Abstract: In order to construct the high-quality graph which can reflect the intrinsic structure of highdimensional data，we propose a novel dimensionality reduction algorithm named DＲAG ( Dimensionality Ｒeduction based on Adaptive Graphs) ． Compared with other graph-based dimensionality reduction algorithms，the proposed DＲAG algorithm avoids the problem of parameter selection in the traditional k nearest neighbors or ε-ball neighborhood criterions and constructs sparse and superior adaptive graphs，taking the local information and noises of input data． The LPP ( Locality Preserving Projection) is applied to acquire a projection matrix，which describes the intrinsic structure of high-dimensional data accurately． Finally，we achieve the purpose of dimensionality reduction． In order to evaluate the performance of the proposed algorithm， we perform classification and clustering experiments on four image databases ( CMU PIE，Extended YaleB，OＲL and COIL 20) ，the experimental results show that the proposed algorithm outperforms some other methods in term of classification and clustering accuracy．

Key words: high-dimensional data, dimensionality reduction, graph construction, adaptive graphs