Nonnegative representation based discriminant projection for face recognition
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ORIGINAL ARTICLE
Nonnegative representation based discriminant projection for face recognition Chao Zhang1 · Huaxiong Li1,2 · Chunlin Chen1,2 · Xianzhong Zhou1,2 Received: 1 May 2020 / Accepted: 7 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 𝓁1-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. Keywords Discriminant projection · Face recognition · Nonnegative representation · Unsupervised dimensionality reduction
1 Introduction The data in real world is usually in high dimension (e.g., images, videos and texts) and it may cause the so-called “curse of dimensionality” problem for pattern analysis [1–3]. Dimensionality Reduction (DR) provides an effective way to deal with such high-dimensional data and greatly improves the computational efficiency. One of the fundamental tasks of DR is to find an appropriate projection matrix such that the original high dimensional data can be projected into * Huaxiong Li [email protected] Chao Zhang [email protected] Chunlin Chen [email protected] Xianzhong Zhou [email protected] 1
Department of Control and Systems Engineering, Nanjing University, Nanjing 210093, China
Research Center for Novel Technology of Intelligent Equipment, Nanjing University, Nanjing 210093, China
2
a low-dimensional space. It can be performed in three ways: supervised [4–7], semi-supervised [8, 9] and unsupervised [10–13], according to whether the label information of data is involved in learning process. The well-known supervised DR methods include Linear Discriminant Analysis (LDA) [14], Marginal Fisher Analysis (MFA) [15], and their various variants [4–6, 16, 17]. Most of these supervised methods attempt to minimize the intra-class scatter and maximize the inter-class scatter in feature space, in which the label information is indispensable. However, in real-world, it is difficult and expensive to
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