Two-step Multiset Regression Analysis (MsRA) Algorithm

In the present work, a multiset regression analysis strategy is developed by designing a two-step feature extraction procedure. Multiple predictor spaces, in which the same variables are measured on different sources of objects or the same number of objects is observed on different variables, are collected, preparing multiple regression data pairs in combination with response spaces. It focuses on finding the common regression structures across predictor spaces, which can be X-Y regression correlations or predictor variations dosely related with each other, for the interpretation of response. Therefore, two different subspaces are separated from each other in each predictor space. One is the common subspace revealing the general regression features shared by all predictor spaces and the other is the specific subspace driven by the unique regression information that is more predictor space-dependent. This is achieved by solving a mathematical optimization problem, in which theoretical support is framed and the related statistical characteristics are analyzed. Its feasibility and performance are illustrated with both a simple numerical case and the experimental data from the literatures. From the cross-set viewpoint, the proposed approach provides a more meaningful characterization of the inherent predictor information for regression modeling. Further development and application potential are suggested.