On the estimation of geodesic paths on sampled manifolds under random projections

In this paper, we focus on the use of random projections as a dimensionality reduction tool for sampled manifolds in highdimensional Euclidean spaces. We show that geodesic paths approximations from nearest neighbors Euclidean distances are well-preserved by Gaussian projections and we characterize the distribution of geodesic lengths in the reduced dimensional point cloud. A stylized application to a real-world data set of human faces is presented to validate our theoretical findings.

• Type: Conference
• Year: 2008
• Where: ICIP
• Authors: Mona Mahmoudi, Pierre Vandergheynst, Matteo Sorci
• Keywords: Dimensionality Reduction Tool, Gaussian Projections, Geodesic Lengths, Geodesic Paths Approximations, ICIP 2008, Image Processing, Neighbors Euclidean Distances