Abstract—The article discusses the inhomogeneous point process intensity reconstruction for the case when a process is given by a realization of its discrete point set, samples, whose intensity of appearance is not known. The specificity of the problem under consideration is that a priori information is also assumed to be associated only with the registered data of previously analyzed similar processes - referred to in the paper as precedents. So, in the frames of the approach the reconstruction problem is posed as the statistical identification of the registered data with already observed precedents, rather than the traditional in statistics problem of hypothesis testing. The solution to the problem is proposed for the special class of point processes - Poisson Point Processes. Identification of the recorded PPP with one of the precedents stored in prepared database is implied up to a shift and scale transforms. The identification procedure synthesis and precedents database refill are considered in the frames of the maximum likelihood approach, whose implementation is carried out according to the principles of machine learning. The description of the point process registered and precedents are chosen as a mixture (superposition) of Gaussian components. Recurrent calculation of the log-likelihood function is structured in the form of EM-like algorithm adapted to the problem.  

Index Terms—inhomogeneous point process, Poison process intensity identification, machine learning, EM algorithm, Gaussian mixtures, effective computational schemes

Cite: Viacheslav Antsiperov and Aleksei Morozov, "Point Process Intensity Shape Identification Based on Available Precedents Stochastic Descriptions," International Journal of Signal Processing Systems, Vol. 7, No. 3, pp. 103-106, September 2019. doi: 10.18178/ijsps.7.3.103-106