Speeding up fuzzy c-means: using a hierarchical data organisation to control the precision of membership calculation

摘要

We examine the run-time behaviour of conventional fuzzy c-means implementations. Investigating into FCM termination conditions and membership update equations, we derive an approximative FCM that yields the same results as a conven- tional implementation within a given precision. We incorporate additional information about the data set by re-organizing the set as a tree. Our modification leads to an FCM algorithm with a significantly different run time behaviour; the gain of using the modified implementation increases with an increasing number of data objects and especially an increasing number of clusters, but is also sensitive to the chosen fuzzifier.