A Method of Proximity Matrix Based Fuzzy Clustering

Clustering algorithms normally require both a method of measuring proximity between patterns and prototypes and of aggregating patterns. However sometimes only the proximities between the patterns are known. Even if patterns are available it may not be possible to find a satisfactory method of aggregating patterns for the purpose of determining prototypes. Now the distances between the membership vectors should be proportional to the distances between the feature vectors. The membership vector is just a type of feature vector. Based on this premise, this paper describes a new method for finding a fuzzy membership matrix that provides cluster membership values for all the patterns based strictly on the proximity matrix. The method involves solving a rather challenging optimization problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle swarm optimization (PSO) attractive for determining the membership matrix for the clustering.