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