# Compute Inter Event Interval-based Metric Between Marked Point Processes This metric considers inter event interval for point processes. ```r ieimetric(S1, S2, measure = "sim", M = NULL, window.length = NULL, variant = "spike", abs.tol = .Machine$double.eps^0.25) ``` ## Arguments - `S1`: marked point process data. - `S2`: marked point process data. - `measure`: `"sim"` for similarity and `"dist"` for distance. Default `"sim"`. - `M`: a precision matrix for filter of marks, i.e., exp( - r' M r) is used for filtering marks. It should be symmetric and positive semi-definite. - `window.length`: width of the window used for splitting the original MPP. If not provided, `max(max(S1$time,S2$time) - min(S1$time,S2$time))` is used. - `variant`: choose from two variants "spike-weighted" or "time-weighted". Default `"spike"`, which is computationally efficient than `"time"`. See the reference for details. - `abs.tol`: absolute tolerance for numerical integration. ## Returns Similarity or distance between two inputs (marked) point process S1 and S2. ## Details `iei` computes inter event interval-based measure between MPP realizations. iei for simple point process does not have any tuning parameter, which can be a desirable property for data analysis. However, it's computational cost is relatively higher than other metrics. ## Examples ```r ##The aftershock data of 26th July 2003 earthquake of M6.2 at the northern Miyagi-Ken Japan. data(Miyagi20030626) ## time longitude latitude depth magnitude ## split events by 7-hour sMiyagi <- splitMPP(Miyagi20030626,h=60*60*7,scaleMarks=TRUE)$S N <- 5 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] <- ieimetric(S1,S2,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 T. Kreuz, J.S. Haas, A. Morelli, H.D.I. Abarbanel, and A. Politi. Measuring spike train synchrony, Journal of Neuroscience Methods, Vol. 165(1), pp. 151-161, 2007.

ieimetric function