Identifies the centres of clusters for 2-dimensional data using a converged form of Choi and Hall's (1999) data sharpening method.

1 | ```
sharp2d(x, y, hspace = 1, htime = 1, v = 1)
``` |

`x` |
the x coordinates of the data |

`y` |
the y coordinates of the data |

`hspace` |
the bandwidth for sharpening in the direction of the x axis |

`htime` |
the bandwidth for sharpening in the y direction |

`v` |
a positive integer representing the number of iterations to perform |

Identifies the centres of clusters based on a converged 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.

Returns a (number of data points x 2) data frame containing the sharpened points x.sharp and y.sharp, respectively.

Douglas G. Woolford, W. John Braun

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 | ```
x <- 1:200
y <- c(rnorm(50,-1,1),rnorm(50,2,2), rnorm(100,0,.5))
data.sharp5 <- sharp2d(x,y,5,10,5)
data.sharp10 <- sharp2d(x,y,5,10,10)
# original data:
plot(x,y)
# sharpened data after 5 iterations:
points(data.sharp5$x.sharp, data.sharp5$y.sharp, col=2,pch=19)
# sharpened data after 10 iterations:
points(data.sharp10$x.sharp, data.sharp10$y.sharp, col=4, pch=19)
``` |

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