Unsupervised Evaluation Metrics for Plane-based Clustering

Clustering is a pivotal subfield within machine learning, with the evaluation metrics holding particular significance. Many traditional evaluation metrics are mainly used to evaluate point-centered clustering models. With the development of clustering models, many excellent clustering models are based on the plane as the center, so the use of these metrics in the plane-based clustering models adopts these metrics which mislead to suitable clustering results. In this paper, we introduce unsupervised evaluation criteria for plane-based clustering. Because both point-based and plane-based clustering models share the common goal of dividing data points into multiple clusters to ensure high similarity within the same cluster and low similarity between different clusters. Hence, in terms of evaluation metrics, the only necessary modification is to transform the measurement of the distance between sample points and cluster centers from the original metric to the measurement of the distance between sample points and the center of the plane. To validate our approach, we conducted comparative experiments on four plane-based clustering models using publicly available datasets. Comprehensive experiments indicate that our improved unsupervised evaluation metric for plane-based clustering performs better compared to the original point-centered metrics.