Linear regression based projections for dimensionality reduction

In graph embedding based dimensionality reduction methods, the number of K-nearest neighbors is usually needed to be manually chosen in high dimensional space. Graph construction by different number of K-nearest neighbor changes dramatically and seriously affects the performance of graph embedding based dimensionality reduction. How to automatically construct a graph is very important. In this paper, first, a discriminative L2-graph is investigated. It computes the edge weights using the class-specific samples and weighted ridge regression, avoiding manually choosing the K-nearest neighbors in traditional graph construction. Second, a discriminative L2-graph based dimensionality reduction method is proposed, named Linear Regression based Projections (LRP). LRP minimizes the ratio between the local compactness information and the total separability information to seek the optimal projection matrix. LRP is much faster than its counterparts, Sparsity Preserving Projections (SPP) and Collaborative Representation based Projections (CRP), since LRP is supervised and computes edge weights using class-specific samples while SPP and CRP are unsupervised and compute edge weights using all samples. The experimental results on benchmark face image databases show that the proposed LRP outperforms many existing representative linear dimensionality reduction methods.