A three-way clustering approach for handling missing data using GTRS

Clustering is an important data analysis task. It becomes a challenge in the presence of uncertainty due to reasons such as incomplete, missing or corrupted data. A three-way approach has recently been introduced to deal with uncertainty in clustering due to missing values. The essential idea is to make a deferment decision whenever it is not clear and possible to decide whether or not to include an object in a cluster. A key issue in the three-way approach is to determine the thresholds that are used to define the three types of decisions, namely, include an object in a cluster, exclude an object from a cluster, or delay (defer) the decision of inclusion or exclusion from a cluster. The existing studies do not sufficiently address the determination of thresholds and generally use its fix values. In this paper, we explore the use of game-theoretic rough set (GTRS) model to handle this issue. In particular, a game is defined where the determination of thresholds is approached based on a tradeoff between the properties of accuracy and generality of clusters. The determined thresholds are then used to induce three-way decisions for clustering uncertain objects. Experimental results on four datasets from UCI machine learning repository suggests that the GTRS significantly improves the generality while keeping similar levels of accuracy in comparison to other three-way and similar models.