mmpp (version 0.1)

fmetric: Compute Filter-based Metrics in the Functional Space Between Marked Point Processes

Description

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.

Usage

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).

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.

Value

• similarity or distance between two inputs (marked) point process S1 and S2.

Details

fmetric computes filter-based measure between MPP instances. 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 instances.

References

M. C. W. van Rossum. 2001. A Novel Spike Distance. Neural Comput. 13, 4 (April 2001), 751-763.

S. Schreiber, J.M. Fellous, P.H. Tiesinga, T.J. Sejnowski, A new correlation-based measure of spike timing reliability, Neurocomputing 2003; 52-54:925--31

Examples

##The aftershock data of 26th July 2003 earthquake of M6.2 at the northern Miyagi-Ken Japan.
data(Miyagi20030626)
##  no. longitude latitude magnitude  time  depth year month day
## split events by 7-day
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)