Multiple networks modules identification by a multi-dimensional Markov chain method

As a general approach to study interactions among small biological molecules such as genes and proteins, network analysis has aroused great interest of people from various research disciplines. However, the construction of network is usually quite sensitive to noise which is unavoidable in real data. Besides, the parameter selections for network construction can also affect the result significantly. These two factors largely decrease the consistency of results generated in network analysis. In particular, we consider detecting closely connected subgraphs named module structure. As an important common property of biological networks, this module structure is often destroyed corrupted by both noise and poor parameter selections in network construction. To conquer these two disadvantages to improve the consistency of module structure identified, we propose to process multiple networks for same set of biological molecules simultaneously for common module structure. More specifically, we combine multiple networks together by building an order 3 tensor data with each layer as one of the multiple networks. Then given any molecule(s) as prior information, a novel tensor-based Markov chain algorithm is proposed to iteratively detect the module that includes the prior node. Moreover, the proposed algorithm is capable of evaluating the contribution scores of each network to the detected module structure. The contribution scores from multiple networks can be not only useful criteria to measure the consistency of module structure, but also valid indicator of corruption in networks. To demonstrate the effectiveness and efficiency of the proposed tensor-based Markov chain algorithm, experimental results on synthetic data set as well as two real gene co-expression data sets of human beings are reported. We also validate that the identified common modules are biologically meaningful.