Rough‐Fuzzy Clustering: GeneralizedcA‐Means Algorithm
Pradipta Maji, Sankar Kumar Pal · 2012
Clustering techniques have been effectively applied to a wide range of engineering and scientific disciplines such as pattern recognition, biology, and remote sensing. A number of clustering algorithms have been proposed to suit different requirements. One of the widely used prototype-based partitional clustering algorithms is hard c-means (HCM). This chapter first briefly introduces the necessary notions of HCM, fuzzy c-means (FCM), and rough c-means (RCM) algorithms. It then describes the rough-fuzzy-possibilistic c-means (RFPCM) algorithm in detail on the basis of the theory of rough sets and FCM. The chapter also presents a mathematical analysis of the convergence property of the RFPCM algorithm. It establishes that the RFPCM algorithm is the generalization of existing c-means algorithms. The chapter reports several quantitative performance measures to evaluate the quality of different algorithms. Finally, it presents a few case studies and an extensive comparison with other methods such as crisp, fuzzy, possibilistic, and RCM. Controlled Vocabulary Terms fuzzy logic; pattern clustering; performance evaluation; rough set theory