关键词: 局部线性嵌入, 维数约减, 高维数据, 离群点, k-最近邻

Abstract: Due to the fact that data distribution is sparse in the high dimensional space, it can’t achieve desired effect in the high dimensional space by using the conventional methods. This paper proposes an Outlier detection method based on Locally Linear Embedding（OLLE）. In the proposed OLLE method, it establishes an effective rough set model which aims to retain the local lineal structure of samples in the lower approximation. Meanwhile, it constructs two weights to keep the local neighbor structure of all points and guarantee outliers away from normal points when high dimensional points are mapped into a low dimensional space. At last, this paper uses a minimum spanning tree-inspired k-nearest neighbors method to detect the outliers in the low dimensional space. A series of simulation experiments show that the OLLE can better keep the local geometric structure, and outliers are detected effectively in the low dimensional space.

Key words: locally linear embedding, dimensionality reduction, high dimensional data, outlier, k-nearest neighbors