Revisiting Silhouette Aggregation
This work addresses a methodological issue in clustering evaluation for researchers and practitioners, but it is incremental as it revisits and refines an existing measure.
The paper tackles the sensitivity of the typical micro-averaging strategy for Silhouette coefficient to cluster imbalance and shows that macro-averaging is more robust, with a proposed per-cluster sampling method improving robustness in experiments on eight real-world datasets.
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 (micro) averaged into a single value. An alternative path, however, that is rarely employed, is to average first at the cluster level and then (macro) average across clusters. As we illustrate in this work with a synthetic example, the typical micro-averaging strategy is sensitive to cluster imbalance while the overlooked macro-averaging strategy is far more robust. By investigating macro-Silhouette further, we find that uniform sub-sampling, the only available strategy in existing libraries, harms the measure's robustness against imbalance. We address this issue by proposing a per-cluster sampling method. An experimental study on eight real-world datasets is then used to analyse both coefficients in two clustering tasks.