This work proposes a novel approach to the deep hierarchical classification task, i.e., the problem of classifying data according to multiple labels organized in a rigid parent-child structure. It consists in a multi-output deep neural network equipped with specific projection operators placed before each output layer. The design of such an architecture, called lexicographic hybrid deep neural network (LH-DNN), has been possible by combining tools from different and quite distant research fields: lexicographic multi-objective optimization, non-standard analysis, and deep learning. To assess the efficacy of the approach, the resulting network is compared against the B-CNN, a convolutional neural network tailored for hierarchical classification tasks, on the CIFAR10, CIFAR100 (where it has been originally and recently proposed before being adopted and tuned for multiple real-world applications) and Fashion-MNIST benchmarks. Evidence states that an LH-DNN can achieve comparable if not superior performance, especially in the learning of the hierarchical relations, in the face of a drastic reduction of the learning parameters, training epochs, and computational time, without the need for ad-hoc loss functions weighting values.

翻译：本研究提出了一种新颖的深度层次分类方法，旨在解决依据严格父子结构组织的多标签数据分类问题。该方法采用配备特定投影算子的多输出深度神经网络，在每个输出层前放置投影算子。通过融合词典序多目标优化、非标准分析与深度学习等不同且相距较远的研究领域工具，实现了称为词典序混合深度神经网络（LH-DNN）的架构设计。为评估该方法的有效性，将所构建网络与专为层次分类任务设计的卷积神经网络B-CNN在CIFAR10、CIFAR100（该数据集最初于近期提出，后经调整应用于多个实际场景）及Fashion-MNIST基准数据集上进行对比。实验结果表明，LH-DNN在显著减少学习参数量、训练周期和计算时间的前提下，无需特定损失函数权重调整，即可取得相当甚至更优的性能，尤其在层次关系学习方面表现突出。