A novel unsupervised feature extraction based on image matrix

By the idea of manifolds learning, this paper presents a new method of dimensionality reduction of high dimensional data. The trait of the method is to exploit image matrixes to directly construct the local scatter matrix and the nonlocal scatter matrix. Its discriminant criterion function is characterized by maximizing the difference between the nonlocal scatter and the local scatter after the samples are projected. The new method is called the two-dimensional marginal discriminant projection (2DMDP). The new discriminant criterion is similar to the maximum margin criterion in form. The criterion main purpose is to find a projection direction (i.e. projection axes) that simultaneously maximizes the nonlocal scatter of projected sample, and minimizes the local scatter of projected sample. The experimental results on YALE face database and ORL face database show that the proposed method outperforms LPP and UDP in terms of recognition rate, and even outperforms LDA when the training sample size per class is small.