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Multilinear Discriminant Analysis for Face Recognition

机译:人脸识别的多线性判别分析

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There is a growing interest in subspace learning techniques for face recognition; however, the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma. In this paper, we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order. First, we propose a discriminant tensor criterion, whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction. Then, a novel approach, called k-mode optimization, is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions. We call this algorithm multilinear discriminant analysis (MDA), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes, 2) for classification problems involving higher order tensors, the MDA algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem, and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k-mode optimization. We provide extensive experiments on ORL, CMU PIE, and FERET databases by encoding face images as second- or third-order tensors to demonstrate that the proposed MDA algorithm based on higher order tensors has the potential to outperform the traditional vector-based subspace learning algorithms, especially in the cases with small sample sizes
机译:对用于面部识别的子空间学习技术的兴趣日益浓厚。然而,数据空间的过大维度常常使算法陷入维度困境的诅咒中。在本文中,我们提出了一种通过将图像对象编码为二阶甚至更高阶的一般张量来解决监督降维问题的新颖方法。首先,我们提出了一个判别张量准则,从而导出多个相互关联的低维判别子空间用于特征提取。然后,提出了一种称为k模式优化的新颖方法,通过沿不同张量方向展开张量来迭代地学习这些子空间。我们将此算法称为多线性判别分析(MDA),它具有以下特征:1)多个相互关联的子空间可以协作来区分不同的类别,2)对于涉及高阶张量的分类问题,MDA算法可以避免维数困境的诅咒,减轻了样本量小的问题,并且3)由于k模式优化中数据尺寸的减少,在很大程度上减少了学习阶段的计算成本。通过将人脸图像编码为二阶或三阶张量,我们在ORL,CMU PIE和FERET数据库上提供了广泛的实验,以证明基于高阶张量的MDA算法具有优于传统的基于向量的子空间学习算法的潜力。 ,尤其是在样本量较小的情况下

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