Interval Generalized Improved Fuzzy Partitions Fuzzy C-Means Under Hausdorff Distance Clustering Algorithm

Abstract

In general, Hausdorff distance considers the maximum distance between two sets, making it less sensitive to outliers. Besides, fuzzy clustering often encounters challenges such as noise and fuzziness in data. Hausdorff distance provides a degree of resistance to such challenges by considering the maximum distance between two sets rather than just the average distance or distance between centroids. This robustness makes it effective in handling fuzzy and uncertain data. Hence, in this paper Hausdorff distance is proposed on interval generalized improved fuzzy partitions fuzzy C-means clustering algorithm for symbolic interval data analysis (SIDA). In general, the SIDA extends traditional statistics to analyze complex data types like intervals, useful for imprecise or aggregated data. In these datasets, noise issues are inevitable. This paper addresses clustering for SIDA, focusing on handling noise. This paper proposes the interval generalized improved fuzzy partitions fuzzy C-means (IGIFPFCM) under Hausdorff distance clustering algorithm, which uses competitive learning to handle symbolic interval data with improved robustness and convergence performance. Besides, this algorithm is less sensitive to small perturbations or outliers in the datasets due to the Hausdorff distance considering the worst-case scenario (the farthest point) rather than averaging distances, which can be skewed by outliers. From the experimental results, the statistical results of convergence and efficiency on performance show that the proposed IGIFPFCM under Hausdorff distance clustering algorithm has better results for SIDA with large outliers and noise under Student's t-distribution.