Outranking-based approaches for multiple criteria partially ordered clustering: A review of existing algorithms, new proposals, and experimental comparison

Abstract

We consider clustering problems that involve categorizing alternatives into partially ordered, initially undefined groups based on their performance across multiple criteria. To achieve this, we use an outranking relation model to reflect the Decision Maker's preferences. We examine various algorithms that not only group the alternatives but also order the clusters in different ways. This analysis includes innovative approaches that use distances in the space of outranking relations or detailed relation profiles, and apply orthogonal non-negative factorization to outranking matrices. Additionally, we discuss a set of measures, including two novel ones, for assessing the effectiveness of clustering when the groupings are partially ordered. Our findings are based on comprehensive computational experiments on real-world and simulated datasets. Beyond evaluating various methods using four quality metrics and computational efficiency, we explore the influence of accessible preference structures and ordering techniques on the clustering outcomes.