Fuzzy Kohonen clustering networks

Abstract

Kohonen networks are well known for cluster analysis (unsupervised learning). This class of algorithms is a set of heuristic procedures that suffers from several major problems (e.g. neither termination or convergence is guaranteed, no model is optimized by the learning strategy, and the output is often dependent on the sequence of data). A fuzzy Kohonen clustering network is proposed which integrates the Fuzzy c-Means (FCM) model into the learning rate and updating strategies of the Kohonen network. This yield an optimization problem related to FCM, and the numerical results show improved convergence as well as reduced labeling errors. It is proved that the proposed scheme is equivalent to the c-Means algorithms. The new method can be viewed as a Kohonen type of FCM, but is “self-organizing” since the “size” of the update neighborhood and learning rate in the competitive layer are automatically adjusted during learning. Anderson's IRIS data is used to illustrate this method; and results are compared with the standard Kohonen approach.