Implementation issues in the fuzzy c-medians clustering algorithm

Abstract

The fuzzy c-Median (FCMED) clustering algorithm is an altemating optimization (AO) method of solving the .fuuy c-Means (FCM) clustering algorithm using the 11 -norm. This algorithm is more resistant to outliers than the FCM-A0 algorithm using the P2-norm.The robustness of the FCMED does not come free, since the -fuzzy median is the cluster-centering statistic and exact evaluation of the fuzzy median usually involves ordering the sample values. The eflciency of calculating the fuzzy median is an important implementation issue. Two other evaluation methods are considered for the fuzzy median: The first is the remedian, which statisticians use to .rimplijj the estimation of the median. A fizzy remedian js defined and used to approximate the fuzzy median. The .record method finds the root of the derivative of the j'unctional equation defining the fuzzy median. Both upproaches are described and illustrated in this paper.

Survey of Clustering Algorithms

“…Kersten suggested that city block distance (or norm) could improve the robustness of FCM to outliers [163]. Furthermore, Hathaway, Bezdek, and Hu extended FCM to a more universal case by using Minkowski distance (or norm, ) and seminorm for the models that operate either directly on the data objects or indirectly on the dissimilarity measures [130].…”

An Overview of Fuzzy C-Means Based Image Clustering Algorithms

“…This occurs due to the fact that d ij = ||x j − c i || 2 2 which can lead to cluster prototypes being pulled away from the main distribution of the cluster. Kersten [22] and Miyamoto and Agusta [27] independently proposed replacing ||x j − c i || L p norm FCM clustering [19] is based on this observation. The objective function employed is hence formulated as…”

“…However, if α has not been properly defined, this can result in a even slower convergence of clustering. To avoid this, Equation 22 can be modified as…”

The Application of Median Fuzzy Clustering and Robust Weighted Averaging for Electronystagmography Signal Processing

“…However, the resulting FCM cluster representatives (prototypes) are the linear statistics of data points which are known to be vulnerable to outliers [7]. Hence, in the presented approach we applied the robust partitioning method based on the fuzzy median (Fuzzy c-Medians, FCMed) [8].…”

“…To increase the efficiency of median calculation we applied the algorithm, defining the prototypes as a root of the derivative of fuzzy median functional [8] which can be found with bisection method.…”