Parameterless reconstructive discriminant analysis for feature extraction

Reconstructive discriminant analysis (RDA) is an effective dimensionality reduction method that can match well with linear regression classification (LRC). RDA seeks to find projections that can minimize the intra-class reconstruction scatter and simultaneously maximize the inter-class reconstruction scatter of samples. However, RDA needs to select the k heterogeneous nearest subspaces of each sample to construct the inter-class reconstruction scatter and it is very difficult to predefine the parameter k in practical applications. To deal with this problem, we propose a novel method called parameterless reconstructive discriminant analysis (PRDA) in this paper. Compared to traditional RDA, our proposed RDA variant cannot only fit LRC well but also has two important characteristics: (1) the performance of RDA depends on the parameter k that requires manual turning, while ours is parameter-free, and (2) it adaptively estimates the heterogeneous nearest classes for each sample to construct the inter-class reconstruction scatter. To evaluate the performance of the proposed algorithm, we test PRDA and some other state-of-the-art algorithms on some benchmark datasets such as the FERET, AR and ORL face databases. The experimental results demonstrate the effectiveness of our proposed method.