ieimetric {mmpp}

Compute Inter Event Interval-based Metric Between Marked Point Processes

Description

This metric considers inter event interval for point processes.

Usage

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.

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.

Value

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

Author(s)

Hideitsu Hino [e-mail], 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.

Examples

##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)