According to the widely use of mobile payment, e.g., Apply pay, personal authentication (PA) on smart phones plays the crucial role in many commercial services. Rather than the password-based approaches, biometric features are more stable and secure than passwords to avoid the lost or forgetfulness of passwords in PA. Moreover, they also prevent the steal or duplication risk because of their uniqueness. When we use smart phones as the payment devices, facial features are the most user-friendly biometric feature because of the build-in camera. However, we have to face on the small training sample problem for face verification. Collecting mass training samples is an inconvenient task for face verification. In order to solve the low verification rate problem due to few training samples, manifold learning and biased discriminant analysis are integrated for face verification. Project face images with a manifold distribution from high dimensional spaces to low dimensional feature spaces increases the rates and decreases feature dimensions. Meanwhile, the distribution of positive samples is considered for the within-class scatter, while the between class scatter is calculated using negative samples in the biased discriminant analysis. The reduced feature space is more suitable for verification task.
In this figure, manifold learning and biased discriminant analysis are illustrated. Here, the rectangles, circles and stars denote the face images of various people. The same shapes represent the face images of same person. The green symbols denote the positive samples, while the symbols in red color denote the negative samples. The goal of this algorithm is to reduce the feature dimensions for minimizing the distances between two positive samples and maximizing the distances between positive and negative samples.