PathFinder: Joint Decompositions of Linked Multimodal Datasets

2026-08-14

AI Summary

This study addresses the limitation of existing multimodal joint decomposition methods that necessitate full-dimensional sharing. To overcome this constraint, we propose PathFinder, a generalized joint low-rank decomposition framework utilizing a path connection mechanism to support non-fully-shared dimensions and unify diverse matrix factorization paradigms. The core contribution of this work lies in enabling cross-modal pattern discovery and missing data prediction across heterogeneous datasets. By effectively resolving structural alignment challenges inherent in complex multimodal fusion, PathFinder provides a more generalizable theoretical foundation and practical solution for the joint analysis of heterogeneous data. This approach significantly extends the applicability of tensor decomposition techniques to real-world scenarios where strict dimensional correspondence is unavailable, thereby advancing robust multimodal learning under incomplete or misaligned data conditions.

Abstract

Low-rank matrix decompositions can uncover patterns and structure in data and have a number of different applications across many disciplines. Extensions to "joint" low-rank decompositions have been proposed to link datasets from different modalities. While these methods enable the discovery of common patterns across modalities, they require that all the multimodal data share one or more dimensions. We propose a new analysis method, PathFinder, that enables co-analysis of datasets that do not necessarily all share a dimension. The key insight is that as long as pairs or subgroups of matrices do share some dimension, and that there are one or more paths that link across the data matrices, a global joint decomposition can be sought out. This enables the joint estimation of common patterns across different modalities, species, or scales, where a one-to-one mapping across all data along some dimension is not necessarily available. We show that PathFinder is a general umbrella under which many matrix decomposition methods fall as special cases. It can be used to discover common patterns across disparate datasets and to make predictions for missing data or modalities.

Problem

• Joint low-rank decomposition
• Multimodal datasets
• Linked datasets
• Common pattern discovery

Innovation

• Joint Decomposition
• Linked Multimodal Datasets
• Low-rank Matrix Factorization
• Missing Data Prediction
• Path-based Integration