Single-solution based metaheuristic approach to a novel restricted clustering problem

Clustering problems have been widely studied in the literature. Multiple types of solutions have been devised depending on the specific problem considered, including ad-hoc heuristics and metaheuristic approaches. In this paper, we centre our attention on a particular clustering problem in which the sizes of the individual clusters are fixed a priori and where a membership restriction due to an initial classification is present. A novel formal description of the problem is presented, and an example of how it appears in practice as a post-processing step of non-negative matrix factorisation analysis is described. Adaptations of three classical single-solution based metaheuristic methods are proposed as possible solution strategies for this problem. Experiments are performed using synthetic data and then using a test dataset constructed from repeated NMF extractions of multiple face images. The efficacy of the various approaches is compared and discussed.