A new face recognition method via semi-discrete decomposition for one sample problem

Fisher linear discriminant analysis (FLDA) is a popular approach which has been widely used for feature extraction in face recognition tasks. FLDA is seeking optimal projection vectors by maximizing the ratio of between-class scatter matrices vs. within-class scatter matrices. However, the within-class scatter matrices cannot be calculated directly when one training sample each object is available. In this case, image decomposition plays an important role in the reconstructed within-class scatter matrices. So, the performance of image decomposition is crucial. In this paper, a based on semi-discrete decomposition (SDD) method is proposed to solve single training sample image per person problem. First, the original single image and its transpose are calculated via using SDD method in the training set. Then, the within-class scatter matrices are constituted by using the original image and its two approximation images of each person. And meanwhile, the optimal projection vectors are obtained via the FLDA algorithm in the new training set. Finally, we use the nearest neighbor classifier to complete the final classification. The performance of proposed method is evaluated on ORL, Yale and FERET databases. The experimental results show that the proposed method is outperforms singular value decomposition (SVD)-based and QR decomposition with column pivoting (QRCP)-based methods in terms of recognition rates.