Dimensionality Reduction Based on Supervised Slow Feature Analysis for Face Recognition

Slow feature analysis (SFA) is motivated by biological model to extracts slowly varying feature from a quickly varying input signal. However, traditional slow feature analysis is an unsupervised method to extract slow or invariant feature and cannot be directly applied on the data set without an obvious temporal structure, i.e. face databases. In this paper, we propose a supervised slow feature analysis to do dimensionality reduction for face recognition. First, a new criterion is developed to construct a Pseudo-time series for data sets without an obvious temporal structure. Then, the first-order derivative at each point in the Pseudo-time series is computed in form of vectors. At last we construct the objective function of SSFA that ensures the secondary moment of first-order derivative as small as possible in the embedding space. SSFA is able to extract the invariant feature for each class and preserve the local structure in embedding space simultaneously. Experimental results on the Yale, ORL, AR, and FERET face databases show the effectiveness of the proposed algorithm.