中文摘要：

目前的局部保持投影算法（Locality and preserving projections,LPP）只考虑样本点的近邻矩阵,但是对于那些处于与该样本点距离最远处的样本特性并没有做出研究,这些最远处的样本同样具有描述数据结构信息的功能。为了更好地保留数据结构信息,在考虑样本的近邻点分布的同时分析其最远处的样本点分布,即同时考虑样本的＂近邻矩阵＂和＂最远矩阵＂,通过二者结合实现数据维数的约简,由此提出基于最近最远距离的保持投影算法（Nearest and farthest distance preserving projections,NFDPP）。将该算法运用于发动机失火状态的仿真数据及实际测试中,通过与主成分分析（Principal component analysis,PCA）、LPP、邻域保持嵌入（Neighborhood preserving embedding,NPE）、线性判别分析（Linear discriminant analysis,LDA）等算法的对比,得出NFDPP算法能够得到更低的识别错误率曲线,证明所提出的NFDPP算法能够有效地识别发动机失火故障状态。

英文摘要：

Most of manifold learning algorithms such as locality and preserving projection（LPP） only concern the neighborhood samples and ignore those farthest ones, which may lead to missing out the global information. Therefore, a novel algorithm, named nearest and farthest distance preserving projection（NFDPP）, is proposed to explore the relationship between the sample and its farthest samples as well as that between it and its nearest neighbors simultaneously. Dimension reduction can be performed by NFDPP with the ＂nearest neighbor matrix＂ and ＂farthest distance matrix＂. Simulation and experiments on the engine misfire are conducted. Experiments results demonstrate that, comparing with principal component analysis（PCA）, LPP, neighborhood preserving embedding（NPE） and linear discriminant analysis（LDA）, the NFDPP can recognize the engine misfire fault effectively.