# nnclean

##### Nearest Neighbour Clutter Removal

Detect features in a 2D or 3D spatial point pattern using nearest neighbour clutter removal.

##### Usage

`nnclean(X, k, ...)` # S3 method for ppp
nnclean(X, k, ...,
edge.correct = FALSE, wrap = 0.1,
convergence = 0.001, plothist = FALSE,
verbose = TRUE, maxit = 50)

# S3 method for pp3
nnclean(X, k, ...,
convergence = 0.001, plothist = FALSE,
verbose = TRUE, maxit = 50)

##### Arguments

- X
A two-dimensional spatial point pattern (object of class

`"ppp"`

) or a three-dimensional point pattern (object of class`"pp3"`

).- k
Degree of neighbour:

`k=1`

means nearest neighbour,`k=2`

means second nearest, etc.- …
Arguments passed to

`hist.default`

to control the appearance of the histogram, if`plothist=TRUE`

.- edge.correct
Logical flag specifying whether periodic edge correction should be performed (only implemented in 2 dimensions).

- wrap
Numeric value specifying the relative size of the margin in which data will be replicated for the periodic edge correction (if

`edge.correct=TRUE`

). A fraction of window width and window height.- convergence
Relative tolerance threshold for testing convergence of EM algorithm.

- maxit
Maximum number of iterations for EM algorithm.

- plothist
Logical flag specifying whether to plot a diagnostic histogram of the nearest neighbour distances and the fitted distribution.

- verbose
Logical flag specifying whether to print progress reports.

##### Details

Byers and Raftery (1998) developed a technique for recognising features in a spatial point pattern in the presence of random clutter.

For each point in the pattern, the distance to the \(k\)th nearest neighbour is computed. Then the E-M algorithm is used to fit a mixture distribution to the \(k\)th nearest neighbour distances. The mixture components represent the feature and the clutter. The mixture model can be used to classify each point as belong to one or other component.

The function `nnclean`

is generic, with methods for
two-dimensional point patterns (class `"ppp"`

)
and three-dimensional point patterns (class `"pp3"`

)
currently implemented.

The result is a point pattern (2D or 3D) with two additional columns of marks:

- class
A factor, with levels

`"noise"`

and`"feature"`

, indicating the maximum likelihood classification of each point.- prob
Numeric vector giving the estimated probabilities that each point belongs to a feature.

The object also has extra information stored in attributes:
`"theta"`

contains the fitted parameters
of the mixture model, `"info"`

contains
information about the fitting procedure, and `"hist"`

contains
the histogram structure returned from `hist.default`

if `plothist = TRUE`

.

##### Value

An object of the same kind as `X`

,
obtained by attaching marks to the points of `X`

.

The object also has attributes, as described under Details.

##### References

Byers, S. and Raftery, A.E. (1998)
Nearest-neighbour clutter removal for estimating features
in spatial point processes.
*Journal of the American Statistical Association*
**93**, 577--584.

##### See Also

##### Examples

```
# NOT RUN {
# shapley galaxy cluster
X <- nnclean(shapley, k=17, plothist=TRUE)
plot(X, which.marks=1, chars=c(".", "+"), cols=1:2,
main="Shapley data, cluster and noise")
plot(X, which.marks=2, cols=function(x)hsv(0.2+0.8*(1-x),1,1),
main="Shapley data, probability of cluster")
Y <- split(X, un=TRUE)
plot(Y, chars="+", cex=0.5)
marks(X) <- marks(X)$prob
plot(cut(X, breaks=3), chars=c(".", "+", "+"), cols=1:3)
# }
```

*Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)*