# sharp3d: Identify Cluster Centres for 3-dimensional Data via Data... In CHsharp: Choi and Hall Style Data Sharpening

## Description

Identifies the centres of clusters for 3-dimensional data using a convergent form of Choi and Hall's (1999) data sharpening method.

## Usage

 `1` ```sharp3d(x, y, z, hspace = 1, htime = 1, v = 1) ```

## Arguments

 `x` the x coordinates of the data `y` the y coordinates of the data `z` the z coordinates of the data `hspace` the bandwidth for sharpening in the direction of the x-y plane `htime` the bandwidth for sharpening in the z direction `v` a positive integer representing the number of iterations to perform

## Details

Identifies the centres of clusters based on a convergent form of Choi and Hall's data sharpening method. This function was originally built for identifying clusters in space-time where space is the x-y plane and time is the z-axis.

## Value

Returns a (number of data points x 3) data frame containing the sharpened points x.sharp, y.sharp and z.sharp, respectively.

## Author(s)

Douglas G. Woolford, W. John Braun

## References

Woolford, D. G. and Braun, W. J. (2004) Exploring lightning and fire ignition data as point processes. 2004 Proceeding of the American Statistical Association, Statistics and the Environment Section [CD-ROM], Alexandria, VA: American Statistical Association.

Choi, E. and Hall, P. (1999) Data sharpening as a prelude to density estimation. Biometrika 86, 941-947.

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```x <- 1:200 y <- c(rnorm(50,-1,1),rnorm(50,2,2), rnorm(100,0,.5)) z <- c(sample(1:50,50), sample(26:75,50), sample(51:150,100)) data.sharp5 <- sharp3d(x,y,z,5,10,5) data.sharp10 <- sharp3d(x,y,z,5,10,10) # original data: dataPlot <- scatterplot3d(x,y,z) # sharpened data after 5 iterations: dataPlot\$points3d(data.sharp5\$x.sharp, data.sharp5\$y.sharp, data.sharp5\$z.sharp, col=2,pch=19) # sharpened data after 10 iterations: dataPlot\$points3d(data.sharp10\$x.sharp, data.sharp10\$y.sharp, data.sharp10\$z.sharp, col=4, pch=19) ```