Two-step Multiset Regression Analysis (MsRA) Algorithm

Abstract

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 XÀY regression correlations or predictor variations closely 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.

Between‐phase calibration modeling and transition analysis for phase‐based quality interpretation and prediction

“…Based on the above analysis, the phase behavior should be modeled in a quite different way from the conventional calibration methods. The MsRA algorithm includes two versions, MsRA‐score and MsRA‐weight, which extract the similar regression scores and weights, respectively. Actually, the quality prediction and interpretation is directly related with the regression scores where the same scores will make the same contribution to quality.…”

“…The between‐phase similarity in quality prediction and interpretation is deemed to be driven by some common regression scores, which are directly related to quality. Using MsRA‐score algorithm, the common regression scores are extracted focusing on two adjacent phases, which can describe the process variables by linear combinations. Here, it should be noted that for each phase, when it is analyzed with different adjacent phases, the subspace separation results may be different, revealing different between‐phase relationships with respect to quality analysis.…”

“…From this motivation, a multiset regression modeling method, termed multiset regression analysis (MsRA), which was proposed to relate the inherent quality‐related predictor variation across multiple data sets, can be used here as the basic modeling method. Following the theoretical developments and its property analysis in the previous work, this study addresses the potential of using the said algorithm to solve one practical problem, the quality prediction and interpretation in multiphase batch processes with between‐phase transitions. It should be noted that here MsRA only focuses on two neighboring phases for between‐phase transition analysis and quality prediction.…”

Between-phase transition analysis for phase-based quality prediction

“…The between-phase similarity in quality prediction and interpretation is deemed to be driven by some common regression scores, which are directly related to quality. Using MsRA algorithm [12], the common regression scores are extracted focusing on two adjacent phases, which can describe the process variables by linear combinations. Here it should be noted that for each phase, when it is analyzed with different adjacent phases, the subspace separation results may be different, revealing different between-phase relationships with respect to quality analysis.…”

“…This also requires the attention to the between-phase transitions and their difference from the steady phases. From this motivation, a multiset regression modeling method, termed MsRA [12], which was proposed to relate the inherent quality-related predictor variation across multiple data sets, can be employed here as the basic modeling method. Following the theoretical developments and its property analysis in the previous work [12], this study addresses the potential of using the said algorithm to solve the quality prediction and interpretation problem in multiphase batch processes with between-phase transitions.…”