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Activity Number: 211
Type: Invited
Date/Time: Tuesday, August 5, 2008 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #300298
Title: Curve and Surface Fitting: From the Viewpoint of Manifold Recovery
Author(s): Edwin Chong and Hari Iyer and Thomas Lee*+ and Haonan Wang
Companies: Colorado State University and Colorado State University and Chinese University/Colorado State University and Colorado State University
Address: , , ,
Keywords: curve estimation ; local linear embedding ; surface fitting
Abstract:

Since its inception, locally linear embedding (LLE, Roweis and Saul, 2000) has become a popular method for recovering unknown low-dimensional structures hidden in high-dimensional data. Numerous successful applications to real-life problems of LLE have been reported in the literature. However, its theoretical properties are largely unknown. In this work, we define a population version of LLE and study its theoretical and statistical properties. This is particularly important for understanding the good empirical performance of LLE.

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Revised September, 2008