Silhouette coefficient is an established internal clustering evaluation measure that produces a score per data point, assessing the quality of its clustering assignment. To assess the quality of the clustering of the whole dataset, the scores of all the points in the dataset are typically averaged into a single value, a strategy which we call as micro-averaging. As we illustrate in this work, by using a synthetic example, this micro-averaging strategy is sensitive both to cluster imbalance and outliers (background noise). To address these issues, we propose an alternative aggregation strategy, which first averages the silhouette scores at a cluster level and then (macro) averages the scores across the clusters. Based on the same synthetic example, we show that the proposed macro-averaged silhouette score is robust to cluster imbalance and background noise. We have conducted an experimental study showing that our macro-averaged variant provides better estimates of the ground truth number of clusters on several cases compared to the typical micro-averaged score.

翻译：轮廓系数是一种成熟的内部聚类评估度量，它为每个数据点生成一个分数，以评估其聚类分配的质量。为了评估整个数据集聚类的质量，通常将数据集中所有点的分数平均为一个单一值，我们将此策略称为微平均。正如我们在本工作中通过一个合成示例所展示的，这种微平均策略对聚类不平衡和异常值（背景噪声）都很敏感。为了解决这些问题，我们提出了一种替代的聚合策略，该策略首先在聚类级别上平均轮廓分数，然后在聚类之间进行（宏观）平均。基于相同的合成示例，我们展示了所提出的宏观平均轮廓分数对聚类不平衡和背景噪声具有鲁棒性。我们进行了一项实验研究，结果表明，与典型的微平均分数相比，我们的宏观平均变体在多个案例中能更好地估计真实聚类数量。