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2008 NIPS NeurIPS 2008

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

Abstract

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.

🌉 Interdisciplinary Bridge — Machine Learning and Mathematics & Optimization
📈 Trend Setter — Geometry
🧭 Keyword Pioneer — local tangent space
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Speech & Audio
🐣 Hot Topic Early Bird — manifold learning

Authors

Andrew Smith , Hongyuan Zha , Xiao-ming Wu

Topics

Machine Learning > Core Methods > Representation Learning Machine Learning > Optimization & Theory > Theory Mathematics & Optimization > Mathematics > Geometry Machine Learning > Core Methods > Dimensionality Reduction

Keywords

manifold learning subspace learning convergence analysis dimension reduction local tangent space perturbation analysis ltsa spectral method ltsa algorithm
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