Title :
Fuzzy order statistics and their application to fuzzy clustering
Author :
Kersten, Paul R.
Author_Institution :
Dept. of Comput. Sci., Midwestern State Univ., Wichita Falls, TX, USA
fDate :
12/1/1999 12:00:00 AM
Abstract :
The median and the median absolute deviation (MAD) are robust statistics based on order statistics. Order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy MAD. The fuzzy c-means (FCM) clustering algorithm is defined for any p-norm (pFCM), including the l1-norm (1FCM), The 1FCM clustering algorithm is implemented via the alternating optimization (AO) method and the clustering centers are shown to be the fuzzy median. The resulting AO-1FCM clustering algorithm is called the fuzzy c-medians (FCMED) clustering algorithm. An example illustrates the robustness of the FCMED
Keywords :
fuzzy set theory; optimisation; pattern clustering; statistics; alternating optimization method; fuzzy c-means clustering algorithm; fuzzy c-medians clustering algorithm; fuzzy median; fuzzy order statistics; l1-norm; median absolute deviation; p-norm; robust statistics; Clustering algorithms; Computer science; Fuzzy sets; Image processing; Minimization methods; Optimization methods; Risk management; Rivers; Robustness; Statistics;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
