The detection of globular clusters in galaxies as a data mining problem

We present an application of self-adaptive supervised learning classifiers derived from the Machine Learning paradigm, to the identification of candidate Globular Clusters in deep, wide-field, single band HST images. Several methods provided by the DAME (Data Mining & Exploration) web application, were tested and compared on the NGC1399 HST data described in Paolillo 2011. The best results were obtained using a Multi Layer Perceptron with Quasi Newton learning rule which achieved a classification accuracy of 98.3%, with a completeness of 97.8% and 1.6% of contamination. An extensive set of experiments revealed that the use of accurate structural parameters (effective radius, central surface brightness) does improve the final result, but only by 5%. It is also shown that the method is capable to retrieve also extreme sources (for instance, very extended objects) which are missed by more traditional approaches.Comment: Accepted 2011 December 12; Received 2011 November 28; in original form 2011 October 1

Empirical Risk Minimization for Probabilistic Grammars: Sample Complexity and Hardness of Learning

Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. They are used ubiquitously in computational linguistics. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of probabilistic grammars using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting. By making assumptions about the underlying distribution that are appropriate for natural language scenarios, we are able to derive distribution-dependent sample complexity bounds for probabilistic grammars. We also give simple algorithms for carrying out empirical risk minimization using this framework in both the supervised and unsupervised settings. In the unsupervised case, we show that the problem of minimizing empirical risk is NP-hard. We therefore suggest an approximate algorithm, similar to expectation-maximization, to minimize the empirical risk. Learning from data is central to contemporary computational linguistics. It is in common in such learning to estimate a model in a parametric family using the maximum likelihood principle. This principle applies in the supervised case (i.e., using annotate