: We propose a new methodology that first computes a robust and sparse correlation matrix of the genes, then decomposes it and projects the patient data onto the first m spectral components of the correlation matrix. After that, a robust and adaptive to noise clustering algorithm is applied. The clustering is set up to optimize the separation between survival curves estimated cluster-wise. The method is able to identify clusters that have different omics signatures and also statistically significant differences in survival time. The proposed methodology is tested on five cancer datasets downloaded from The Cancer Genome Atlas repository. The proposed method is compared with the Similarity Network Fusion (SNF) approach, and model based clustering based on Student's t-distribution (TMIX). Our method obtains a better performance in terms of survival separability, even if it uses a single gene expression view compared to the multi-view approach of the SNF method. Finally, a pathway based analysis is accomplished to highlight the biological processes that differentiate the obtained patient groups. Availability and implementation: Our R source code is available online at https://github.com/angy89/RobustClusteringPatientSubtyping. Supplementary information: Supplementary data are available at Bioinformatics online.

Motivation: Microarray technology can be used to study the expression of thousands of genes across a number of different experimental conditions, usually hundreds. The underlying principle is that genes sharing similar expression patterns, across different samples, can be part of the same co-expression system, or they may share the same biological functions. Groups of genes are usually identified based on cluster analysis. Clustering methods rely on the similarity matrix between genes. A common choice to measure similarity is to compute the sample correlation matrix. Dimensionality reduction is another popular data analysis task which is also based on covariance/correlation matrix estimates. Unfortunately, covariance/correlation matrix estimation suffers from the intrinsic noise present in high-dimensional data. Sources of noise are: sampling variations, presents of outlying sample units, and the fact that in most cases the number of units is much larger than the number of genes. Results: In this paper, we propose a robust correlation matrix estimator that is regularized based on adaptive thresholding. The resulting method jointly tames the effects of the high-dimensionality, and data contamination. Computations are easy to implement and do not require hand tunings. Both simulated and real data are analyzed. A Monte Carlo experiment shows that the proposed method is capable of remarkable performances. Our correlation metric is more robust to outliers compared with the existing alternatives in two gene expression datasets. It is also shown how the regularization allows to automatically detect and filter spurious correlations. The same regularization is also extended to other less robust correlation measures. Finally, we apply the ARACNE algorithm on the SyNTreN gene expression data. Sensitivity and specificity of the reconstructed network is compared with the gold standard. We show that ARACNE performs better when it takes the proposed correlation matrix estimator as input. Availability and implementation: The R software is available at https://github.com/angy89/RobustSparseCorrelation. Contact: [email protected] or [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

The robust improper maximum likelihood estimator (RIMLE) is a new method for robust multivariate clustering finding approximately Gaussian clusters. It maximizes a pseudo- likelihood defined by adding a component with improper constant density for accommodating outliers to a Gaussian mixture. A special case of the RIMLE is MLE for multivariate finite Gaussian mixture models. In this paper we treat existence, consistency, and breakdown theory for the RIMLE comprehensively. RIMLE's existence is proved under non-smooth covariance matrix constraints. It is shown that these can be implemented via a computationally feasible Expectation-Conditional Maximization algorithm.