Normalize the transition matrix.

normalize(x, ...)

Arguments

x

object of class 'Transition*'

...

optional argument method (see Details)

Value

an object of class TransitionLayer

Details

argument method passed through ... a character for the normalization method the default is 'row' users can set the optional method argument to either "col" or "symm"

Normalization of the weighted adjacency matrix in the Transition* object. Matrix values are divided by their respective row-sums, column-sums, or the product of the square-roots of both (symmetric normalization).

The default method is row-normalization. To use the other normalization methods, users can set the optional method argument to either "col" or "symm".

For random walk calculations a symmetric matrix is needed (method = "symm").

References

von Luxburg, U. 2007. A tutorial on spectral clustering. Statistics and Computing 17(4), 395-416. http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.0189v1.pdf

Chung, F. 1997. Spectral Graph Theory. Conference Board of the Mathematical Sciences, Washington.

Examples

library("raster")
r <- raster(ncol=36,nrow=18)
r <- setValues(r,rep(1,times=ncell(r)))
tr <- transition(r, mean, directions=8)

normalize(tr)

normalize(tr, method="symm")