Lie PCA: Density estimation for symmetric manifolds

被引：0
|
作者：
Cahill, Jameson [1 ]
Mixon, Dustin G. [2 ,3 ]
Parshall, Hans [4 ]
机构：
[1] Univ North Carolina Wilmington, Dept Math & Stat, Wilmington, NC USA
[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
[3] Ohio State Univ, Translat Data Analyt Inst, Columbus, OH 43210 USA
[4] Western Washington Univ, Dept Math, Bellingham, WA USA
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2023年 / 65卷
关键词：
Density estimation; Manifold learning; Principal component analysis;
D O I：
10.1016/j.acha.2023.03.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce an extension to local principal component analysis for learning symmetric manifolds. In particular, we use a spectral method to approximate the Lie algebra corresponding to the symmetry group of the underlying manifold. We derive the sample complexity of our method for various manifolds before applying it to various data sets for improved density estimation.(c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：279 / 295
页数：17
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