New Aspects of the Elastic Net Algorithm for Cluster Analysis

The elastic net algorithm, formulated by Durbin-Willshaw as an heuristic method and initially applied to solve the travelling salesman problem, can be used as a tool for data clustering in n-dimensional space. With the help of statistical mechanics it can be formulated as an deterministic annealing method in which a chain of nodes interacts at different temperatures with the data cloud. From a given temperature on the nodes are found to be the optimal centroid’s of fuzzy clusters, if the number of nodes is much smaller then number of data points.

We show in this contribution that for this temperature the centroid’s of hard clusters, defined by the nearest neighbor clusters of every node, are in the same position as the optimal centroid’s of the fuzzy clusters. This result can be used as a stopping criterion for the annealing process. The stopping temperature and the number and size of the hard clusters depend on the number of nodes in the chain.

Test were made with homogeneous and inhomogeneous artificial clusters in two dimensions.