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