A series of feature extraction algorithms based on locality preserving projection were proposed. Principal Component Analysis (PCA) algorithm must be firstly used for high-dimensional samples when these algorithms are applied in such as face recognition. Therefore，using unsupervised discriminant analysis algorithm as the theoretical basis，a direct unsupervised orthogonal locality preserving algorithm is proposed. Through the corresponding matrix decomposition according to the properties of the Laplace matrix, the projection matrix can be directly extracted from the original high-dimensional space without first using PCA algorithm processing and the proposed algorithm can solve the small sample size problem. To further improve the recognition performance, the orthogonal projection matrix obtained based on QR decomposition is given. Experimental results on face database and palmprint database demonstrate the effectiveness of the proposed method.