[2311.03757] Manifold learning: what, how, and why

Abstract:Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high dimensional point clouds, and allow one to visualize, de-noise and interpret them. This survey presents the principles underlying ML, the representative methods, as well as their statistical foundations from a practicing statistician's perspective. It describes the trade-offs, and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

View PDF HTML (experimental) Abstract:Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high dimensional point clouds, and allow one to visualize, de-noise and interpret them. This survey presents the principles underlying ML, the representative methods, as well as their statistical foundations from a practicing statistician's…

saved by

• Didier Lampard

related reading

• Machine Learning for Inverse Problems and Data Assimilationarxiv.org
• Deep Learning is Not So Mysterious or Differentarxiv.org
• Modular Manifolds - Thinking Machines Labthinkingmachines.ai
• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugesarxiv.org
• 2.2. Manifold learning — scikit-learn 1.9.0 documentationscikit-learn.org
• Neural Networks, Manifolds, and Topology -- colah's blogcolah.github.io
• [2604.21691] There Will Be a Scientific Theory of Deep Learningarxiv.org
• NL.pdfabehrouz.github.io
• Neural Manifold Ordinary Differential Equationsarxiv.org
• The Local Learning Coefficient: A Singularity-Aware Complexity Measurearxiv.org
• Dimensionality reduction in neural data analysisxcorr.net
• [2604.21691] There Will Be a Scientific Theory of Deep Learningarxiv.org