Robust EM algorithm for model-based curve clustering

Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful approaches in cluster analysis. The mixture density estimation is generally performed by maximizing the observed-data log-likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the EM algorithm initialization is crucial. In addition, the standard EM algorithm requires the number of clusters to be known a priori. Some solutions have been provided in [31, 12] for model-based clustering with Gaussian mixture models for multivariate data. In this paper we focus on model-based curve clustering approaches, when the data are curves rather than vectorial data, based on regression mixtures. We propose a new robust EM algorithm for clustering curves. We extend the model-based clustering approach presented in [31] for Gaussian mixture models, to the case of curve clustering by regression mixtures, including polynomial regression mixtures as well as spline or B-spline regressions mixtures. Our approach both handles the problem of initialization and the one of choosing the optimal number of clusters as the EM learning proceeds, rather than in a two-fold scheme. This is achieved by optimizing a penalized log-likelihood criterion. A simulation study confirms the potential benefit of the proposed algorithm in terms of robustness regarding initialization and funding the actual number of clusters.Comment: In Proceedings of the 2013 International Joint Conference on Neural Networks (IJCNN), 2013, Dallas, TX, US

The impact of enhanced He and CNONa abundances on globular cluster relative age-dating methods

The impact that unrecognised differences in the chemical patterns of Galactic globular clusters have on their relative age determinations is studied. The two most widely used relative age-dating methods, horizontal and vertical, together with the more recent relative MS-fitting method, were carefully analyzed on a purely theoretical basis. The BaSTI library was adopted to perform the present analysis. We find that relative ages derived using the horizontal and vertical methods are largely dependent on the initial He content and heavy element distribution. Unrecognized cluster-to-cluster chemical abundance differences can lead to an error in the derived relative ages as large as ~0.5 (or ~6 Gyr if an age of 12.8 Gyr is adopted for normalization), and even larger for some extreme cases. It is shown that the relative MS-fitting method is by far the age-dating technique for which undetected cluster-to-cluster differences in the He abundance have less impact. Present results are used in order to pose constraints on the maximum possible spread in the He and CNONa elements abundances on the basis of the estimates - taken from the literature - of the Galactic globular clusters relative age dispersion obtained with the various relative age-dating techniques. Finally, it is shown that the age-metallicity relation found for young Galactic globular clusters by the GC Treasury program is a real age sequence and cannot be produced by variations in the He and/or heavy element distribution.Comment: 26 pages, 8 figures, accepted for publication in ApJ

Proximity effect in granular superconductor-normal metal structures

We fabricated three-dimensional disordered Pb-Cu granular structures, with various metal compositions. The typical grain size of both metals is smaller than the superconductor and normal metal coherence lengths, thus satisfying the Cooper limit. The critical temperature of the samples was measured and compared with the critical temperature of bilayers. We show how the proximity effect theories, developed for bilayers, can be modified for random mixtures and we demonstrate that our experimental data fit well the de Gennes weak coupling limit theory in the Cooper limit. Our results indicate that, in granular structures, the Cooper limit can be satisfied over a wide range of concentrations.Comment: 15 pages, 4 figure

Joint Clustering and Registration of Functional Data

Curve registration and clustering are fundamental tools in the analysis of functional data. While several methods have been developed and explored for either task individually, limited work has been done to infer functional clusters and register curves simultaneously. We propose a hierarchical model for joint curve clustering and registration. Our proposal combines a Dirichlet process mixture model for clustering of common shapes, with a reproducing kernel representation of phase variability for registration. We show how inference can be carried out applying standard posterior simulation algorithms and compare our method to several alternatives in both engineered data and a benchmark analysis of the Berkeley growth data. We conclude our investigation with an application to time course gene expression

Phase separation and critical percolation in bidimensional spin-exchange models

Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phase-separate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this dynamics first takes a system with equal density of the two species to a critical percolation state. We prove this claim and we determine the time-dependence of the growing length associated to this process with the scaling analysis of the statistical and morphological properties of the clusters of the two phases.Comment: 6 pages, 9 figure