Implementation issues in the fuzzy c-medians clustering algorithm

The fuzzy c-median (FCMED) clustering algorithm is an alternating optimization (AO) method of solving the fuzzy c-means (FCM) clustering algorithm using the l₁-norm. This algorithm is more resistant to outliers than the FCM-AO algorithm using the l₂-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 efficiency 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 simplify the estimation of the median. A fuzzy remedian is defined and used to approximate the fuzzy median. The second method finds the root of the derivative of the functional equation defining the fuzzy median. Both approaches are described and illustrated