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

arXiv: https://arxiv.org/abs/2412.01102 · HTML: https://mlsanity.com/paper/2412.01102/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 81 references that are in the map.
- First posted on arXiv 2 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach](https://mlsanity.com/paper/1804.05307/) (2018)
- [Spectrum Cartography via Coupled Block-Term Tensor Decomposition](https://mlsanity.com/paper/1911.12468/) (2019)
- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [Computing Large-Scale Matrix and Tensor Decomposition with Structured Factors: A Unified Nonconvex Optimization Perspective](https://mlsanity.com/paper/2006.08183/) (2020)
- [A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings](https://mlsanity.com/paper/2007.09605/) (2020)
- [Super-Resolution for Hyperspectral and Multispectral Image Fusion Accounting for Seasonal Spectral Variability](https://mlsanity.com/paper/1808.10072/) (2018)
- [Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms](https://mlsanity.com/paper/1811.11091/) (2018)
- [Tensor Completion from Regular Sub-Nyquist Samples](https://mlsanity.com/paper/1903.00435/) (2019)
- [Tensor-Based Fusion of EEG and FMRI to Understand Neurological Changes in Schizophrenia](https://mlsanity.com/paper/1612.02189/) (2016)
- [AFFIRM: Affinity Fusion-based Framework for Iteratively Random Motion correction of multi-slice fetal brain MRI](https://mlsanity.com/paper/2205.05851/) (2022)
- [Personalized Dictionary Learning for Heterogeneous Datasets](https://mlsanity.com/paper/2305.15311/) (2023)
- [Heterogeneous Matrix Factorization: When Features Differ by Datasets](https://mlsanity.com/paper/2305.17744/) (2023)
- [Tensor Analysis and Fusion of Multimodal Brain Images](https://mlsanity.com/paper/1506.06040/) (2015)
- [Common and Distinct Components in Data Fusion](https://mlsanity.com/paper/1607.02328/) (2016)
- [Stochastic Mirror Descent for Low-Rank Tensor Decomposition Under Non-Euclidean Losses](https://mlsanity.com/paper/2104.14562/) (2021)
- [Double Coupled Canonical Polyadic Decomposition for Joint Blind Source Separation](https://mlsanity.com/paper/1612.09466/) (2016)
- [Deep Hyperspectral and Multispectral Image Fusion with Inter-image Variability](https://mlsanity.com/paper/2208.11376/) (2022)
- [Coupled CP tensor decomposition with shared and distinct components for multi-task fMRI data fusion](https://mlsanity.com/paper/2211.14253/) (2022)
- [Determining the Dimension and Structure of the Subspace Correlated Across Multiple Data Sets](https://mlsanity.com/paper/1901.11366/) (2019)

## Built on by (most cited first, 2 of 2)

- [Anisotropic Tensor Deconvolution of Hyperspectral Images](https://mlsanity.com/paper/2601.11694/) (2026)
- [Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis](https://mlsanity.com/paper/2607.22262/) (2026)

## Abstract (arXiv)

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.