Mmpp: A Package for Calculating Similarity and Distance Metrics for Simple and Marked Temporal Point Processes

Hideitsu Hino,Ken Takano,Noboru Murata

doi:10.32614/rj-2015-033

Abstract

A simple temporal point process (SPP) is an important class of time series, where the sample realization of the process is solely composed of the times at which events occur. Particular examples of point process data are neuronal spike patterns or spike trains, and a large number of distance and similarity metrics for those data have been proposed. A marked point process (MPP) is an extension of a simple temporal point process, in which a certain vector valued mark is associated with each of the temporal points in the SPP. Analyses of MPPs are of practical importance because instances of MPPs include recordings of natural disasters such as earthquakes and tornadoes. In this paper, we introduce the R package mmpp, which implements a number of distance and similarity metrics for SPPs, and also extends those metrics for dealing with MPPs.

Highlights

A random point process is a mathematical model for describing a series of discrete events (Snyder and Miller, 1991)
To complement the above mentioned packages, in mmpp (Hino et al, 2015), we focus on the similarity or distance metrics between realizations of point processes
Since a spike train is a realization of a simple point process, the original metrics developed in the field of neuroscience do not consider marked point process (MPP) realizations. mmpp extends conventional metrics for simple temporal point process (SPP) to MPPs

Summary

Introduction

A random point process is a mathematical model for describing a series of discrete events (Snyder and Miller, 1991). As for the distance and similarity metric for point processes, vast amount of methods are developed in the field of neuroscience (Kandel et al, 2000). In this field, neural activities are recorded as sequences of spikes (called spike trains), which is nothing but a realization of a simple point process (SPP). Since a spike train is a realization of a simple point process, the original metrics developed in the field of neuroscience do not consider marked point process (MPP) realizations. 2. to support MPPs to offer a platform for performing metric-based analysis of earthquakes, tornados, epidemics, or stock exchange data

Distances and similarities for point processes

Filtering to a continuous function

Intensity inner products

Inter event interval

Extension to marked point processes

Filtering to continuous function

Intensity inner product