Hierarchical multilinear models for multiway data

TL;DR

This paper introduces a hierarchical multilinear modeling approach for multiway data, extending reduced-rank decompositions to handle diverse data types with exchangeable latent factors for greater pattern flexibility.

Contribution

It presents a novel hierarchical model-based decomposition method that generalizes reduced-rank techniques to various data types with exchangeable latent factors.

Findings

Applicable to longitudinal social networks and multivariate data

Allows modeling of complex, exchangeable latent structures

Enhances flexibility in pattern representation

Abstract

Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a model-based version of such a decomposition, extending the scope of reduced rank methods to accommodate a variety of data types such as longitudinal social networks and continuous multivariate data that are cross-classified by categorical variables. The proposed model-based approach is hierarchical, in that the latent factors corresponding to a given dimension of the array are not {\it a priori} independent, but exchangeable. Such a hierarchical approach allows more flexibility in the types of patterns that can be represented.