Normality-based validation for crisp clustering

This is the author’s version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition, 43, 36, (2010) DOI 10.1016/j.patcog.2009.09.018We introduce a new validity index for crisp clustering that is based on the average normality of the clusters. Unlike methods based on inter-cluster and intra-cluster distances, this index emphasizes the cluster shape by using a high order characterization of its probability distribution. The normality of a cluster is characterized by its negentropy, a standard measure of the distance to normality which evaluates the difference between the cluster's entropy and the entropy of a normal distribution with the same covariance matrix. The definition of the negentropy involves the distribution's differential entropy. However, we show that it is possible to avoid its explicit computation by considering only negentropy increments with respect to the initial data distribution, where all the points are assumed to belong to the same cluster. The resulting negentropy increment validity index only requires the computation of covariance matrices. We have applied the new index to an extensive set of artificial and real problems where it provides, in general, better results than other indices, both with respect to the prediction of the correct number of clusters and to the similarity among the real clusters and those inferred.This work has been partially supported with funds from MEC BFU2006-07902/BFI, CAM S-SEM-0255-2006 and CAM/UAM CCG08-UAM/TIC-442

The effect of low number of points in clustering validation via the negentropy increment

This is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Neurocomputing, 74, 16, (2011) DOI: 10.1016/j.neucom.2011.03.023Selected papers of the 10th International Work-Conference on Artificial Neural Networks (IWANN2009)We recently introduced the negentropy increment, a validity index for crisp clustering that quantifies the average normality of the clustering partitions using the negentropy. This index can satisfactorily deal with clusters with heterogeneous orientations, scales and densities. One of the main advantages of the index is the simplicity of its calculation, which only requires the computation of the log-determinants of the covariance matrices and the prior probabilities of each cluster. The negentropy increment provides validation results which are in general better than those from other classic cluster validity indices. However, when the number of data points in a partition region is small, the quality in the estimation of the log-determinant of the covariance matrix can be very poor. This affects the proper quantification of the index and therefore the quality of the clustering, so additional requirements such as limitations on the minimum number of points in each region are needed. Although this kind of constraints can provide good results, they need to be adjusted depending on parameters such as the dimension of the data space. In this article we investigate how the estimation of the negentropy increment of a clustering partition is affected by the presence of regions with small number of points. We find that the error in this estimation depends on the number of points in each region, but not on the scale or orientation of their distribution, and show how to correct this error in order to obtain an unbiased estimator of the negentropy increment. We also quantify the amount of uncertainty in the estimation. As we show, both for 2D synthetic problems and multidimensional real benchmark problems, these results can be used to validate clustering partitions with a substantial improvement.This work has been funded by DGUI-CAM/UAM (Project CCG10-UAM/TIC-5864

Fast response and temporal coherent oscillations in small-world networks

We have investigated the role that different connectivity regimes play in the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random topologies give rise to fast system response yet are unable to produce coherent oscillations in the average activity of the network; on the other hand, regular topologies give rise to coherent oscillations, but in a temporal scale that is not in accordance with fast signal processing. Finally, small-world topologies, which fall between random and regular ones, take advantage of the best features of both, giving rise to fast system response with coherent oscillations.We acknowledge G. Laurent, A. Bäcker, M. Bazhenov, M. Rabinovich, and H. Abarbanel for insightful discussions. We thank the Dirección General de Enseñanza Superior e Investigación Científica for financial support (PB97-1448), the CAM for financial support to L. F. L., and the CCCFC (UAM) for the use of computation resources

Fast response and coherent oscillations in small-world Hodgkin-Huxley neural networks

This is an electronic version of the paper presented at the I Jornadas Técnicas de la ETS de Informática, held in Madrid on 200

An autonomous robot that learns approach-avoidance behaviors: lessons from the brain to the robot

This is an electronic version of the paper presented at the I Jornadas Técnicas de la ETS de Informática, held in Madrid on 200

Tensiones en los modelos epistemológicos sobre la ciencia en estudiantes de ciencias exactas y naturales de la UNPa, Río Gallegos

Este trabajo se enmarca en el PI 29/A-338 “Filosofía de las ciencias: por qué y cómo incorporarla en los planes de estudio de nivel superior”. Los objetivos fueron: conocer los supuestos sobre la ciencia que presentan los alumnos ingresantes a la UNPA previa al cursado de la asignatura Introducción al Conocimiento Científico, correspondiente al primer año; indagar el posible origen de las concepciones de los estudiantes; y relevar los cambios operados en sus ideas luego de la cursada de la asignatura y describir en qué aspectos se producen dichos cambios.Eje 5: Exploraciones diagnósticas sobre diversas problemáticas educativasFacultad de Ciencias Exacta

Tensiones en los modelos epistemológicos sobre la ciencia en estudiantes de ciencias exactas y naturales de la UNPa, Río Gallegos

Este trabajo se enmarca en el PI 29/A-338 “Filosofía de las ciencias: por qué y cómo incorporarla en los planes de estudio de nivel superior”. Los objetivos fueron: conocer los supuestos sobre la ciencia que presentan los alumnos ingresantes a la UNPA previa al cursado de la asignatura Introducción al Conocimiento Científico, correspondiente al primer año; indagar el posible origen de las concepciones de los estudiantes; y relevar los cambios operados en sus ideas luego de la cursada de la asignatura y describir en qué aspectos se producen dichos cambios.Eje 5: Exploraciones diagnósticas sobre diversas problemáticas educativasFacultad de Ciencias Exacta