1d:T782,# Compute Intensity Inner Product Metrics For the analysis of point process, intensity function plays a central roll. Paiva et al. (2009) proposed to use the intensity function for defining the inner product between point process realizations. ```r iipmetric(S1, S2, measure = "sim", tau = 1, M = NULL) ``` ## Arguments - `S1`: marked point process data. - `S2`: marked point process data. - `measure`: `"sim"` for similarity and `"dist"` for distance. Default `"sim"`. - `tau`: a parameter for filtering function. - `M`: a precision matrix for filter of marks, i.e., exp( - r' M r) is used for filtering marks. It should be symmetric and positive semi-definite. ## Returns Similarity or distance between two inputs (marked) point process S1 and S2. ## Details `iipmetric` computes intensity inner product metric. Intensity function for the point process realization is estimated by kernel density estimator. This function adopts Gaussian kernels for the sake of computational efficiency. ## Examples ```r ##The aftershock data of 26th July 2003 earthquake of M6.2 at the northern Miyagi-Ken Japan. data(Miyagi20030626) ## time longitude latitude depth magnitude ## split events by 7-hour sMiyagi <- splitMPP(Miyagi20030626,h=60*60*7,scaleMarks=TRUE)$S N <- 10 tau <- 0.1 sMat <- matrix(0,N,N) cat("calculating intensity inner product...") for(i in 1:(N)){ cat(i," ") for(j in i:N){ S1 <- sMiyagi[[i]]$time;S2 <- sMiyagi[[j]]$time sMat[i,j] <- iipmetric(S1,S2,tau=tau,M=diag(1,4)) } } sMat <- sMat+t(sMat) tmpd <- diag(sMat) <- diag(sMat)/2 sMat <- sMat/sqrt(outer(tmpd,tmpd)) image(sMat) ``` ## Author(s) Hideitsu Hino hinohide@cs.tsukuba.ac.jp , Ken Takano, Yuki Yoshikawa, and Noboru Murata ## References A.R.C. Paiva, I. Park, and J.C. Principe. A reproducing kernel Hilbert space framework for spike train signal processing, Neural Computation, Vol. 21(2), pp. 424-449, 2009.

iipmetric function