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Catalogs of periodic variable stars contain large numbers of periodiclight-curves (photometric time series data from the astrophysics domain).Separating anomalous objects from well-known classes is an important steptowards the discovery of new classes of astronomical objects. Most anomalydetection methods for time series data assume either a single continuous timeseries or a set of time series whose periods are aligned. Light-curve dataprecludes the use of these methods as the periods of any given pair oflight-curves may be out of sync. One may use an existing anomaly detectionmethod if, prior to similarity calculation, one performs the costly act ofaligning two light-curves, an operation that scales poorly to massive datasets. This paper presents PCAD, an unsupervised anomaly detection method forlarge sets of unsynchronized periodic time-series data, that outputs a rankedlist of both global and local anomalies. It calculates its anomaly score foreach light-curve in relation to a set of centroids produced by a modifiedk-means clustering algorithm. Our method is able to scale to large data setsthrough the use of sampling. We validate our method on both light-curve dataand other time series data sets. We demonstrate its effectiveness at findingknown anomalies, and discuss the effect of sample size and number of centroidson our results. We compare our method to naive solutions and existing timeseries anomaly detection methods for unphased data, and show that PCAD'sreported anomalies are comparable to or better than all other methods. Finally,astrophysicists on our team have verified that PCAD finds true anomalies thatmight be indicative of novel astrophysical phenomena.

Finding Anomalous Periodic Time Series: An Application to Catalogs of Periodic Variable Stars