Deep Cascade Model-Based Face Recognition: When Deep-Layered Learning Meets Small Data

Lei Zhang, Ji Liu, Bob Zhang, David Zhang, Ce Zhu

Abstract: Sparse representation based classification (SRC), nuclear-norm matrix regression (NMR), and deep learning (DL) have achieved a great success in face recognition (FR). However, there still exist some intrinsic limitations among them. SRC and NMR based coding methods belong to one-step model, such that the latent discriminative information of the coding error vector cannot be fully exploited. DL, as a multi-step model, can learn powerful representation, but relies on large-scale data and computation resources for numerous parameters training with complicated back-propagation. Straightforward training of deep neural networks from scratch on small-scale data is almost infeasible. Therefore, in order to develop efficient algorithms that are specifically adapted for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">small-scale</i> data, we propose to derive the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deep</i> models of SRC and NMR. Specifically, in this paper, we propose an end-to-end deep cascade model (DCM) based on SRC and NMR with hierarchical learning, nonlinear transformation and multi-layer structure for corrupted face recognition. The contributions include four aspects. First, an end-to-end deep cascade model for small-scale data without back-propagation is proposed. Second, a multi-level pyramid structure is integrated for local feature representation. Third, for introducing nonlinear transformation in layer-wise learning, softmax vector coding of the errors with class discrimination is proposed. Fourth, the existing representation methods can be easily integrated into our DCM framework. Experiments on a number of small-scale benchmark FR datasets demonstrate the superiority of the proposed model over state-of-the-art counterparts. Additionally, a perspective that deep-layered learning does not have to be <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">convolutional neural network</i> with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">back-propagation</i> optimization is consolidated. The demo code is available in <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/liuji93/DCM</uri>