iipmetric {mmpp}

Compute Intensity Inner Product Metrics

Description

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.

Usage

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.

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.

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

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.

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)$S
N <- 10
tau <- 0.1
sMat <- matrix(0,N,N)
  cat("calculating intensity inner product...")
 for(i in 1:(N)){
   cat(i," ")
   for(j in i:N){
     S1 <- sMiyagi[[i]]$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)