Unsupervised Learning of Curved Manifolds

Summary

We describe a variant of the Isomap manifold learning algorithm [1], called ‘C-Isomap’. Isomap was designed to learn non-linear mappings which are isometric embeddings of a flat, convex data set. C-Isomap is designed to recover mappings in the larger class of conformal embeddings, provided that the original sampling density is reasonably uniform. We compare the performance of both versions of Isomap and other algorithms for manifold learning (MDS, LLE, GTM) on a range of data sets.

The authors gratefully acknowledge the support of the DARPA Human ID project, the Office of Naval Research, and the National Science Foundation (grant DMS-Ol01364). The authors also thank Sam Roweis for stimulating discussions, and Larry Saul for suggesting the conformal fishbowl example as a test case.