The effect of cooling functions on ensemble clustering using simulated annealing

Simulated Annealing (SA) has been adopted by many Ensemble Clustering methods to achieve global combinational optimisation. However the performance of SA is sensitive to the settings of its parameters. Much work has been done for optimising the settings of these parameters over the last two decades, but few of them analysed the behaviour of different cooling functions for Ensemble Clustering. Our work has demonstrated that the clustering results could be invalid if we use SA for Ensemble Clustering without a good understanding of the behaviour of cooling functions. Therefore this paper aims to present the findings of how different cooling functions may affect the performance of Ensemble Clustering methods that use SA. We analyse the effect of cooling functions from three aspects: the convergence rate, the final value of the objective function, and the accuracy of results. Ten different cooling functions are tested on two Ensemble Clustering methods, and thirteen different datasets have been used for the experiments. The findings are particularly helpful for those who are interested in Ensemble Clustering methods as well as those who want to obtain a deep understanding of the behaviour of the cooling functions.