PathFinder Uncovers Patterns in Linked Multimodal Datasets

Low-rank matrix decompositions are powerful tools for revealing underlying patterns and structures within datasets across various disciplines. While existing "joint" decomposition methods extend this to link multiple datasets, they typically require that all multimodal data share at least one common dimension. This limitation can hinder analysis when datasets are related but lack a direct, universal shared axis. A novel analytical method called PathFinder addresses this by enabling the co-analysis of datasets that do not necessarily share a dimension across all modalities. Its core innovation lies in recognizing that as long as pairs or subgroups of matrices are linked by shared dimensions, and a "path" exists across the entire collection of data matrices, a global joint decomposition can still be achieved. This approach facilitates the discovery of common patterns across diverse modalities, species, or scales, even when a one-to-one mapping across all data is unavailable. PathFinder is presented as a general framework that encompasses many existing matrix decomposition techniques as special cases, offering capabilities for identifying shared patterns and predicting missing data or modalities.