New aspects of the elastic net algorithm for cluster analysis

The elastic net algorithm formulated by Durbin-Willshaw as a heuristic method and initially applied to solve the traveling salesman problem can be used as a tool for data clustering in n-dimensional space. With the help of statistical mechanics, it is formulated as a deterministic annealing method, where a chain with a fixed number of nodes interacts at different temperatures with the data cloud. From a given temperature on the nodes are found to be the optimal centroids of fuzzy clusters, if the number of nodes is much smaller than the number of data points. We show in this contribution that for this temperature, the centroids of hard clusters, defined by the nearest neighbor clusters of every node, are in the same position as the optimal centroids of the fuzzy clusters. The same is true for the standard deviations. This result can be used as a stopping criterion for the annealing process. The stopping temperature and the number and sizes of the hard clusters depend on the number of nodes in the chain. Test was made with homogeneous and nonhomogeneous artificial clusters in two dimensions. A medical application is given to localize tumors and their size in images of a combined measurement of X-ray computed tomography and positron emission tomography. © 2010 The Author(s)

A New Adaptive Elastic Net Method for Cluster Analysis

Clustering is inherently a highly challenging research problem. The elastic net algorithm is designed to solve the traveling salesman problem initially, now is verified to be an efficient tool for data clustering in n-dimensional space. In this paper, by introducing a nearest neighbor learning method and a local search preferred strategy, we proposed a new Self-Organizing NN approach, called the Adaptive Clustering Elastic Net (ACEN) to solve the cluster analysis problems. ACEN consists of the adaptive clustering elastic net phase and a local search preferred phase. The first phase is used to find a cyclic permutation of the points as to minimize the total distances of the adjacent points, and adopts the Euclidean distance as the criteria to assign each point. The local search preferred phase aims to minimize the total dissimilarity within each clusters. Simulations were made on a large number of homogeneous and nonhomogeneous artificial clusters in n dimensions and a set of publicly standard problems available from UCI. Simulation results show that compared with classical partitional clustering methods, ACEN can provide better clustering solutions and do more efficiently

Memoria Investigación UC Temuco 2010/2011

Nuestra institución ha decidido priorizar la investigación aplicada con impacto regional, orientada a los procesos de generación de valor económico y social de La Araucanía y la macro región sur. La presente memoria desarrollada por la Dirección General de Investigación y Postgrado, da cuenta de los logros alcanzados durante el periodo 2010-2011.Our institution has decided to give priority to applied research with a regional impact, oriented towards the generation of economic and social value in La Araucanía and the southern macroregion. The present memorandum, drawn up by the General Directorate of Research and Postgraduate Studies, reports on the achievements of the period 2010-2011

New aspects of the elastic net algorithm for cluster analysis

The elastic net algorithm formulated by Durbin-Willshaw as a heuristic method and initially applied to solve the traveling salesman problem can be used as a tool for data clustering in n-dimensional space. With the help of statistical mechanics, it is formulated as a deterministic annealing method, where a chain with a fixed number of nodes interacts at different temperatures with the data cloud. From a given temperature on the nodes are found to be the optimal centroids of fuzzy clusters, if the number of nodes is much smaller than the number of data points. We show in this contribution that for this temperature, the centroids of hard clusters, defined by the nearest neighbor clusters of every node, are in the same position as the optimal centroids of the fuzzy clusters. The same is true for the standard deviations. This result can be used as a stopping criterion for the annealing process. The stopping temperature and the number and sizes of the hard clusters depend on the number of nodes in the chain. Test was made with homogeneous and nonhomogeneous artificial clusters in two dimensions. A medical application is given to localize tumors and their size in images of a combined measurement of X-ray computed tomography and positron emission tomography