For deep ordinal classification, learning a well-structured feature space specific to ordinal classification is helpful to properly capture the ordinal nature among classes. Intuitively, when Euclidean distance metric is used, an ideal ordinal layout in feature space would be that the sample clusters are arranged in class order along a straight line in space. However, enforcing samples to conform to a specific layout in the feature space is a challenging problem. To address this problem, in this paper, we propose a novel Constrained Proxies Learning (CPL) method, which can learn a proxy for each ordinal class and then adjusts the global layout of classes by constraining these proxies. Specifically, we propose two kinds of strategies: hard layout constraint and soft layout constraint. The hard layout constraint is realized by directly controlling the generation of proxies to force them to be placed in a strict linear layout or semicircular layout (i.e., two instantiations of strict ordinal layout). The soft layout constraint is realized by constraining that the proxy layout should always produce unimodal proxy-to-proxies similarity distribution for each proxy (i.e., to be a relaxed ordinal layout). Experiments show that the proposed CPL method outperforms previous deep ordinal classification methods under the same setting of feature extractor.

翻译：对于深度序数分类，学习一个专门针对序数分类的结构化特征空间有助于正确捕捉类别间的序数性质。直观上，当使用欧氏距离度量时，特征空间中的理想序数布局应是样本簇沿空间中的一条直线按类别顺序排列。然而，强制样本在特征空间中符合特定布局是一个具有挑战性的问题。为解决这一问题，本文提出了一种新颖的约束代理学习（CPL）方法，该方法可为每个序数类别学习一个代理，然后通过约束这些代理来调整类别的全局布局。具体而言，我们提出了两种策略：硬布局约束和软布局约束。硬布局约束通过直接控制代理的生成来实现，迫使它们被放置在严格的线性布局或半圆形布局中（即严格序数布局的两种实例化）。软布局约束通过约束代理布局，使得每个代理的代理间相似度分布总是呈现单峰形态（即成为松弛的序数布局）来实现。实验表明，在相同的特征提取器设置下，所提出的CPL方法优于以往的深度序数分类方法。