Learning function relations or understanding structures of data lying in manifolds embedded in huge dimensional Euclidean spaces is an important topic in learning theory. In this ...
The Random Projection Tree (RPTREE) structures proposed in [1] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of da...
Recently the problem of dimensionality reduction has received a lot of interests in many fields of information processing. We consider the case where data is sampled from a low d...
Manifold learning can discover the structure of high dimensional data and provides understanding of multidimensional patterns by preserving the local geometric characteristics. Ho...
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 ...