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Local graph clustering is an important machine learning task that aims to find a well-connected cluster near a set of seed nodes. Recent results have revealed that incorporating higher order information significantly enhances the results of graph clustering techniques. The majority of existing research in this area focuses on spectral graph theory-based techniques. However, an alternative perspective on local graph clustering arises from using max-flow and min-cut on the objectives, which offer distinctly different guarantees. For instance, a new method called capacity releasing diffusion (CRD) was recently proposed and shown to preserve local structure around the seeds better than spectral methods. The method was also the first local clustering technique that is not subject to the quadratic Cheeger inequality by assuming a good cluster near the seed nodes. In this paper, we propose a local hypergraph clustering technique called hypergraph CRD (HG-CRD) by extending the CRD process to cluster based on higher order patterns, encoded as hyperedges of a hypergraph. Moreover, we theoretically show that HG-CRD gives results about a quantity called motif conductance, rather than a biased version used in previous experiments. Experimental results on synthetic datasets and real world graphs show that HG-CRD enhances the clustering quality., Comment: 18 pages, 6 figures

miRNA and gene expression profiles have been proved useful for classifying cancer samples. Efficient classifiers have been recently sought and developed. A number of attempts to classify cancer samples using miRNA/gene expression profiles are known in literature. However, the use of semi-supervised learning models have been used recently in bioinformatics, to exploit the huge corpuses of publicly available sets. Using both labeled and unlabeled sets to train sample classifiers, have not been previously considered when gene and miRNA expression sets are used. Moreover, there is a motivation to integrate both miRNA and gene expression for a semi-supervised cancer classification as that provides more information on the characteristics of cancer samples. In this paper, two semi-supervised machine learning approaches, namely self-learning and co-training, are adapted to enhance the quality of cancer sample classification. These approaches exploit the huge public corpuses to enrich the training data. In self-learning, miRNA and gene based classifiers are enhanced independently. While in co-training, both miRNA and gene expression profiles are used simultaneously to provide different views of cancer samples. To our knowledge, it is the first attempt to apply these learning approaches to cancer classification. The approaches were evaluated using breast cancer, hepatocellular carcinoma (HCC) and lung cancer expression sets. Results show up to 20% improvement in F1-measure over Random Forests and SVM classifiers. Co-Training also outperforms Low Density Separation (LDS) approach by around 25% improvement in F1-measure in breast cancer., Comment: 8 pages, 4 figures, 10 tables, conference