Dimensionality reduction is an effective method for treating high dime nsional data. Subspace learning is widely used in pattern recognition due to its low complexit y and desirable performance,and most of the subspace learning algorithms can be plugged into the graph embedding framework.Sparse representation gains much attention in recent years, and has wide applications in signal processing and pattern recognition,but it is time consum ing.Based on sparse representation,collaborative representation is proposed.Compared with spa rse representation,collaborative representation has a tractable closed-form solution and better discriminative power,so it i s widely used in data representation and visual classification.In this paper,the graph embedding is formulated as a manner of collaborative representation.By mini mizing the intra-class reconstructive error scatter and maximizing the inter-class recons tructive error scatter, a new graph embedding algorithm called reconstructive discriminant analysis is p roposed,and is applied in this regression model,then the solution is reduced to a generalized eigen-value problem,which to some extent can avoid the singularity problem in subspace lear ning algorithms. Various experiments on face recognition demonstrate the correctiveness and effec tiveness of the proposed algorithm.