Gaia eclipsing binary and multiple systems. Supervised classification and self-organizing maps
1 Dept. of Astronomy, University of Geneva, Chemin d’Ecogia 16, 1290 Versoix, Switzerland
2 Dept. of Astronomy, University of Geneva, Chemin des Maillettes 51, 1290 Versoix, Switzerland
3 Villanova University, Dept. of Astrophysics and Planetary Science, 800 Lancaster Ave, Villanova PA 19085, USA
4 Dept. of Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Received: 13 September 2016
Accepted: 27 December 2016
Context. Large surveys producing tera- and petabyte-scale databases require machine-learning and knowledge discovery methods to deal with the overwhelming quantity of data and the difficulties of extracting concise, meaningful information with reliable assessment of its uncertainty. This study investigates the potential of a few machine-learning methods for the automated analysis of eclipsing binaries in the data of such surveys.
Aims. We aim to aid the extraction of samples of eclipsing binaries from such databases and to provide basic information about the objects. We intend to estimate class labels according to two different, well-known classification systems, one based on the light curve morphology (EA/EB/EW classes) and the other based on the physical characteristics of the binary system (system morphology classes; detached through overcontact systems). Furthermore, we explore low-dimensional surfaces along which the light curves of eclipsing binaries are concentrated, and consider their use in the characterization of the binary systems and in the exploration of biases of the full unknown Gaia data with respect to the training sets.
Methods. We have explored the performance of principal component analysis (PCA), linear discriminant analysis (LDA), Random Forest classification and self-organizing maps (SOM) for the above aims. We pre-processed the photometric time series by combining a double Gaussian profile fit and a constrained smoothing spline, in order to de-noise and interpolate the observed light curves. We achieved further denoising, and selected the most important variability elements from the light curves using PCA. Supervised classification was performed using Random Forest and LDA based on the PC decomposition, while SOM gives a continuous 2-dimensional manifold of the light curves arranged by a few important features. We estimated the uncertainty of the supervised methods due to the specific finite training set using ensembles of models constructed on randomized training sets.
Results. We obtain excellent results (about 5% global error rate) with classification into light curve morphology classes on the Hipparcos data. The classification into system morphology classes using the Catalog and Atlas of Eclipsing binaries (CALEB) has a higher error rate (about 10.5%), most importantly due to the (sometimes strong) similarity of the photometric light curves originating from physically different systems. When trained on CALEB and then applied to Kepler-detected eclipsing binaries subsampled according to Gaia observing times, LDA and SOM provide tractable, easy-to-visualize subspaces of the full (functional) space of light curves that summarize the most important phenomenological elements of the individual light curves. The sequence of light curves ordered by their first linear discriminant coefficient is compared to results obtained using local linear embedding. The SOM method proves able to find a 2-dimensional embedded surface in the space of the light curves which separates the system morphology classes in its different regions, and also identifies a few other phenomena, such as the asymmetry of the light curves due to spots, eccentric systems, and systems with a single eclipse. Furthermore, when data from other surveys are projected to the same SOM surface, the resulting map yields a good overview of the general biases and distortions due to differences in time sampling or population.
Key words: methods: data analysis / methods: statistical / binaries: eclipsing / surveys
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