A Non-Iterative Method for the Difference of Means on the Lie Group of Symmetric Positive-Definite Matrices

• Published in: Mathematics (Basel) Vol. 10; no. 2; p. 255
• Main Authors: Duan, Xiaomin, Ji, Xueting, Sun, Huafei, Guo, Hao
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2022
• Subjects: Algebra; Algorithms; Cluster analysis; Clustering; differential geometry; Euclidean geometry; Invariants; Iterative methods; Lie group of symmetric positive-definite matrices; Lie groups; log-Euclidean metric; Logarithms; Mathematical analysis; Mathematics; Matrices (mathematics); mean matrix; Noise; point cloud denoising; Vector quantization

A non-iterative method for the difference of means is presented to calculate the log-Euclidean distance between a symmetric positive-definite matrix and the mean matrix on the Lie group of symmetric positive-definite matrices. Although affine-invariant Riemannian metrics have a perfect theoretical f...