A two-step basis vector extraction strategy for multiset variable correlation analysis

In the present work, multiple data spaces, in which the same variables are measured on different sources of objects, are related with each other by a two-step analysis strategy, which focuses on finding their common structure in variable correlations. Common basis vectors, which are closely related with each other over sets, are extracted and deemed to enclose the cross-set similar correlations. Therefore, two different subspaces are separated from each other in each dataset. One is the common subspace driven by the common bases, in which, variable correlations are deemed to be consistent over sets; and the residual is the specific subspace, in which, variable correlations are unique to each definite data table. 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 the laboratory experiment data from the literatures. The proposed approach provides an insight into the inherent variable correlations of multiple-set data with further application potential.