# A Novel Adaptive FCM with Cooperative Multi-Population Differential Evolution Optimization
## 4 Proposed Co-Evolutionary Framework
### Evaluation of Clustering Results
A novel fitness evaluation function based on two cluster validity measures is also proposed. The proposed method called cooperative differential evolution for fuzzy c-means (CDE-FCM) is compared to some state-of-art improvements of FCM and also to the original FCM with random initial cluster prototypes implemented for a range of values for the number of clusters. The comparison is performed using a distinct set of cluster validity indices. In many of the cases with synthetic two-dimensional data and larger dimensional data from the UCI ML repository, the proposed algorithm performs better than the methods compared, and in almost all the cases, is almost as effective as the best of the other methods. The proposed method is also used on a real-world experimental dataset to partition rolling-bearing fault data. The technique worked well in real time and with very minimal improvements can be deployed to a live data analysis project such as this. For future work, modifications to improve the proposed methodology will be investigated. Although the fitness evaluation and candidate evolution in the multi-population method are not resource intensive for parallel implementation, they can both be improved further. Statistical testing to evaluate the level of significance in performance improvement of the proposed method will also be performed as part of future work. This will result in ranking the comparative clustering methods used in this paper over other datasets from the UCI ML repository and on other benchmark datasets. Conceptualization, A.B. ; methodology, A.B. ; software, A.B. and LA.-M.; validation, A.B. ; formal analysis, A.B. ; investigation, A.B. and I.A.-M.; resources, A.B. and I.A.-M.; data curation, A.B. and I.A.-M.; writing--original draft preparation, A.B. ; writing--review and editing, A.B. and I.A.-M.; visualization, A.B. and I.A.-M.; supervision, A.B. ; project administration, A.B. and I.A.-M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Data availability Statement: Data used in this study can be made available by request. The authors declare no conflict of interest. ## References

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