Part of Advances in Neural Information Processing Systems 21 (NIPS 2008)
Andrew Smith, Hongyuan Zha, Xiao-ming Wu
We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA . The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive a worst-case upper bound of errors for LTSA which naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.