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.
A novel dimensionality reduction and feature extraction method based on manifold learning, locally preserving principal component analysis(LPPCA) is proposed. In order to overcome the defects that the traditional PCA can only keep the structure in global and can not maintain the manifold structure in local, the idea of locality preserving is incorporated into the optimization goals of the PCA. The fault detection based on LPPCA is researched. The validity and superiority of the LPPCA are verified by the S-Curve numerical simulation, Swiss-roll surface numerical simulation and TE process simulation.