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

页码：279 / 295

页数：17

共 50 条

[11] Fedosov connections on Kahler symmetric manifolds and trace density computation
Tamarkin, DE
JOURNAL OF DIFFERENTIAL GEOMETRY, 1998, 50 (02) : 387 - 413
[12] On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds
Isidro, Jose E. M.
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2007, 5 (04): : 696 - 709
[13] INTRINSIC SHAPE ANALYSIS: GEODESIC PCA FOR RIEMANNIAN MANIFOLDS MODULO ISOMETRIC LIE GROUP ACTIONS REJOINDER
Huckemann, Stephan
Hotz, Thomas
Munk, Axel
STATISTICA SINICA, 2010, 20 (01) : 84 - 100
[14] INTRINSIC SHAPE ANALYSIS: GEODESIC PCA FOR RIEMANNIAN MANIFOLDS MODULO ISOMETRIC LIE GROUP ACTIONS COMMENT
Patrangenaru, Vic
STATISTICA SINICA, 2010, 20 (01) : 79 - 84
[15] Density estimation on the spaces of symmetric and rectangular matrices
Chikuse, Y
LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 264 : 265 - 290
[16] Kernel Density Estimation on Riemannian Manifolds: Asymptotic Results
Guillermo Henry
Daniela Rodriguez
Journal of Mathematical Imaging and Vision, 2009, 34 : 235 - 239
[17] Kernel Density Estimation on Riemannian Manifolds: Asymptotic Results
Henry, Guillermo
Rodriguez, Daniela
JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2009, 34 (03) : 235 - 239
[18] Actions of Lie Groups and Lie Algebras on Manifolds
Hirsch, M. W.
CELEBRATION OF THE MATHEMATICAL LEGACY OF RAOUL BOTT, 2010, 50 : 69 - 78
[19] Nonparametric density estimation for symmetric distributions by contaminated data
Maiboroda, Rostyslav
Sugakova, Olena
METRIKA, 2012, 75 (01) : 109 - 126
[20] Nonparametric density estimation for symmetric distributions by contaminated data
Rostyslav Maiboroda
Olena Sugakova
Metrika, 2012, 75 : 109 - 126

← 1 2 3 4 5 →