Data sets are often modeled as samples from a probability distribution in RD, for D large. It is
often assumed that the data has some interesting low-dimensional structure, for example …

We discuss recent work based on multiscale geometric analyis for the study of large data
sets that lie in high-dimensional spaces but have low-dimensional structure. We present …

Large data sets arise in a wide variety of applications and are often modeled as samples
from a probability distribution in high-dimensional space. It is sometimes assumed that the …

Data sets are often modeled as point clouds in¿ D, for D large. It is often assumed that the
data has some interesting low-dimensional structure, for example that of a d-dimensional …

We present a novel approach for estimating the intrinsic dimension of certain point clouds:
we assume that the points are sampled from a manifold M of dimension k, with k<< D, and …

This work deals with the problem of estimating the intrinsic dimension of noisy, high-
dimensional point clouds. A general class of sets which are locally well-approximated by k …

We develop a novel geometric multiresolution analysis for analyzing intrinsically low-
dimensional point clouds in highdimensional spaces, modeled as samples from a d …

Data sets are often modeled as samples from a probability distribution in RD, for D large. It is
often assumed that the data has some interesting low-dimensional structure, for example …

The problem of estimating the intrinsic dimensionality of a point cloud is of interest in a wide
variety of problems. To cite some important instances, it is equivalent to estimating the …