用多维阈值优化多分类模型，提升预测性能并提供新评估方式
Multiclass threshold-based classification and model evaluation
- 以几何视角替代软最大输出的概率解释，通过多维阈值决策
- 阈值调优使多个网络在不同数据集上性能均有提升
- 提出基于ROC云和距离点得分的新评估方法，适配模型后处理
本文提出一种基于阈值的多分类框架，将标准argmax规则推广为多维单纯形上的几何决策。该方法用多维阈值替代软最大输出的概率解释，使任何训练好的分类网络均可通过事后阈值调优进一步优化分类性能，类似二分类中的常规操作。实验表明，多维阈值调优在多种网络与数据集上均带来性能提升。此外，我们基于ROC云（单个多分类阈值产生的可达成的(FPR,TPR)点集合）构建了多分类ROC分析，并引入距离点(DFP)得分来汇总这些点至(0,1)的距离，形成对标准One-vs-Rest曲线的连贯替代方案，且与观察到的调优增益一致。
原文摘要 · Abstract (English)
In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the multidimensional simplex, where the classification depends on a multidimensional threshold. This change of perspective enables for any trained classification network an \textit{a posteriori} optimization of the classification score by means of threshold tuning, as usually carried out in the binary setting, thus allowing for a further refinement of the prediction capability of any network. Our experiments show indeed that multidimensional threshold tuning yields performance improvements across various networks and datasets. Moreover, we derive a multiclass ROC analysis based on \emph{ROC clouds} -- the attainable (FPR,TPR) operating points induced by a single multiclass threshold -- and summarize them via a \emph{Distance From Point} (DFP) score to $(0,1)$. This yields a coherent alternative to standard One-vs-Rest (OvR) curves and aligns with the observed tuning gains.
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