correDimEst: Correlation dimension estimation

In Yanhao29/GeoRatio: Nonlinear dimension reduction and clustering

Description

Takes in pair-wise distance of data and number of epsilons to estimate intrinsic dimension of data. Function returns, log(epsi) (stored in x), log(C2) (stored in y) values and the numerical derivative of log(C2) w.r.t log(epsi) (stored in deri). The estimated dimension is the level of the plateau (stable part) of the deriative of y w.r.t. x.

Usage

correDimEst(num, distance)

Arguments

num	Number of epsilons.
distance	Distance object (upper triangle) from dist() fn.

Value

a list of log(epsi) (x), lob(C2) (y) and derivatives of y.

Examples

############################## example I: Spiral data
## load data
data(spiral)

## intrinsic dimension of the data
trueDim = 1

## number of epsilons
num = 50

## pair-wise Euclidean distance
dis = dist(spiral,method = "euclidean", diag = FALSE, upper = TRUE)

## correlation dimension estimation
est = correDimEst(num,dis)

## plot correlation dimension estimation
par(mfrow=c(1,2))
plot(spiral,xlab='',ylab='')
# plot(est$x,est$y,xlab="log(epsilon)",ylab="log(C2(epsilon))",main="log-log plot")
plot(est$x[2:(length(est$x)-1)],est$deri,type="l",ylim=c(0,10),xlab="log(epsilon)",ylab="est. correlation dimension",
     main="Estimated correlation dimension")
abline(trueDim,0,lty=3,col="gray60",lwd=2)


############################## example II: Open box data
library(rgl) ## for open3d(), 3d plot

## load data
data(OpenBox)

## intrinsic dimension of the data
trueDim = 2

## number of epsilons
num = 50

## pair-wise Euclidean distance
dis = dist(OpenBox,method = "euclidean", diag = FALSE, upper = TRUE)

## correlation dimension estimation
est = correDimEst(num,dis)

## plot correlation dimension estimation
open3d()
plot3d(OpenBox,col=col.f,axes=FALSE,box=FALSE,xlab = "", ylab = "", zlab = "",xlim=c(0,2),ylim=c(0,2),zlim=c(0,2),cex.lab=1)

par(mfrow=c(1,1))
# plot(est$x,est$y,xlab="log(epsilon)",ylab="log(C2(epsilon))",main="log-log plot")
plot(est$x[2:(length(est$x)-1)],est$deri,type="l",ylim=c(0,10),xlab="log(epsilon)",ylab="est. correlation dimension",
     main="Estimated correlation dimension")
abline(trueDim,0,lty=3,col="gray60",lwd=2)

Yanhao29/GeoRatio documentation built on May 10, 2019, 12:05 a.m.