Multi-Way Data Analysis

Abstract

Temporal pooling does not necessarily reflect the temporal variation within a three-way feature array sufficiently, as—depending on the choice of the pooling function—only certain statistical properties of the variation are retained in the resulting two-way feature array. Multi-way data analysis therefore aims to avoid any pooling and applies Multi-way data analysis methods directly to the multi-way data, in our case represented by the three-way feature array. One can either apply two-way data analysis methods on the multi-way data resulting in two-way models or use directly multi-way data analysis methods leading to multi-way models. In this chapter, two methods to perform two-way data analysis on three-way data without previous pooling are discussed: unfolding and bilinear 2D-PCR. This is followed by a brief review of the extension of two-way component model concepts to multi-way component models with Tucker3 and PARAFAC. Using the multi-way component models as a starting point, the three-way data analysis method used in this book for video quality metrics, the trilinear PLSR, which is the three-way extension of the two-way PLSR, is discussed. As the feature array for video sequences is a three-way array, the focus is on three-way data analysis, but most of the presented methods can be extended straightforwardly to n-way arrays.