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kdr

Kernel density ridge estimation

Description

Kernel density ridge estimation for 2- to 3-dimensional data.

Usage

kdr(x, y, H, p=1, max.iter=400, tol.iter, tol.seg, min.seg.size,
    keep.path=FALSE, gridsize, xmin, xmax, binned, bgridsize, w, fhat,
    density.cutoff, verbose=FALSE)

Arguments

`x`	matrix of data values
`y`	matrix of initial values
`p`	dimension of density ridge
`H`	bandwidth matrix/scalar bandwidth. If missing, `Hpi(x,deriv,order=2)` is called by default.
`max.iter`	maximum number of iterations. Default is 400.
`tol.iter`	distance under which two successive iterations are considered convergent. Default is 0.001*min marginal IQR of `x`.
`tol.seg`	distance under which two segments are considered to form one segment. Default is 0.01*max marginal IQR of `x`.
`min.seg.size`	minimum length of a segment of a density ridge. Default is `round(0.001*nrow(y),0)`.
`keep.path`	flag to store the density gradient ascent paths. Default is FALSE.
`gridsize`	vector of number of grid points
`xmin,xmax`	vector of minimum/maximum values for grid
`binned`	flag for binned estimation.
`bgridsize`	vector of binning grid sizes
`w`	vector of weights. Default is a vector of all ones.
`fhat`	kde of `x`. If missing `kde(x=x,w=w)` is executed.
`density.cutoff`	density threshold under which the `y` are excluded from the density ridge estimation. Default is `contourLevels(fhat, cont=99)`.
`verbose`	flag to print out progress information. Default is FALSE.

Details

Kernel density ridge estimation is based on reduced dimension kernel mean shift. See Ozertem & Erdogmus (2011).

If y is missing, then it defaults to the grid of size gridsize spanning from xmin to xmax.

If the bandwidth H is missing, then the default bandwidth is the plug-in selector for the density gradient Hpi(x,deriv.order=2). Any bandwidth that is suitable for the density Hessian is also suitable for the kernel density ridge.

Value

A kernel density ridge set is an object of class kdr which is a list with fields:

`x,y`	data points - same as input
`end.points`	matrix of final iterates starting from `y`
`H`	bandwidth matrix
`names`	variable names
`tol.iter,tol.clust,min.seg.size`	tuning parameter values - same as input
`binned`	flag for binned estimation
`names`	variable names
`w`	vector of weights
`path`	list of density gradient ascent paths where `path[[i]]` is the path of `y[i,]` (only if `keep.path=TRUE`)

References

Ozertem, U. & Erdogmus, D. (2011), Locally defined principal curves and surfaces, Journal of Machine Learning Research, 12, 1249-1286.

Examples

if(interactive()){
library(maps)
data(quake) 
quake <- quake[quake$prof==1,]  ## Pacific Ring of Fire 
quake$long[quake$long<0] <- quake$long[quake$long<0] + 360
quake <- quake[, c("long", "lat")]
data(plate)                     ## tectonic plate boundaries
plate <- plate[plate$long < -20 | plate$long > 20,]
plate$long[plate$long<0 & !is.na(plate$long)] <- plate$long[plate$long<0
& !is.na(plate$long)] + 360

dr.quake <- kdr(x=quake, xmin=c(70,-70), xmax=c(310, 80))
map("world2", xlim=c(85, 305), ylim=c(-70, 70), lty=2)
lines(plate[,1:2], col=3, lwd=2)
points(dr.quake$end.points, cex=0.5, pch=16, col=2)}

ks

Kernel Smoothing

v1.12.0

GPL-2 | GPL-3

Authors

Tarn Duong [aut, cre], Matt Wand [ctb], Jose Chacon [ctb], Artur Gramacki [ctb]

Initial release

2021-02-06

kdr