Identify Cluster Centres for 3-dimensional Data via Data Sharpening

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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.

See Also

sharp3dB

Examples

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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)