A bidirectional between-set statistical analysis method and its applications

Abstract

In this work, a bidirectional statistical modeling and analysis approach is developed to relate two data tables (X₁ and X₂) under the supervision of each other. Different from quality prediction where the interest was to interpret one set of variables by another set, the current task lies in modeling simultaneously both data spaces in bidirectional fashion (X₁ ↔ X₂) responding to different between-set relationships. It is performed in two steps. The first step aims at a bidirectional latent variable (Bi-LV) extraction and preparation, by which the between-set covarying relationship is preliminarily set up. In the second step, where a joint postprocessing is performed on the Bi-LV modeling result (here termed Bi-JPLV algorithm), different types of systematic variations are decomposed in each space. Correlated and unique variations are discriminated and evaluated in specific model parameters separately revealing between-set similarity and dissimilarity, respectively. The proposed method gives a good interpretation of the underlying information within each data space from a bidirectional viewpoint, revealing practical application potential. The feasibility and performance of the proposed method are illustrated with both numerical and real industrial cases. © 2010 American Institute of Chemical Engineers AIChE J, 2011