Abstract
Dimensionality reduction (DR) has been widely used to deal with high-dimensional data, and plays an important role in alleviating the so-called “curse of dimensionality”. In this paper, we propose a novel unsupervised DR method with applications to face recognition, i.e., Nonnegative Representation based Discriminant Projection (NRDP). Different with other locality or globality preserving DR methods, NRDP focuses on both locality and nonlocality of data points and learns a discriminant projection by maximizing the nonlocal scatter and minimizing the local scatter simultaneously. A nonnegative representation model is designed in NRDP to discover the local structure and nonlocal structure of data. The $$\ell _1$$ -norm is used as metric in nonnegative representation to enhance the robustness against noises, and an iterative algorithm is presented to solve the optimization model. NRDP is able to learn features with large inter-class or subspace scatter and small intra-class scatter in the case that label information is unavailable, which significantly improves the representation power and discrimination. Experimental results on several popular face datasets demonstrate the effectiveness of our proposed method.
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