Dictionary-based classification has been promising in knowledge discovery from image data, due to its good performance and interpretable theoretical system. Dictionary learning effectively supports both small- and large-scale datasets, while its robustness and performance depends on the atoms of the dictionary most of the time. Empirically, using a large number of atoms is helpful to obtain a robust classification, while robustness cannot be ensured when setting a small number of atoms. However, learning a huge dictionary dramatically slows down the speed of classification, which is especially worse on the large-scale datasets. To address the problem, we propose a Fast and Robust Dictionary-based Classification (FRDC) framework, which fully utilizes the learned dictionary for classification by staging - and -norms to obtain a robust sparse representation. The new objective function, on the one hand, introduces an additional -norm term upon the conventional -norm optimization, which generates a more robust classification. On the other hand, the optimization based on both - and -norms is solved in two stages, which is much easier and faster than current solutions. In this way, even when using a limited size of dictionary, which makes sure the classification runs very fast, it still can gain higher robustness for multiple types of image data. The optimization is then theoretically analyzed in a new formulation, close but distinct to elastic-net, to prove it is crucial to improve the performance under the premise of robustness. According to our extensive experiments conducted on four image datasets for face and object classification, FRDC keeps generating a robust classification no matter whether using a small or large number of atoms. This guarantees a fast and robust dictionary-based image classification. Furthermore, when simply using deep features extracted via some popular pre-trained neural networks, it outperforms many state-of-the-art methods on the specific datasets.

中文翻译：

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图像数据的快速和稳健的基于字典的分类

基于字典的分类由于其良好的性能和可解释的理论体系，在图像数据的知识发现中一直很有前景。字典学习有效地支持小型和大型数据集，而其鲁棒性和性能在大多数情况下取决于字典的原子。根据经验，使用大量原子有助于获得稳健的分类，而在设置少量原子时无法保证稳健性。然而，学习一个庞大的字典会大大减慢分类的速度，这在大规模数据集上尤其糟糕。为了解决这个问题，我们提出了一个快速和鲁棒的基于字典的分类（FRDC）框架，它充分利用学习的字典进行分类。 - 和 -norms 以获得稳健的稀疏表示。一方面，新的目标函数引入了一个额外的 - 常规术语 -norm 优化，生成更稳健的分类。另一方面，基于两者的优化 - 和 -norms 分两个阶段解决，这比当前的解决方案更容易和更快。这样，即使使用有限大小的字典，确保分类运行速度非常快，它仍然可以获得对多种类型图像数据的更高鲁棒性。然后在一个新的公式中对优化进行理论上的分析，与弹性网络接近但又不同，以证明在鲁棒性的前提下提高性能是至关重要的。根据我们对四个用于面部和对象分类的图像数据集进行的广泛实验，无论使用少量还是大量原子，FRDC 都会不断生成稳健的分类。这保证了快速和健壮的基于字典的图像分类。此外，当简单地使用通过一些流行的预训练神经网络提取的深度特征时，