LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT)

Abstract

Most of the existing local linear embedding algorithms assume that the original data set is located in Euclidean space, but in reality almost all the original space is non-Euclidean space. Aiming at the problem that Euclidean space cannot effectively describe the nonlinear structure of the data and affects the performance of the feature extraction of the local linear embedding（LLE） algorithm, a local linear embedding algorithm based on the parameter matrix measurement on a symmetric positive definite（SPD-PMM-LLE） manifold is proposed. First, in order to find a suitable measurement method on the symmetric positive definite manifold to improve the performance of the algorithm, an efficient Riemann space metric learning method is introduced. The parameter matrix obtained by learning transforms the original manifold to a new and distinguishable manifold. Then use the locally linear embedding algorithm to mine the salient features. Finally, the efficiency of this method is verified by experimental results on multiple bearing data sets.

Keywords

• Feature extraction;Symmetric positive definite manifold;Local linear embedding;Riemann space metric learning;Euclidean space