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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.
Pattern matching, graph theory, graph algorithms, Markov processes, machine learning, data mining, image databases.

Y. Keller, R. R. Coifman and S. Lafon, "Data Fusion and Multicue Data Matching by Diffusion Maps," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 28, no. , pp. 1784-1797, 2006.
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