A calibration method for non-positive definite covariance matrix in multivariate data analysis

Covariance matrices that fail to be positive definite arise often in covariance estimation. Approaches addressing this problem exist, but are not well supported theoretically. In this paper, we propose a unified statistical and numerical matrix calibration, finding the optimal positive definite surrogate in the sense of Frobenius norm. The proposed algorithm can be directly applied to any estimated covariance matrix. Numerical results show that the calibrated matrix is typically closer to the true covariance, while making only limited changes to the original covariance structure

Integration of breast cancer gene signatures based on graph centrality

<p>Abstract</p> <p>Background</p> <p>Various gene-expression signatures for breast cancer are available for the prediction of clinical outcome. However due to small overlap between different signatures, it is challenging to integrate existing disjoint signatures to provide a unified insight on the association between gene expression and clinical outcome.</p> <p>Results</p> <p>In this paper, we propose a method to integrate different breast cancer gene signatures by using graph centrality in a context-constrained protein interaction network (PIN). The context-constrained PIN for breast cancer is built by integrating complete PIN and various gene signatures reported in literatures. Then, we use graph centralities to quantify the importance of genes to breast cancer. Finally, we get reliable gene signatures that are consisted by the genes with high graph centrality. The genes which are well-known breast cancer genes, such as TP53 and BRCA1, are ranked extremely high in our results. Compared with previous results by functional enrichment analysis, graph centralities, especially the eigenvector centrality and subgraph centrality, based gene signatures are more tightly related to breast cancer. We validate these signatures on genome-wide microarray dataset and found strong association between the expression of these signature genes and pathologic parameters.</p> <p>Conclusions</p> <p>In summary, graph centralities provide a novel way to connect different cancer signatures and to understand the mechanism of relationship between gene expression and clinical outcome of breast cancer. Moreover, this method is not only can be used on breast cancer, but also can be used on other gene expression related diseases and drug studies.</p

Identifying protein complexes from interaction networks based on clique percolation and distance restriction

Background: Identification of protein complexes in large interaction networks is crucial to understand principles of cellular organization and predict protein functions, which is one of the most important issues in the post-genomic era. Each protein might be subordinate multiple protein complexes in the real protein-protein interaction networks.Identifying overlapping protein complexes from protein-protein interaction networks is a considerable research topic. Result: As an effective algorithm in identifying overlapping module structures, clique percolation method (CPM) has a wide range of application in social networks and biological networks. However, the recognition accuracy of algorithm CPM is lowly. Furthermore, algorithm CPM is unfit to identifying protein complexes with meso-scale when it applied in protein-protein interaction networks. In this paper, we propose a new topological model by extending the definition of k-clique community of algorithm CPM and introduced distance restriction, and develop a novel algorithm called CP-DR based on the new topological model for identifying protein complexes. In this new algorithm, the protein complex size is restricted by distance constraint to conquer the shortcomings of algorithm CPM. The algorithm CP-DR is applied to the protein interaction network of Sacchromyces cerevisiae and identifies many well known complexes. Conclusion: The proposed algorithm CP-DR based on clique percolation and distance restriction makes it possible to identify dense subgraphs in protein interaction networks, a large number of which correspond to known protein complexes. Compared to algorithm CPM, algorithm CP-DR has more outstanding performance

Detecting Conserved Protein Complexes Using a Dividing-and-Matching Algorithm and Unequally Lenient Criteria for Network Comparison

The increase of protein–protein interaction (PPI) data of different species makes it possible to identify common subnetworks (conserved protein complexes) across species via local alignment of their PPI networks, which benefits us to study biological evolution. Local alignment algorithms compare PPI network of different species at both protein sequence and network structure levels. For computational and biological reasons, it is hard to find common subnetworks with strict similar topology from two input PPI networks. Consequently some methods introduce less strict criteria for topological similarity. However those methods fail to consider the differences of the two input networks and adopt equally lenient criteria on them. In this work, a new dividing-and-matching-based method, namely UEDAMAlign is proposed to detect conserved protein complexes. This method firstly uses known protein complexes or computational methods to divide one of the two input PPI networks into subnetworks and then maps the proteins in these subnetworks to the other PPI network to get their homologous proteins. After that, UEDAMAlign conducts unequally lenient criteria on the two input networks to find common connected components from the proteins in the subnetworks and their homologous proteins in the other network. We carry out network alignments between S. cerevisiae and D. melanogaster, H. sapiens and D. melanogaster, respectively. Comparisons are made between other six existing methods and UEDAMAlign. The experimental results show that UEDAMAlign outperforms other existing methods in recovering conserved protein complexes that both match well with known protein complexes and have similar functions

A semiparametric mixture regression model for longitudinal data

A normal semiparametric mixture regression model is proposed for longitudinal data. The proposed model contains one smooth term and a set of possible linear predictors. Model terms are estimated using the penalized likelihood method with the EM algorithm. A computationally feasible alternative method that provides an approximate solution is also introduced. Simulation experiments and a real data example are used to illustrate the methods