Fuzzy clustering with squared Minkowski distances

✍ Scribed by Patrick J.F. Groenen; Krzysztof Jajuga

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 129 KB
• Volume: 120
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00403-5

✦ Synopsis

This paper presents a new fuzzy clustering model based on a root of the squared Minkowski distance which includes squared and unsquared Euclidean distances and the L1-distance. An algorithm is presented that is based on iterative majorization and yields a convergent series of monotone nonincreasing loss function values. This algorithm coincides under some condition with the ISODATA algorithm of Dunn (J. Cybernet. 3 (1974) 32-57) and the fuzzy c-means algorithm of Bezdek (Ph.D. Thesis, Cornell University, Ithaca, 1973) for squared Euclidean distance and with an algorithm of Jajuga (Fuzzy Sets and Systems 39 (1991) 43-50) for L1-distances. To ÿnd a global minimum we compare a special strategy called fuzzy steps with fuzzy Kohonen clustering networks (FKCN) (Pattern Recognition 27 (1994) 757-764) and multistart. Fuzzy steps and FKCN are based on ÿnding updates for a decreasing weighting exponent, which seems to work particularly well for hard clustering. To assess the performance of the methods, two numerical experiments and a simulation study are performed.