Exploring Latent Structure Similarity For Bayesian Nonparameteric Model With Mixture Of Nhpp Sequence

Temporal point process data has been widely observed in many applications including finance, health, and infrastructures, so that it has become an important topic in data analytics domain. Generally, a point process only records occurrence of a type of event as 1 or 0. To interpret the temporal point process, it is important to estimate the intensity of the occurrence of events, which is challenging especially when the intensity is dynamic over time, for example non-homogeneous Poisson process (NHPP) which is exactly what we will analyse in this paper. We performed a joint task to determine which two NHPP sequences are in the same group and to estimate the intensity resides in that group. Distance dependent Chinese Restaurant Process (ddCRP) provides a prior to cluster data points within a Bayesian nonparametric framework, alleviating the required knowledge to set the number of clusters which is sensitive in clustering problems. However, the distance in previous studies of ddCRP is designed for data points, in this paper such distance is measured by dynamic time warping (DTW) due to its wide application in ordinary time series (e.g. observed values are in R). The empirical study using synthetic and real-world datasets shows promising outcome compared with the alternative techniques.