Locally linear representation Fisher criterion

In this paper, a novel supervised dimensionality reduction method based on LLE is put forward, which is titled locally linear representation Fisher criterion (LLRFC). In the proposed LLRFC, the class information of the original data has been fully considered, according to which an inter-class graph and an intra-class graph can be well modeled respectively. Meanwhile, the neighborhoods in the inter-class graph consist of samples with various labels and the neighborhoods in the intra-graph are just composed of points sampled from the same class. Then the least locally linear representation technique is introduced to optimize the reconstruction weights in both graphs. At last, the Fisher criterion with maximum inter-class scatter and minimum intra-class scatter is reasoned. Experiments on some benchmark face data sets have been conducted and the results validate the proposed method's performance.