关键词: 局部线性嵌入, 流形学习, 降维, GRDLLE算法

Abstract: Euclidean distance is normally used to measure the similarity between samples in Localiy Linear Embedding algorithm（LLE）, But for some high dimensional data with low-dimensional manifold structure, Euclidean distance does not measure the relative position of two points in a manifold. A Local Linear Embedding algorithm based on Geodesic Rank-order Distance（GRDLLE） is proposed. Firstly, the algorithm approximates the geodesic distance between any two sample points by using the shortest path length to find the shortest path algorithm（Dijkstra algorithm）. Then the Rank-order distance is calculated for the similarity measurement of the LLE algorithm. GRDLLE, other improved LLE manifold learning algorithms and 2DPCA algorithm are compared on ORL and Yale data sets. The face recognition rate of data is improved after dimension-reduction using GRDLLE algorithm. The results show that the GRDLLE algorithm has good dimensional reduction effect.

Key words: locally linear embedding, manifold learning, dimensionality reduction, GRDLLE algorithm