In recent years, nonlinear dimensionality reduction (NLDR) techniques have attracted much attention in visual perception and many other areas of science. We propose an efficient al...
Algorithms for nonlinear dimensionality reduction (NLDR) find meaningful hidden low-dimensional structures in a high-dimensional space. Current algorithms for NLDR are Isomaps, Loc...
The dimensionality of the input data often far exceeds their intrinsic dimensionality. As a result, it may be difficult to recognize multidimensional data, especially if the number...
Embedding images into a low dimensional space has a wide range of applications: visualization, clustering, and pre-processing for supervised learning. Traditional dimension reduct...
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...