提出新归一化方法，分离分类错误中相似性与分布偏差的影响
On the Normalization of Confusion Matrices: Methods and Geometric Interpretations
- 用迭代比例拟合实现双随机归一化，解耦类别相似性与分布偏差
- 能更准确诊断模型错误来源，指导针对性优化
- 揭示归一化与内部类别表征的几何关系，提升可解释性
混淆矩阵是评估分类器的常用工具，可揭示各类别的错误模式。在异质设置下，其数值受两类主要因素影响：类别相似性（模型混淆两类的难易程度）和分布偏移（训练与测试集分布不均）。然而，混淆矩阵值混合了这两者的影响，难以区分各自贡献。为此，我们引入基于迭代比例拟合的双随机归一化，作为行/列归一化的推广。该方法能恢复类别相似性的底层结构，有效解耦误差来源，使模型行为诊断更精准，并支持针对性改进。我们还发现，标准与双随机归一化在模型内部类别表征空间中具有几何对应关系，为归一化所揭示的信息提供了深层理解。
原文摘要 · Abstract (English)
The confusion matrix is a standard tool for evaluating classifiers by providing insights into class-level errors. In heterogeneous settings, its values are shaped by two main factors: class similarity -- how easily the model confuses two classes -- and distribution bias, arising from skewed distributions in the training and test sets. However, confusion matrix values reflect a mix of both factors, making it difficult to disentangle their individual contributions. To address this, we introduce bistochastic normalization using Iterative Proportional Fitting, a generalization of row and column normalization. Unlike standard normalizations, this method recovers the underlying structure of class similarity. By disentangling error sources, it enables more accurate diagnosis of model behavior and supports more targeted improvements. We also show a correspondence between confusion matrix normalizations and the model's internal class representations. Both standard and bistochastic normalizations can be interpreted geometrically in this space, offering a deeper understanding of what normalization reveals about a classifier.
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