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

Information processing in neural systems: oscillations, network topologies and optimal representations

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Escuela Politécnica Superior, Departamento de Ingeniería informática. Fecha de lectura: 1-07-200

Computer simulation of vapor-liquid equilibria of linear dipolar fluids: Departures from the principle of corresponding states

Liquid-vapor equilibrium of linear dipolar fluids has been determined by using the Gibbs ensemble simulation technique. Several elongations and values of the dipole moment were considered. Dipole moment increases the critical temperature and affects slightly the critical density and pressure. Compressibility factor at the critical point decreases as the dipole moment of the molecule increases. Dipole moment provokes deviations from the principle of corresponding states. It is shown that the temperature-density coexistence curve is broadened and that the slope of the vapor pressure curve increases with increasing dipole moment. We propose a new way of reducing the dipole moment so that the increase of the critical temperature becomes almost independent on the molecular elongation. We have also obtained the vapor-liquid equilibrium of models having both a dipole and a quadrupole moment. The obtained data were used to describe the behavior of some relatively complex fluids, namely, 1,1,1-trifluoroethane and 2,2,2-trifluoroethanol. Good agreement for coexistence densities and pressures was obtained. The results presented in this work for linear dipolar fluids along with previous work on linear quadrupolar fluids provide a very comprehensive view of the effect of polar forces on the vapor-liquid equilibrium of linear fluids

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

A novel orientation-dependent potential model for prolate mesogens

An intermolecular potential is introduced for the study of molecular mesogenic fluids. The model combines distinct features of the well-known Gay-Berne and Kihara potentials by incorporating dispersive interactions dependent on the relative pair orientation to a spherocylinder molecular core. Results of a Monte Carlo simulation study focused on the liquid crystal phases exhibited by the model fluid are presented. For the chosen potential parameters, molecular aspect ratio L*55 and temperatures T*52, 3, and 5, isotropic, nematic, smectic-A, and hexatic phases are found. The location of the phase boundaries as well as the equation of state of the fluid and further thermodynamical and structural parameters are discussed and contrasted to the Kihara fluid. In comparison to this latter fluid, the model induces the formation of ordered liquid crystalline phases at lower packing fractions and it favors, in particular, the appearance of layered hexatic ordering as a consequence of the greater attractive interaction assigned to the parallel side-to-side molecular pair configurations. The results contribute to the evaluation of the role of specific interaction energies in the mesogenic behavior of prolate molecular liquids in dense environments

Liquid crystal behavior of the Kihara fluid

The liquid crystal phases of the Kihara fluid have been studied in computer simulations. The work focuses on the isotropic–nematic–smectic-A triple point region, especially relevant for the understanding of the properties and the design of real mesogens with specific phase diagrams. The Kihara interaction resembles more appropriately than other related models, the shape of elongated polymers and biomolecules, and a closer assertion is provided for the role of the configurational entropy and the dispersive interactions in the behavior of such molecules in dense phases or under macromolecular crowding conditions.Dirección Genaral de Investigación Científico y Técnica BQU2001-3615-C02Instituto de Salud Carlos III 01/1664Plan Andaluz de Investigación FQM-205, FQM-31

Use of Parsons-Lee and Onsager theories to predict nematic and demixing behavior in binary mixtures of hard rods and hard spheres

Parsons-Lee and Onsager theories are formulated for the isotropic-nematic transition in a binary mixture of hard rods and hard spheres. Results for the phase coexistence and for the equation of state in both phases for mixtures with different relative sizes and composition are presented. The two theories explain correctly the general behavior observed in experiments and computer simulations for these fluids. In particular, the theory accounts for the destabilization of the nematic phase when spherical or globular macromolecules are added to a system of rodlike colloids, and the entrance of the system into a demixed regime at high volume fractions of the spherical particles. Upon demixing a nematic state rich in rods coexists in equilibrium with an isotropic state much more diluted in the rodlike component. Onsager theory fails on quantitative grounds for aspect ratios of the rodlike molecules smaller than 100, and in the cases where the molar fractions of spheres becomes close to unity. On the contrary, the Parsons-Lee approximation remains accurate down to aspect ratios as small as 5. The spinodal analysis indicates that the isotropic-isotropic and nematic-nematic coexistences become feasible for sufficiently large spheres and long rods, respectively. The latter type of coexistence interferes partially with the isotropic-nematic coexistence regime of interest to the present work. Overall, the study serves to rationalize and control key aspects of the behavior of these binary nematogenic colloidal systems, which can be tuned with an appropriate choice of the relative size and molar fractions of the particles.Ministerio de Educación y Ciencia CTQ2004- 07730-C02 VEM2003-20574-C03Junta de Andalucía PAI FQM-205 FQM-31