Nonlinear dimensionality reduction methods are often used to visualize high-dimensional data, although the existing methods have been designed for other related tasks such as mani...
Jarkko Venna, Jaakko Peltonen, Kristian Nybo, Hele...
Dimensionality reduction is an important preprocessing step in high-dimensional data analysis without losing intrinsic information. The problem of semi-supervised nonlinear dimensi...
Many applications require analyzing vast amounts of textual data, but the size and inherent noise of such data can make processing very challenging. One approach to these issues i...
David G. Underhill, Luke McDowell, David J. Marche...
For effective retrieval of visual information, statistical learning plays a pivotal role. Statistical learning in such a context faces at least two major mathematical challenges: ...
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...