Our research focuses on developing techniques for efficiently representing high dimensional

data, extracting features and information, and automatic learning. We shall develop techniques

which will perform well when the data, while being embedded in a high dimensional space,

has in fact an intrinsic geometric structure that is very low-dimensional.

This type of phenomenon has been widely recognized empirically in the past several years across multiple data types and applications, and lead to new paradigms in thinking about high-dimensional data sets in the applied mathematics, machine learning and statistical communities. These paradigms often try to exploit the intrinsic geometry of the data to extract feature, efficiently represent the data, and perform inference tasks, or cluster or classify the data. This hypothesis of intrinsically low-dimensional data

is verified in many data sets in high-dimensional spaces, for example arising from sensor measurements, such as images (including infrared, hyper-spectral, etc.), sounds, text documents, just to name a few, and in fact, the ability to compress some of data (especially sounds and images) is an indirect proof of such a statement.....