Manifold Learning: What, How, and Why

被引:7
|
作者
Meila, Marina [1 ]
Zhang, Hanyu [2 ]
机构
[1] Univ Washington, Dept Stat, Seattle, WA 98195 USA
[2] ByteDance Inc, Bellevue, WA USA
基金
美国国家科学基金会;
关键词
nonlinear dimension reduction; manifold learning; embedding; NONLINEAR DIMENSIONALITY REDUCTION; T-SNE; RIEMANNIAN-MANIFOLDS; GRAPH LAPLACIANS; TANGENT-SPACE; CONVERGENCE; REGULARIZATION; EMBEDDINGS; KINETICS; KERNELS;
D O I
10.1146/annurev-statistics-040522-115238
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Manifold learning (ML), also known as nonlinear 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, denoise, and interpret them. This review presents the underlying principles of ML, its representative methods, and their statistical foundations, all 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.
引用
收藏
页码:393 / 417
页数:25
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