On Machine-Learned Classification of Variable Stars With Sparse and Noisy Time-Series Data

Abstract

With the coming data deluge from synoptic surveys, there is a growing need for frameworks that can quickly and automatically produce calibrated classification probabilities for newly-observed variables based on a small number of time-series measurements. In this paper, we introduce a methodology for variable-star classification, drawing from modern machine-learning techniques. We describe how to homogenize the information gleaned from light curves by selection and computation of real-numbered metrics (features), detail methods to robustly estimate periodic light-curve features, introduce treeensemble methods for accurate variable star classification, and show how to rigorously evaluate the classification results using cross validation. On a 25-class data set of 1542 well-studied variable stars, we achieve a 22.8% overall classification error using the random forest classifier; this represents a 24% improvement over the best previous classifier on these data. This methodology is effective for identifying samples of specific science classes: for pulsational variables used in Milky Way tomography we obtain a discovery efficiency of 98.2% and for eclipsing systems we find an efficiency of 99.1%, both at 95% purity. We show that the random forest (RF) classifier is superior to other machine-learned methods in terms of accuracy, speed, and relative immunity to features with no useful class information; the RF classifier can also be used to estimate the importance of each feature in classification. Additionally, we present the first astronomical use of hierarchical classification methods to incorporate a known class taxonomy in the classifier, which further reduces the catastrophic error rate to 7.8%. Excluding low-amplitude sources, our overall error rate improves to 14%, with a catastrophic error rate of 3.5%. 5 High-precision photometry missions (Kepler, MOST, CoRoT, etc.) are already challenging the theoretical understanding of the origin of variability and the connection of some specific sources to established classes of variables. 6 General Catalog of Variable Stars, http://www.sai.msu.su/groups/cluster/gcvs/gcvs/ 7 Not discussed herein are the challenges associated with discovery of variability. See Shin et al. (2009) for a review.

A New Catalog of Variable Stars in the Field of the Open Cluster M37

“…But the latter is rather ambiguous, since it is not always possible to characterize flux variation and to define a reliable range for some parameters. To overcome this difficulty, Richards et al (2011) calculated many basic statistics that can describe the distribution of fluxes even in the limit of few data points. One interesting approach is to select stochastically varying features in quasar-like sources.…”

The Catalina Surveys Southern periodic variable star catalogue

“…In contrast, RRab's generally have M t > 0.5 (and longer periods), while RRc's have M t values near 0.4. The effect of M t is similar to that of non-parametric skew, which is effective in separating eclipsing binaries from other types of variables (see for example Richards et al 2011;Dubath et al 2011). However, M t is also useful for separating other types of variables from each other.…”

New insights into time series analysis

“…Indeed automatic classifiers also use these parameters to facilitate the classification of variable stars (e.g. Richards et al 2011). The variability indices are a fundamental tool to improving all processes of the time domain analysis.…”

“…Automatic classifiers based on machine learning have been applied to several large time-series data sets (e.g. Woźniak et al 2004;Debosscher et al 2007;Sarro et al 2009;Blomme et al 2010;Richards et al 2011;Dubath et al 2011). The inclusion of periodic and non-periodic features, statistics, and more sophisticated model parameters have improved automatic classifiers (e.g.…”

“…The inclusion of periodic and non-periodic features, statistics, and more sophisticated model parameters have improved automatic classifiers (e.g. Richards et al 2011). Misclassification, fuzzy boundaries between variable stars' classes, mis-labelled training sets, as well as full processing of terabytes of data are current scientific challenges (Eyer 2006).…”