# Compute Filter-based Metrics in a Functional Space Between Marked Point Processes The most commonly used and intensively studied metrics for spike trains, which is based on the continuation of event sequence to a real valued continuous function using a smoother function. ```r fmetric(S1, S2, measure = "sim", h = "laplacian", tau = 1, M = NULL, abs.tol = .Machine$double.eps^0.25) ``` ## Arguments - `S1`: marked point process data. - `S2`: marked point process data. - `measure`: `"sim"` for similarity and `"dist"` for distance. Default `"sim"`. - `h`: filtering function. Default `"laplacian"` offers significant computational advantage. A function can be specified here like `h=function(x,tau) exp(-x^2/tau)`. The function should be square integrable and non-negative (not checked in the code). - `tau`: parameter for filtering function. - `M`: a precision matrix for filter of marks, i.e., exp( - r' M r) is used for filtering marks. It should be symmetric and positive semi-definite. - `abs.tol`: absolute tolerance for numerical integration. ## Returns Similarity or distance between two inputs (marked) point process S1 and S2. ## Details `fmetric` computes filter-based measure between MPP realizations. Discrete event timings are transformed into a continuous function by using a kernel smoother, and usual l2 inner product is adopted for defining the similarity between two point process realizations. ## Examples ```r ##The aftershock data of 26th July 2003 earthquake of M6.2 at the northern Miyagi-Ken Japan. data(Miyagi20030626) ## time longitude latitude depth magnitude ## split events by 7-hour sMiyagi <- splitMPP(Miyagi20030626,h=60*60*7,scaleMarks=TRUE)$S N <- 10 tau <- 0.1 sMat <- matrix(0,N,N) cat("calculating fmetric with tau ",tau,"...") for(i in 1:(N)){ cat(i," ") for(j in i:N){ S1 <- sMiyagi[[i]]$time;S2 <- sMiyagi[[j]]$time sMat[i,j] <- fmetric(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 M. C. W. van Rossum. A Novel Spike Distance. Neural Computation, Vol. 13(4), pp. 751-763, 2001. S. Schreiber, J.M. Fellous, P.H. Tiesinga, and T.J. Sejnowski. A new correlation-based measure of spike timing reliability, Neurocomputing, Vols. 52-54, pp. 925-931, 2003.

fmetric function