computeGap {uHMM}

Compute gap between eigenvalues of a similarity matrix

Description

Find the highest gap between eigenvalues of a similarity matrix. The 2 first eigenvalues are considered as equal to each other (the gap between the 2 first eigenvalues is set to 0).

Usage

computeGap(similarity, Gmax)

Arguments

similarity

a similarity matrix.

Gmax

the maximum gap value allowed (only the first Gmax eigenvalues will be taken into account).

Value

The function returns a list containing the following components:

gap

a vector indicating the gap between similarity matrix eigenvalues (the gap between the 2 first eigenvalues is set to 0)

Kmax

an integer indicating the index of the highest gap (the highest gap is between the Kmax-th and the (Kmax+1)-th eigenvalues)

Examples

x <- rbind(matrix(rnorm(50, mean = 0, sd = 0.3), ncol = 2), 
           matrix(rnorm(50, mean = 2, sd = 0.3), ncol = 2), 
           matrix(rnorm(50, mean = 4, sd = 0.3), ncol = 2))

similarity<-ZPGaussianSimilarity(x,7)
Gap<-computeGap(similarity,10)
plot(1:length(Gap$gap),Gap$gap,type="h",
main=paste("Gap criteria =",Gap$K),ylab="gap value",xlab="eigenvalues")



x=(runif(1000)*4)-2;y=(runif(1000)*4)-2
keep<-which((x**2+y**2<0.5)|(x**2+y**2>1.5**2 & x**2+y**2<2**2 ))
data<-data.frame(x,y)[keep,]
plot(data)

similarity<-ZPGaussianSimilarity(data,1)
Gap<-computeGap(similarity,10)
plot(1:length(Gap$gap),Gap$gap,type="h",
main=paste("Gap criteria =",Gap$K),ylab="gap value",xlab="eigenvalues")