Rough possibilistic meta-clustering of retail datasets

In this paper, we develop a new meta-clustering approach using possibility and rough set theories to handle imperfection in real-world retail datasets. Our proposal is a soft meta-clustering approach that provides a framework for handling uncertainty in the belonging of an object to different clusters. The soft meta-clustering approach is based on the k-modes algorithm devoted for categorical data. Possibility theory is used to represent the uncertainty between objects and clusters through possibilistic membership degrees. Rough set theory is applied to indicate clusters with rough boundaries. The meta-clustering consists of double clustering a retail dataset that contains customer and product data. The meta-clustering is improved by the application of the possibility and rough set theories. An initial clustering of the customer data is performed. Then, a second clustering of product data using the results of the first clustering is applied. The two clustering schemes then evolve iteratively affecting each other recursively. We detail our results and describe the structure of the final clusters of customers and products to prove the effectiveness of our proposal.