L1-NORM BASED FUZZY CLUSTERING

The paper presents the L1 version of the well-known fuzzy clustering method, namely fuzzy ISODATA, proposed by Bezdek and Dunn. Due to their robustness, L1-norm based methods gained much attention in statistics. The presented fuzzy clustering problem uses the distance between observations and location parameter vectors, which is based on the L1-norm, instead of the inner product induced norm used in classical fuzzy ISODATA. Two alternative methods to solve the L1 fuzzy clustering problem are derived. In practice both membership grades and location parameter vectors are unknown. The paper presents two iterative algorithms, each the implementation of the derived method. Finally, numerical examples are presented. One of them refers to famous Iris data.