提出加权MCC，让分类器在重要样本上表现更好时得分更高。
Weighted MCC: A Robust Measure of Multiclass Classifier Performance for Observations with Individual Weights
- 基于Pearson相关系数改进，为每个样本引入权重
- 权重变化≤ε时，度量值变化≤ε（二分类）或ε²（多分类）
- 适合需要关注关键样本的医疗、金融等场景
现有分类性能评估指标无法处理样本权重差异。本文提出用于二分类的加权皮尔逊-马修斯相关系数（MCC）及相应的多分类加权度量。加权MCC取值范围为-1到1，且对高权重样本表现优异的分类器评分更高，能有效区分整体性能相似但侧重不同样本的模型。理论证明：在二分类中，权重变动不超过ε时，度量值变化不超过ε；多分类中变化不超过ε²。实验表明，加权度量可清晰识别在高权重样本上表现更好的分类器，而原始未加权度量对此完全不敏感。
原文摘要 · Abstract (English)
Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new weighted Pearson-Matthews Correlation Coefficient (MCC) for binary classification as well as weighted versions of related multiclass measures. The weighted MCC varies between $-1$ and $1$. But crucially, the weighted MCC values are higher for classifiers that perform better on highly weighted observations, and hence is able to distinguish them from classifiers that have a similar overall performance and ones that perform better on the lowly weighted observations. Furthermore, we prove that the weighted measures are robust with respect to the choice of weights in a precise manner: if the weights are changed by at most $ε$, the value of the weighted measure changes at most by a factor of $ε$ in the binary case and by a factor of $ε^2$ in the multiclass case. Our computations demonstrate that the weighted measures clearly identify classifiers that perform better on higher weighted observations, while the unweighted measures remain completely indifferent to the choices of weights.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。