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...
Nonlinear dimensionality reduction methods often rely on the nearest-neighbors graph to extract low-dimensional embeddings that reliably capture the underlying structure of high-d...
In this paper, our main contribution is a framework for the automatic configuration of any spectral dimensionality reduction methods. This is achieved, first, by introducing the m...
Michal Lewandowski, Dimitrios Makris, Jean-Christo...
We equate nonlinear dimensionality reduction (NLDR) to graph embedding with side information about the vertices, and derive a solution to either problem in the form of a kernel-ba...
Embedding images into a low dimensional space has a wide range of applications: visualization, clustering, and pre-processing for supervised learning. Traditional dimension reduct...