对称正定流形上参数矩阵度量的局部线性嵌入算法  

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

作　　者：刘庆强[1] 何红凯 郑长敏 孙艳茹 刘子轩 LIU QingQiang;HE HongKai;ZHENG ChangMin;SUN YanRu;LIU ZiXuan(School of Electrical Information Engineering,Northeast Petroleum University,Daqing 163000,China;Institute of Geology,Daqing Yushulin Oilfield Development Co.,Ltd􀆰,Daqing 163000,China)

机构地区：[1]东北石油大学电气信息工程学院,大庆163000 [2]大庆榆树林油田开发有限责任公司地质研究所,大庆163000

出　　处：《机械强度》2022年第6期1307-1314,共8页Journal of Mechanical Strength

基　　金：国家重大科技专项(2017ZX05019-005);黑龙江自然科学基金项目(LH2019F004)资助。

摘　　要：现有的局部线性嵌入算法大部分假设原始数据集位于欧氏空间,但现实中几乎所有的原始空间都是非欧氏空间。针对欧氏空间无法有效地描述数据的非线性结构,影响局部线性嵌入算法的特征提取的性能问题,提出了一种对称正定流形上参数矩阵度量的局部线性嵌入算法。首先在对称正定流形上寻找一个合适的度量方法来提高该算法的性能,引入了一种高效的黎曼空间度量学习方法,通过学习得到的参数矩阵将原始流形变换到新的易区分的流形上。再利用局部线性嵌入算法挖掘显著特征。最后,通过在多个轴承数据集上的实验结果验证方法的高效性。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.

关 键 词：特征提取 对称正定流形 局部线性嵌入 黎曼空间度量学习 欧氏空间 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]