Grid neighbourhood based three way clustering (3WC)

Abstract

The key idea behind three-way clustering (3WC) is to group items into three regions to reveal patterns that might not be apparent using two-way clustering. Three-way clustering, contrasting with two-way, considers data across three regions instead of two regions. The three regions are referred to as inside, outside, and partial regions, contrary to the two-way clustering that uses inside and outside regions. The objects in the inside region are members of a cluster, whereas those in the outside region are not, and partial objects may be members of a cluster. Three-way clustering encounters two challenges: 1) Investigation of sophisticated evaluation functions. 2) Finding an optimized pair of thresholds used to identify three regions for a cluster. In the context of Three-Way Clustering (3WC), applying conditional probability can be beneficial for assessing the likelihood of patterns or relationships within each region. In this study, the first challenge is addressed by employing a grid-based approach for a sophisticated evaluation function based on conditional probability. Whereas the second challenge is addressed by employing the elbow-based method to determine a pair of thresholds within a grid-based histogram. Further, two approaches namely the OGN3 and RGN3 are introduced to discover clear and crisp clusters. Experimental results on UCI and Kaggle datasets indicate improvements for commonly used F1 measures for OGN3 and RGN3 up to 4.97% and 12.88%, respectively