Interaction Detection For Hybrid Decomposable Problems

In this paper, we present a perturbation-based linkage identification algorithm that employs a novel metric to detect linkages. The proposed metric is a combination of linearity and multiplicative relationship. The proposed method is called Interaction Detection for Hybrid Decomposable Problems (IDHDP) algorithm. Our algorithm can be applied to the additive and multiplicative decomposable problems and problems that have both kind of decomposability, i.e. hybrid decomposability. By using IDHDP, an interaction matrix is computed that represents the degree of interaction between pairs of loci. To extract linkage groups from the interaction matrix, a local threshold is calculated for each variable by the two-means algorithm. We apply IDHDP to problems with different types of decomposability. A comparison with some existing algorithms shows the efficiency and effectiveness of IDHDP.