We propose an enhanced variant of the traditional Fuzzy C-Means (FCM) algorithm tailored for leveraging neighbourhood information in non-image datasets residing in Euclidean space. Our novel methodology aims to capitalize on spatial contextual cues inherent in such datasets, thereby complementing the inherent fuzziness of individual data points. Through the incorporation of neighbourhood information, our approach extends beyond the limitations of conventional FCM, leading to improved clustering performance. We validate the efficacy of our method using synthetic and real datasets, demonstrating its superiority over conventional FCM in capturing spatial relationships within the data. Our findings underscore the effectiveness of our approach in enhancing clustering outcomes by strategically incorporating neighbourhood information into the FCM framework for non-image data in Euclidean space.

Clustering, spatial FCM, nonimage data, Euclidian neighbour, FCMS.

[1] J. C. Bezdek, “Patteren recognition with fuzzy objective function algorithms”. New York: Plenum, 1981.
[2] J. C. Bezdek and S. Pal, “Fuzzy models for pattern recognition: Methods that search for structures in data”. IEEE Transactions on Systems, Man, and Cybernetics, Vol. 26(3), pp. 388-402, 1996.
[3] Y. Cheng & H. Zhang, “Fuzzy c-means clustering and classification algorithms”, IEEE Transactions on Systems, Man, and Cybernetics- Part B, Vol. 28(3), pp. 418-428, 1996.
[4] I. Despotovic, B. Goossens, W. Philips, “MRI segmentation of the human brain: challenges, methods, and applications”, Computational and Mathematical methods in medicine, Article ID 450341, 2015.
[5] S. K. Adhikari, J. K. Sing, D. K. Basu, M. Nasipuri, “Conditional spatial fuzzy c-means clustering algorithm for segmentation of MRI images”, Applied Soft Computing, Vol. 34, pp. 758-769, 2015.
[6] D. L. Pham, “Fuzzy clustering with spatial constraints”, Proceedings of International Conference on Image Processing, Vol. 2, IEEE, 2002.
[7] K. S. Chuang, H. L. Tzeng, S. Chen, J. Wu, T. J. Chen, “Fuzzy c-means clustering with spatial information for image segmentation”, Computerized medical imaging and graphics, Vol. 30 (1), pp. 9-15, 2006.
[8] W. Cai, S. Chen, D. Zhang, “Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation”, Pattern Recognition, Vol. 40 (3), pp. 825-838, 2007.
[9] H. Y. Yu, J. L. “Fan, Three-level image segmentation based on maximum fuzzy partition entropy of 2-D histogram and quantum genetic algorithm”, International Conference on Intelligent Computing, Springer, pp. 484-493, 2008.
[10] N. P. Caldairou, P. A. Habas, C. Studholme, F. Rousseau, “A non-local fuzzy segmentation method: application to brain MRI”, Pattern Recognition, Vol. 44 (9), pp. 1916-1927, 2011.
[11] F. Zhao, L. Jiao, H. Liu, “Fuzzy C-means clustering with non-local spatial information for noisy image segmentation”, Frontiers of Computer Science in China, Vol. 5 (1), pp. 45-56, 2011.
[12] W. Q. Deng, X. M. Li, X. Gao, C. M. Zhang, “A modified fuzzy c-means algorithm for brain MRI image segmentation and bias field correction”, Journal of Computer Science and Technology, Vol. 31 (3), pp. 501-511, 2016.
[13] H. Zhang, J. Liu, “Fuzzy c-means clustering algorithm with deformable spatial information for image segmentation”, Multimedia tools and applications, Springer link, Vol. 81, pp. 11239-11258, 2022
[14] X. Zeyu, L. Xiao, Z. Defang, “Fuzzy c-means clustering algorithm based on superpixel merging and multi-feature adaptive fusion measurement”, IET Image Processing, September, 2023.
[15] Q. Wang, X. Wang, C. Fang and W. Yang, “Robust fuzzy c-means clustering algorithm with adaptive spatial & intensity constraint and membership linking for noise image segmentation”, Applied Soft Computing, Vol. 92, 2020.
[16] L. Wang, S. Niu and L. Geng, “Kernel Fuzzy c-means clustering with new spatial constraints”, International conference on Artificial Intelligence and Security, Vol. 1253, pp. 3-14, 2020.
[17] R. Solanki and D. Kumar, “Probabilistic intuitionistic fuzzy c-means algorithm with spatial constraint for human brain MRI segmentation”, Multimedia tools and applications, Vol. 82, pp. 33663-33692, 2023.
[18] H. Zhang, H. Li, N. Chen, “Novel fuzzy clustering algorithm with variable multi-pixel fitting spatial information for image segmentation”, Pattern recognition, Vol. 121, 2022.
[19] C. Wang, W. Pedrycz, Z. Li, M. Zhou, S. S. Ge, “G-image segmentation: similarity-preserving fuzzy c-means with spatial information constraint in wavelet space”. IEEE Transactions on Fuzzy systems, pp: 3887-3898, 2020.
[20] M. N. Ahmed, S. M. Yamany, N. Mohamed, A. A. Farag, and T. Moriarty, “A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data”, IEEE Transaction on Medical Imaging, Vol. 21, pp. 193-199, 2002.
[21] S. Chen and D. Zhang, “Robust Image Segmentation Using FCM With Spatial Constraints Based on New Kernel-Induced Distance Measure”, IEEE Transaction on Systems, Man, and Cybernetics, Vol. 34, No. 4, 2004.
[22] A. Strehl and J. Ghosh, “Cluster ensembles-a knowledge reuse framework for combining multiple partitions”, Journal of Machine Learning Research, Vol. 3, pp. 583-617, 2002.
[23] G. Fisher, “The adjusted rand statistics: A SAS macro”, Computational Psychometrica, Vol. 53, No. 3, pp. 417-423, 1988.
[24] E. Hullermeier, M. Rifqi, S. Henzgen and R. Senge, “Comparing fuzzy partitions: a generalization of the rand index and related measures”, IEEE Transactions on Fuzzy Systems, pp. 546 - 556 Vol. 20, Issue: 3, 2012.