Multi-view diffusion geometry using intertwined diffusion trajectories

TL;DR

This paper presents a unified framework for multi-view diffusion geometry using intertwined diffusion trajectories, enabling flexible data fusion, theoretical analysis, and improved manifold learning and clustering.

Contribution

It introduces a novel class of inhomogeneous diffusion processes called MDTs, unifies existing models, and provides new methods for learning and evaluating multi-view diffusion operators.

Findings

MDT operators improve manifold learning accuracy

Theoretical properties like ergodicity are established

MDT-based embeddings enhance data clustering

Abstract

This paper introduces a comprehensive unified framework for constructing multi-view diffusion geometries through intertwined multi-view diffusion trajectories (MDTs), a class of inhomogeneous diffusion processes that iteratively combine the random walk operators of multiple data views. Each MDT defines a trajectory-dependent diffusion operator with a clear probabilistic and geometric interpretation, capturing over time the interplay between data views. Our formulation encompasses existing multi-view diffusion models, while providing new degrees of freedom for view interaction and fusion. We establish theoretical properties under mild assumptions, including ergodicity of both the point-wise operator and the process in itself. We also derive MDT-based diffusion distances, and associated embeddings via singular value decompositions. Finally, we propose various strategies for learning MDT operators within the defined operator space, guided by internal quality measures. Beyond enabling flexible model design, MDTs also offer a neutral baseline for evaluating diffusion-based approaches through comparison with randomly selected MDTs. Experiments show the practical impact of the MDT operators in a manifold learning and data clustering context.