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In cancer biology, it is very important to understand the phenotypic changes of the patients and discover new cancer subtypes. Recently, microarray-based technologies have shed light on this problem based on gene expression profiles which may contain outliers due to either chemical or electrical reasons. These undiscovered subtypes may be heterogeneous with respect to underlying networks or pathways, and are related with only a few of interdependent biomarkers. This motivates a need for the robust gene expression-based methods capable of discovering such subtypes, elucidating the corresponding network structures and identifying cancer related biomarkers. This study proposes a penalized model-based Student's t clustering with unconstrained covariance (PMT-UC) to discover cancer subtypes with cluster-specific networks, taking gene dependencies into account and having robustness against outliers. Meanwhile, biomarker identification and network reconstruction are achieved by imposing an adaptive [Formula: see text] penalty on the means and the inverse scale matrices. The model is fitted via the expectation maximization algorithm utilizing the graphical lasso. Here, a network-based gene selection criterion that identifies biomarkers not as individual genes but as subnetworks is applied. This allows us to implicate low discriminative biomarkers which play a central role in the subnetwork by interconnecting many differentially expressed genes, or have cluster-specific underlying network structures. Experiment results on simulated datasets and one available cancer dataset attest to the effectiveness, robustness of PMT-UC in cancer subtype discovering. Moveover, PMT-UC has the ability to select cancer related biomarkers which have been verified in biochemical or biomedical research and learn the biological significant correlation among genes.

Detecting protein complexes from protein-protein interaction (PPI) networks is a challenging task in computational biology. A vast number of computational methods have been proposed to undertake this task. However, each computational method is developed to capture one aspect of the network. The performance of different methods on the same network can differ substantially, even the same method may have different performance on networks with different topological characteristic. The clustering result of each computational method can be regarded as a feature that describes the PPI network from one aspect. It is therefore desirable to utilize these features to produce a more accurate and reliable clustering. In this paper, a novel Bayesian Nonnegative Matrix Factorization (NMF)-based weighted Ensemble Clustering algorithm (EC-BNMF) is proposed to detect protein complexes from PPI networks. We first apply different computational algorithms on a PPI network to generate some base clustering results. Then we integrate these base clustering results into an ensemble PPI network, in the form of weighted combination. Finally, we identify overlapping protein complexes from this network by employing Bayesian NMF model. When generating an ensemble PPI network, EC-BNMF can automatically optimize the values of weights such that the ensemble algorithm can deliver better results. Experimental results on four PPI networks of Saccharomyces cerevisiae well verify the effectiveness of EC-BNMF in detecting protein complexes. EC-BNMF provides an effective way to integrate different clustering results for more accurate and reliable complex detection. Furthermore, EC-BNMF has a high degree of flexibility in the choice of base clustering results. It can be coupled with existing clustering methods to identify protein complexes.

Revealing functional units in protein-protein interaction (PPI) networks are important for understanding cellular functional organization. Current algorithms for identifying functional units mainly focus on cohesive protein complexes which have more internal interactions than external interactions. Most of these approaches do not handle overlaps among complexes since they usually allow a protein to belong to only one complex. Moreover, recent studies have shown that other non-cohesive structural functional units beyond complexes also exist in PPI networks. Thus previous algorithms that just focus on non-overlapping cohesive complexes are not able to present the biological reality fully. Here, we develop a new regularized sparse random graph model (RSRGM) to explore overlapping and various structural functional units in PPI networks. RSRGM is principally dominated by two model parameters. One is used to define the functional units as groups of proteins that have similar patterns of connections to others, which allows RSRGM to detect non-cohesive structural functional units. The other one is used to represent the degree of proteins belonging to the units, which supports a protein belonging to more than one revealed unit. We also propose a regularizer to control the smoothness between the estimators of these two parameters. Experimental results on four S. cerevisiae PPI networks show that the performance of RSRGM on detecting cohesive complexes and overlapping complexes is superior to that of previous competing algorithms. Moreover, RSRGM has the ability to discover biological significant functional units besides complexes.