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Data of the form of event times arise in various applications. A simple modelfor such data is a non-homogeneous Poisson process (NHPP) which is specified bya rate function that depends on time. We consider the problem of having accessto multiple independent observations of event time data, observed on a commoninterval, from which we wish to classify or cluster the observations accordingto their rate functions. Each rate function is unknown but assumed to belong toa finite number of rate functions each defining a distinct class. We model therate functions using a spline basis expansion, the coefficients of which needto be estimated from data. The classification approach consists of usingtraining data for which the class membership is known, to calculate maximumlikelihood estimates of the coefficients for each group, then assigning testobservations to a group by a maximum likelihood criterion. For clustering, byanalogy to the Gaussian mixture model approach for Euclidean data, we considermixtures of NHPP and use the expectation-maximisation algorithm to estimate thecoefficients of the rate functions for the component models and groupmembership probabilities for each observation. The classification andclustering approaches perform well on both synthetic and real-world data sets.Code associated with this paper is available athttps://github.com/duncan-barrack/NHPP .

Classification and clustering for observations of event time data using non-homogeneous Poisson process models