A robust fuzzy cluster validity index based on local distances
Bin Yan, Zheng yu Xie · Expert Systems with Applications · 2025
It is difficult to appropriately determine the cluster number in the absence of a priori knowledge. For diverse application contexts, a number of fuzzy cluster validity indices (CVIs) have been developed. They might function admirably in certain circumstances but poorly in others. In reality, clusters could have peculiar shapes and varying sizes/densities that aren’t known beforehand. It is meaningful to develop a reliable fuzzy CVI that can perform well in various conditions without being specifically designed for a particular set of circumstances. Using the knowledge of neighborhood distances as inspiration, a new membership degree model was developed. Instead of modeling the distance to each cluster center, the new membership degree model focuses on the distance of the observation to the closest point in each group. The novel method is more resistant to data sets with strange shapes, varied sizes (densities), and outliers than the conventional membership degree model. Thus, the gap between clusters and the compactness inside the cluster are modified. As a result, the RFCV fuzzy CVI was proposed. In comparison to the standard CVIs, extensive simulation tests demonstrate that the proposed RFCV is effective in a wide range of scenarios, including clusters with irregular geometries and varying densities.