In this paper, several two-dimensional extensions of principal component analysis (PCA) and linear discriminant analysis (LDA) techniques has been applied in a lossless dimensionality reduction framework, for face recognition application. In this framework, the benefits of dimensionality reduction were used to improve the performance of its predictive model, which was a support vector machine (SVM) classifier. At the same time, the loss of the useful information was minimized using the projection penalty idea. The well-known face databases were used to train and evaluate the proposed methods. The experimental results indicated that the proposed methods had a higher average classification accuracy in general compared to the classification based on Euclidean distance, and also compared to the methods which first extracted features based on dimensionality reduction technics, and then used SVM classifier as the predictive model.