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提出一种新的基于流形学习的数据降维及特征提取方法:局部保持PCA算法(LPPCA).通过在PCA的优化目标中融入流形学习的思想,不仅使投影得到的低维空间和原始样本空间具有相似的全局结构,并且保持了相似的局部近邻结构,克服了传统PCA方法只关注全局结构特征而忽略局部流形特征的缺陷,同时给出了LPPCA在故障检测中的应用方法.S-Curve和Swiss-roll曲面数值仿真和TE过程仿真验证了算法的有效性和优越性.
This paper proposes a new method of data dimensionality reduction and feature extraction based on manifold learning: Local Preserving PCA Algorithm (LPPCA). By incorporating the idea of manifold learning into the optimization goal of PCA, not only the low dimensional space obtained by projection and the original The sample space has a similar global structure and maintains a similar local neighbors structure, overcomes the defects that the traditional PCA method only focuses on the global structure features and ignores the local manifold features, and also gives the application of LPPCA in fault detection.S The simulation and TE simulation of Curve and Swiss-roll surfaces validate the effectiveness and superiority of the proposed algorithm.