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.

降维（DR）已被广泛用于处理高维数据，并且在缓解所谓的“维数诅咒”中发挥着重要作用。在本文中，我们提出了一种新的无监督的DR方法在人脸识别中的应用，即基于非负表示的判别投影（NRDP）。与其他保留局部性或全局性的DR方法不同，NRDP着重于数据点的局部性和非局部性，并且通过最大化非局部散布和最小化局部散布来学习判别投影。在NRDP中设计了一个非负表示模型，以发现数据的局部结构和非局部结构。的\（\ ELL _1 \）-norm在非负表示中用作度量以增强抗噪声的鲁棒性，并提出了一种迭代算法来求解优化模型。在标签信息不可用的情况下，NRDP能够学习具有较大的类间或子空间散点以及较小的类内散点的特征，从而显着提高了表示能力和辨别力。在几个流行的面部数据集上的实验结果证明了我们提出的方法的有效性。