Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motiva...
This paper examines the problem of extracting lowdimensional manifold structure given millions of highdimensional face images. Specifically, we address the computational challenge...
We give a tutorial overview of several geometric methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the da...
Non-linear dimensionality reduction of noisy data is a challenging problem encountered in a variety of data analysis applications. Recent results in the literature show that spect...
Many unsupervised algorithms for nonlinear dimensionality reduction, such as locally linear embedding (LLE) and Laplacian eigenmaps, are derived from the spectral decompositions o...