The application of machine learning to inference problems in biology is dominated by supervised learning problems of regression and classification, and unsupervised learning problems of clustering and variants of low-dimensional projections for visualization. A class of problems that have not gained much attention is detecting outliers in datasets, arising from reasons such as gross experimental, reporting or labelling errors. These could also be small parts of a dataset that are functionally distinct from the majority of a population. Outlier data are often identified by considering the probability density of normal data and comparing data likelihoods against some threshold. This classical approach suffers from the curse of dimensionality, which is a serious problem with omics data which are often found in very high dimensions. We develop an outlier detection method based on structured low-rank approximation methods. The objective function includes a regularizer based on neighbourhood information captured in the graph Laplacian. Results on publicly available genomic data show that our method robustly detects outliers whereas a density-based method fails even at moderate dimensions. Moreover, we show that our method has better clustering and visualization performance on the recovered low-dimensional projection when compared with popular dimensionality reduction techniques.

Recent advances in high throughput technologies have made large amounts of biomedical omics data accessible to the scientific community. Single omic data clustering has proved its impact in the biomedical and biological research fields. Multi-omic data clustering and multi-omic data integration techniques have shown improved clustering performance and biological insight. Cancer subtype clustering is an important task in the medical field to be able to identify a suitable treatment procedure and prognosis for cancer patients. State of the art multi-view clustering methods are based on non-convex objectives which only guarantee non-global solutions that are high in computational complexity. Only a few convex multi-view methods are present. However, their models do not take into account the intrinsic manifold structure of the data. In this paper, we introduce a convex graph regularized multi-view clustering method that is robust to outliers. We compare our algorithm to state of the art convex and non-convex multi-view and single view clustering methods, and show its superiority in clustering cancer subtypes on publicly available cancer genomic datasets from the TCGA repository. We also show our method's better ability to potentially discover cancer subtypes compared to other state of the art multi-view methods.