multisom.batch: MultiSOM for batch version
In multisom: Clustering a Data Set using Multi-SOM Algorithm

Description Usage Arguments Details Value Author(s) References Examples

This function implements the batch version of MultiSOM algorithm.

multisom.batch(data= NULL,xheight,xwidth,topo=c("rectangular",
           "hexagonal"),min.radius,max.radius,maxit=1000,
           init=c("random","sample","linear"),radius.type=
           c("gaussian","bubble","cutgauss","ep"),index="all")

`data`	data to be used
`xheight`	the x-dimension of the map
`xwidth`	the y-dimension of the map
`topo`	the topology used to build the grid.The following are permitted: `"hexagonal"` `"rectangular"`
`min.radius`	the minimum neighbourhood radius
`max.radius`	the maximum neighbourhood radius
`maxit`	the maximum number of iterations to be done
`init`	the method to be used to initialize the prototypes.The following are permitted: `"random"` uses random draws from N(0,1); `"sample"` uses a radom sample from the data; `"linear"` uses the linear grids upon the first two principle components direction.
`radius.type`	the neighborhood function type. The following are permitted: `"gaussian"` `"bubble"` `"cutgauss"` `"ep"`
`index`	vector of the index to be calculated. This should be one of : "db", "dunn", "silhouette", "ptbiserial", "ch", "cindex", "ratkowsky", "mcclain", "gamma", "gplus", "tau", "ccc", "scott", "marriot", "trcovw", "tracew", "friedman", "rubin", "ball", "sdbw", "dindex", "hubert", "sv", "xie-beni", "hartigan", "ssi", "xu", "rayturi", "pbm", "banfeld", "all" (all indices will be used)

Index	Optimal number of clusters
1. "db" or "all"	Minimum value of the index
(Davies and Bouldin 1979)
2. "dunn" or "all"	Maximum value of the index
(Dunn 1974)
3. "silhouette" or "all"	Maximum value of the index
(Rousseeuw 1987)
4. "ptbiserial" or "all"	Maximum value of the index
(Milligan 1980, 1981)
5. "ch" or "all"	Maximum value of the index
(Calinski and Harabasz 1974)
6. "cindex" or "all"	Minimum value of the index
(Hubert and Levin 1976)
7. "ratkowsky" or "all"	Maximum value of the index
(Ratkowsky and Lance 1978)
8. "mcclain" or "all"	Minimum value of the index
(McClain and Rao 1975)
9. "gamma" or "all"	Maximum value of the index
(Baker and Hubert 1975)
10. "gplus" or "all"	Minimum value of the index
(Rohlf 1974) (Milligan 1981)
11. "tau" or "all"	Maximum value of the index
(Rohlf 1974) (Milligan 1981)
12. "ccc" or "all"	Maximum value of the index
(Sarle 1983)
13. "scott" or "all"	Max. difference between hierarchy
(Scott and Symons 1971)	levels of the index
14. "marriot" or "all"	Max. value of second differences
(Marriot 1971)	between levels of the index
15. "trcovw" or "all"	Max. difference between hierarchy
(Milligan and Cooper 1985)	levels of the index
16. "tracew" or "all"	Max. value of absolute second
(Milligan and Cooper 1985)	differences between levels of the index
17. "friedman" or "all"	Max. difference between hierarchy
(Friedman and Rubin 1967)	levels of the index
18. "rubin" or "all"	Min. value of second differences
(Friedman and Rubin 1967)	between levels of the index
19. "ball" or "all"	Max. difference between hierarchy
(Ball and Hall 1965)	levels of the index
20. "sdbw" or "all"	Minimum value of the index
(Halkidi and Vazirgiannis 2001)
21. "dindex" or "all"	Graphical method
(Lebart et al. 2000)
22. "hubert" or "all"	Graphical method
(Hubert and Arabie 1985)
23. "sv" or "all"	Maximum value of the index
(Zalik and Zalik, 2011)
24. "xie-beni" or "all"	Minimum value of the index
(Xie and Beni 1991)
25. "hartigan" or "all"	Maximum difference between
(Hartigan 1975)	hierarchy levels of the index
26. "ssi" or "all"	Maximum value of the index
(Dolnicar,Grabler and Mazanec 1999)
27. "xu" or "all"	Max. value of second differences
(Xu 1997)	between levels of the index
28. "rayturi" or "all"	Minimum value of the index
(Ray and Turi 1999)
29. "pbm" or "all"	Maximum value of the index
(Bandyopadhyay,Pakhira and Maulik 2004)
30. "banfeld" or "all"	Minimum value of the index
(Banield and Raftery 1974)

`All.index.by.layer`	Values of indices for each layer
`Best.nc`	Best number of clusters proposed by each index and the corresponding index value.
`Best.partition`	Partition that corresponds to the best number of clusters

Sarra Chair and Malika Charrad

Charrad M., Ghazzali N., Boiteau V., Niknafs A. (2014). "NbClust: An R Package for Determining the Relevant Number of Clusters in a Data Set.", "Journal of Statistical Software, 61(6), 1-36.", "URL http://www.jstatsoft.org/v61/i06/".

Khanchouch, I., Charrad, M., & Limam, M. (2014). A Comparative Study of Multi-SOM Algorithms for Determining the Optimal Number of Clusters. Journal of Statistical Software, 61(6), 1-36.

## A 4-dimensional example

set.seed(1)

data<-rbind(matrix(rnorm(100,sd=0.3),ncol=2),
         matrix(rnorm(100,mean=2,sd=0.3),ncol=2),
         matrix(rnorm(100,mean=4,sd=0.3),ncol=2),
         matrix(rnorm(100,mean=8,sd=0.3),ncol=2))

res<- multisom.batch(data,xheight= 8, xwidth= 8,"hexagonal",
                min.radius=0.00010,max.radius=0.002,
                maxit=1000,"random","gaussian","ch")

res$All.index.by.layer
res$Best.nc
res$Best.partition