Data fusion and multicue data matching by diffusion maps.

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.

Diffusion maps and coarse-graining: A unified framework for dimensionality reduction, graph partitioning, and data set parameterization.

We provide evidence that nonlinear dimensionality reduction, clustering, and data set parameterization can be solved within one and the same framework. The main idea is to define a system of coordinates with an explicit metric that reflects the connectivity of a given data set and that is robust to noise. Our construction, which is based on a Markov random walk on the data, offers a general scheme of simultaneously reorganizing and subsampling graphs and arbitrarily shaped data sets in high dimensions using intrinsic geometry.