Data Fusion and Multicue Data Matching by Diffusion Maps

TLDR

Data fusion and multicue data matching are fundamental tasks of high‑dimensional data analysis. The paper applies the diffusion framework to address these tasks. The authors develop a Laplace‑Beltrami density‑invariant embedding, refine Nyström with geometric harmonics, apply it to data assimilation, and propose a multicue matching scheme using nonlinear spectral graph alignment. The proposed methods were validated on lipreading and image sequence alignment tasks.

Abstract

Data fusion and multicue data matching are fundamental tasks of high-dimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is three-fold: First, we present the Laplace-Beltrami approach for computing density invariant embeddings which are essential for integrating different sources of data. Second, we describe a refinement of the Nyström extension algorithm called "geometric harmonics." We also explain how to use this tool for data assimilation. Finally, we introduce a multicue data matching scheme based on nonlinear spectral graphs alignment. The effectiveness of the presented schemes is validated by applying it to the problems of lipreading and image sequence alignment.