Personalized Coupled Tensor Decomposition for Multimodal Data Fusion: Uniqueness and Algorithms

TL;DR

This paper introduces a personalized coupled tensor decomposition framework for multimodal data fusion, addressing heterogeneity and dataset-specific information, with proven uniqueness conditions and two algorithms demonstrating improved performance.

Contribution

It proposes a novel personalized CTD model that separates common and dataset-specific factors, with new uniqueness conditions and algorithms for efficient computation.

Findings

The framework effectively captures shared and unique features across datasets.

Proposed algorithms outperform existing methods in experiments.

The model generalizes several existing CTD approaches.

Abstract

Coupled tensor decompositions (CTDs) perform data fusion by linking factors from different datasets. Although many CTDs have been already proposed, current works do not address important challenges of data fusion, where: 1) the datasets are often heterogeneous, constituting different "views" of a given phenomena (multimodality); and 2) each dataset can contain personalized or dataset-specific information, constituting distinct factors that are not coupled with other datasets. In this work, we introduce a personalized CTD framework tackling these challenges. A flexible model is proposed where each dataset is represented as the sum of two components, one related to a common tensor through a multilinear measurement model, and another specific to each dataset. Both the common and distinct components are assumed to admit a polyadic decomposition. This generalizes several existing CTD models. We provide conditions for specific and generic uniqueness of the decomposition that are easy to interpret. These conditions employ uni-mode uniqueness of different individual datasets and properties of the measurement model. Two algorithms are proposed to compute the common and distinct components: a semi-algebraic one and a coordinate-descent optimization method. Experimental results illustrate the advantage of the proposed framework compared with the state of the art approaches.