2D-NPP: An Extension of Neighborhood Preserving Projection

A novel method to reduce dimensionality for face representation and recognition was proposed in this paper. This technique attempts to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry. It is derived from ONPP. The main difference between ONPP and 2d-NPP is that the latter does not change the input images to vectors, and works well under the undersampled size situation. First, an "affinity" graph was built for the data in 2D- NPP, in a way that is similar to the method of LLE. While the input was mapped to the reduced spaces implicitly in LLE, 2D-NPP employs an explicit linear mapping between the two. So it is trivial to handle the new data just by a simple linear transformation. We also show that is easy to apply the method in a supervised setting. Numerical experiments are reported to illustrate the performance of 2D-NPP and to compare it with a few competing methods.