Global pattern of pairwise relationship in genetic network.

In recent times genetic network analysis has been found to be useful in the study of gene-gene interactions, and the study of gene-gene correlations is a special analysis of the network. There are many methods for this goal. Most of the existing methods model the relationship between each gene and the set of genes under study. These methods work well in applications, but there are often issues such as non-uniqueness of solution and/or computational difficulties, and interpretation of results. Here we study this problem from a different point of view: given a measure of pair wise gene-gene relationship, we use the technique of pattern image restoration to infer the optimal network pair wise relationships. In this method, the solution always exists and is unique, and the results are easy to interpret in the global sense and are computationally simple. The regulatory relationships among the genes are inferred according to the principle that neighboring genes tend to share some common features. The network is updated iteratively until convergence, each iteration monotonously reduces entropy and variance of the network, so the limit network represents the clearest picture of the regulatory relationships among the genes provided by the data and recoverable by the model. The method is illustrated with a simulated data and applied to real data sets.