Optimizing Fuzzy Cluster Ensemble in String Representation

In this paper, we present a novel optimization-based method for the combination of cluster ensembles. The information among the ensemble is formulated in 0-1 bit strings. The suggested model de ̄nes a constrained nonlinear objective function, called fuzzy string objective function (FSOF), which maximizes the agreement between the ensemble members and minimizes the disagreement simultaneously. Despite the crisp primary partitions, the suggested model employs fuzzy logic in the mentioned objective function. Each row in a candidate solution of the model includes membership degrees indicating how much data point belongs to each cluster. The de ̄ned nonlinear model can be solved by every nonlinear optimizer; however; we used genetic algorithm to solve it. Accordingly, three suitable crossover and mutation operators satisfying the constraints of the problem are devised. The proposed crossover operators exchange information between two clusters. They use a novel relabeling method to ̄nd corresponding clusters between two partitions. The algorithm is applied on multiple standard datasets. The obtained results show that the modi ̄ed genetic algorithm operators are desirable in exploration and exploitation of the big search space.