An extension of PARAFAC to analyze multi-group three-way data

Abstract

This paper introduces a novel methodology for analyzing three-way array data with a multi-group structure. Three-way arrays are commonly observed in various domains, including image analysis, chemometrics, and real-world applications. In this paper, we use a practical case study of process modeling in additive manufacturing, where batches are structured according to multiple groups. Vast volumes of data for multiple variables and process stages are recorded by sensors installed on the production line for each batch. For these three-way arrays, the link between the final product and the observations creates a grouping structure in the observations. This grouping may hamper gaining insight into the process if only some of the groups dominate the controlled variability of the products. In this study, we develop an extension of the PARAFAC model that takes into account the grouping structure of three-way data sets. With this extension, it is possible to estimate a model that is representative of all the groups simultaneously by finding their common structure. The proposed model has been applied to three simulation data sets and a real manufacturing case study. The capability to find the common structure of the groups is compared to PARAFAC and the insights into the importance of variables delivered by the models are discussed.