Personal authentication based on generalized symmetric max minimal distance in subspace

We introduce an improved classification algorithm based on the concept of symmetric maximized minimal distance in subspace (SMMS). Given the training data of authentic samples and imposter samples in the feature space, our previous approach, SMMS, tried to identify a subspace in which all the authentic samples were projected onto the origin and all the imposter samples were far away from the origin. The optimality of the subspace was determined by maximizing the minimal distance between the origin and the imposter samples in the subspace. The generalized SMMS relaxes the constraint of fitting all the authentic samples to the origin in the subspace to achieve the optimality and considers the optimal direction of the linear support-vector machines (SVM) as a feasible solution in our optimization procedure to guarantee that our result is no worse than the linear SVM. We present a procedure to achieve such optimality and to identify the subspace and the decision boundary. Once the subspace is trained, the verification procedure is simple since we only need to project the test sample onto the subspace and compare it against the decision boundary. Using face authentication as an example, we show that the proposed algorithm outperforms the linear classifier based on SMMS and SVM. The proposed algorithm also applies to multimodal feature spaces. The features can come from any modalities, such as face images, voices, fingerprints, etc.