Convergence and Rate of Convergence of a Manifold-Based Dimension Reduction Algorithm

Part of Advances in Neural Information Processing Systems 21 (NIPS 2008)

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Andrew Smith, Hongyuan Zha, Xiao-ming Wu


We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA [13]. 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.