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...
We investigate the optimality of (1+ )-approximation algorithms obtained via the dimensionality reduction method. We show that: • Any data structure for the (1 + )-approximate n...
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 doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2k balls of raThis concept for abstract metrics has been proposed as a na...
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...