Clustering without Use of Prototypes with Gradient Descent for Cluster Optimization

The first stage of organizing entities is to partition them into groups or clusters. The clustering is generally done on pattern vectors representing the entities. Clustering algorithms normally require a method of aggregating patterns and of measuring proximity between patterns. Because of the nature of the patterns it may not always be possible however to find a satisfactory method of aggregating patterns. Some of the features may not be numeric. Sometimes patterns may not even be available and only the proximities between patterns are known. This paper describes a method for finding a fuzzy membership matrix that provides cluster membership values for all the patterns based strictly on the proximity matrix. The method is based on the premise that the proximities between the membership vectors should be proportional to the proximities between the feature vectors. The membership matrix is found by applying gradient descent to an error function with the objective of reducing it to zero. Simulations show the method to be quite effective.