Determining data clusters' fine center, extents, and membership functions using a modified mountain method
James A. Kelly, Ronald R. Yager · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
This paper describes a stand alone Mountain Method (MM) to determine clusters' fine center position, extents, and membership functions. The motivation for this fuzzy clustering algorithm is to improve the approximate cluster centers resulting from the MM without experiencing the problem of local minima, and provide the additional cluster information necessary to fuzzify a system. After briefly reviewing the MM, this paper discusses the methodological considerations for effective cluster determination, modifications to the MM, and classical data set results using the MM, fuzzy c-mean (FCM) and the modified Mountain Method (MMM). The MMM compared to FCM algorithm achieved cluster centers resulting in a standard error of 0.166 and 0.052 with respect to Anderson's Iris, and Yager and Filev's data sets. The methodology discussed herein is the subject of a US patent, entitled 'Multiple Target Discrimination Algorithm', serial number 5,396,252, assigned to United Technologies Corporation. The patent addresses discriminating multiple targets or clusters of digitized sensor data for determining fine position and extents thereof.