A New Cluster Validity Index Based on Local Density of Data Points

Multiple cluster validity indices (CVIs) have been introduced for diverse applications. In practice, clusters exhibit varying shapes, sizes, densities, and closely spaced centers, which are typically unknown beforehand. It is desirable to develop a versatile CVI that performs well in general settings rather than being tailored to specific ones. Drawing inspiration from distance based on local density, where it is observed that cluster centers feature higher densities than their neighbors and are relatively distant from higher-density points, this paper introduces a novel CVI. This CVI employs a modified distance, adjusted for local density, to measure cluster compactness, replacing the traditional Euclidean distance with the minimum distance to a higher-density point. This adjustment accounts for cluster shapes and densities. The experimental results highlight the proposed index’s dual capability: it not only outperforms conventional methods by a remarkable margin of 32 percentage points in controlled synthetic environments but also maintains a 23+ percentage-point accuracy lead in real-world data regimes characterized by noise and heterogeneity. This consistency validates its generalizability across data modalities.