In this work, several 2D extensions of the principal component analysis (PCA) and linear discriminant analysis (LDA) techniques were applied in a lossless dimensionality reduction framework for face recognition applications. 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 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 obtained indicated that the proposed methods had a higher average classification accuracy, in general, compared to the classification based on the Euclidean distance, and also compared to the methods that first extracted the features based on the dimensionality reduction technics, and then used the SVM classifier as the predictive model.