  We introduce a new periodicity detection algorithm for binary time series of
event onsets, the Gaussian Mixture Periodicity Detection Algorithm (GMPDA). The
algorithm approaches the periodicity detection problem to infer the parameters
of a generative model. We specified two models - the Clock and Random Walk -
which describe two different periodic phenomena and provide a generative
framework. The algorithm achieved strong results on test cases for single and
multiple periodicity detection and varying noise levels. The performance of
GMPDA was also evaluated on real data, recorded leg movements during sleep,
where GMPDA was able to identify the expected periodicities despite high noise
levels. The paper's key contributions are two new models for generating
periodic event behavior and the GMPDA algorithm for multiple periodicity
detection, which is highly accurate under noise.
