Silhouettes: a graphical aid to the interpretation and validation of cluster analysis
Journal of Computational and Applied Mathematics
Cooling schedules for optimal annealing
Mathematics of Operations Research
Simulated annealing: theory and applications
Simulated annealing: theory and applications
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Fuzzy Models and Algorithms for Pattern Recognition and Image Processing
Fuzzy Models and Algorithms for Pattern Recognition and Image Processing
Simulated Annealing: A Proof of Convergence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Cluster ensembles --- a knowledge reuse framework for combining multiple partitions
The Journal of Machine Learning Research
Combining Multiple Weak Clusterings
ICDM '03 Proceedings of the Third IEEE International Conference on Data Mining
Solving cluster ensemble problems by bipartite graph partitioning
ICML '04 Proceedings of the twenty-first international conference on Machine learning
On combining multiple clusterings
Proceedings of the thirteenth ACM international conference on Information and knowledge management
Clustering Ensembles: Models of Consensus and Weak Partitions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 9th annual conference on Genetic and evolutionary computation
New Introduction to Multiple Time Series Analysis
New Introduction to Multiple Time Series Analysis
Multi-Optimisation Consensus Clustering
IDA '09 Proceedings of the 8th International Symposium on Intelligent Data Analysis: Advances in Intelligent Data Analysis VIII
A new efficient approach in clustering ensembles
IDEAL'07 Proceedings of the 8th international conference on Intelligent data engineering and automated learning
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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.