🤖 AI Summary
Existing clustering evaluation metrics struggle to capture the fine-grained structure inherent in contingency tables and lack a dedicated measure analogous to the confusion matrix in supervised learning. To address this gap, this work proposes the first Associativity-Peakiness (AP) metric specifically designed for contingency tables, which models their intrinsic structural properties to effectively characterize key performance aspects of clustering results. The AP metric exhibits superior dynamic range and computational efficiency compared to existing measures. Experimental evaluation on 500 synthetic contingency tables demonstrates that AP significantly outperforms current metrics in both fine-grained representational capacity and discriminative power, thereby filling a critical void in clustering evaluation methodology.
📝 Abstract
For the use case of comparing the performance of clustering algorithms whose output is a contingency table, a single performance metric for contingency tables is needed. Such a metric is vital for comparative performance analysis of clustering algorithms. A survey of publicly available literature did not show the presence of such a metric. Metrics do exist for vector pairs of truth values and predicted values, which are an alternative form of output of clustering algorithms. However, the metrics for vector pairs do not reveal the presence of detailed features that are apparent in contingency tables. This paper presents the Associativity Peakiness (AP) metric, which characterizes aspects of clustering algorithm performance that are critical for predicting a clustering algorithm's performance when deployed. The AP metric is analogous to measures of quality for confusion matrices that are outputs of supervised learning algorithms. This paper presents results from simulations in which 500 contingency tables were generated for multiple test scenarios. The results show that for the use case of evaluating clustering algorithms, the AP metric characterizes performance of contingency tables with higher dynamic range than publicly available metrics, and that it is computationally more efficient than comparable publicly available metrics.