The trainSOM function returns a somRes class object which contains the outputs of the algorithm.

trainSOM(x.data, ...)

# S3 method for somRes
print(x, ...)

# S3 method for somRes
summary(object, ...)

## Arguments

x.data

a data frame or matrix containing the observations to be mapped on the grid by the SOM algorithm.

...

Further arguments to be passed to the function initSOM for specifying the parameters of the algorithm. The default values of the arguments maxit and dimension are calculated according to the SOM type if the user does not set them:

• maxit is equal to (number of rows+number of columns)*5 if the SOM type is korresp. It is equal to number of rows*5 in all other SOM types

• dimension: for a korresp SOM, is approximately equal to the square root of the number of observations to be classified divided by 10 but it is never smaller than 5 or larger than 10.

x

an object of class somRes.

object

an object of class somRes.

## Value

The trainSOM function returns an object of class somReswhich contains the following components:

• clustering the final classification of the data.

• prototypes the final coordinates of the prototypes.

• energy the final energy of the map. For the numeric case, energy with data having missing entries is based on data imputation as described in Cottrell and Letrémy (2005b).

• backup a list containing some intermediate backups of the prototypes coordinates, clustering, energy and the indexes of the recorded backups, if nb.save is set to a value larger than 1.

• data the original dataset used to train the algorithm.

• parameters a list of the map's parameters, which is an object of class paramSOM as produced by the function initSOM.

The function summary.somRes also provides an ANOVA (ANalysis Of VAriance) of each input numeric variables in function of the map's clusters. This is helpful to see which variables participate to the clustering.

## Details

The version of the SOM algorithm implemented in this package is the stochastic version.

Several variants able to handle non-vectorial data are also implemented in their stochastic versions: type="korresp" for contingency tables, as described in Cottrell et al. (2004) (with weights as in Cottrell and Letrémy, 2005a); type = "relational" for dissimilarity matrices, as described in Olteanu et al. (2015), with the fast implementation introduced in Mariette et al. (2017).

Missing values are handled as described in Cottrell et al. (2005b), not using missing entries of the selected observation during winner computation or prototype updates. This allows to proceed with the imputation of missing entries with the corresponding entries of the cluster prototype (with impute).

summary produces a complete summary of the results that displays the parameters of the SOM, quality criteria and ANOVA. For type = "numeric" the ANOVA is performed for each input variable and test the difference of this variable across the clusters of the map. For type = "relational" a dissimilarity ANOVA is performed (Anderson, 2001), except that in the present version, a crude estimate of the p-value is used which is based on the Fisher distribution and not on a permutation test.

## Note

Warning! Recording intermediate backups with the argument nb.save can strongly increase the computational time since calculating the entire clustering and the energy is time consuming. Use this option with care and only when it is strictly necessary.

## References

Anderson M.J. (2001). A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26, 32-46.

Kohonen T. (2001) Self-Organizing Maps. Berlin/Heidelberg: Springer-Verlag, 3rd edition.

Cottrell M., Ibbou S., Letrémy P. (2004) SOM-based algorithms for qualitative variables. Neural Networks, 17, 1149-1167.

Cottrell M., Letrémy P. (2005a) How to use the Kohonen algorithm to simultaneously analyse individuals in a survey. Neurocomputing, 21, 119-138.

Cottrell M., Letrémy P. (2005b) Missing values: processing with the Kohonen algorithm. Proceedings of Applied Stochastic Models and Data Analysis (ASMDA 2005), 489-496.

Olteanu M., Villa-Vialaneix N. (2015) On-line relational and multiple relational SOM. Neurocomputing, 147, 15-30.

Mariette J., Rossi F., Olteanu M., Mariette J. (2017) Accelerating stochastic kernel SOM. In: M. Verleysen, XXVth European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017), i6doc, Bruges, Belgium, 269-274.

See initSOM for a description of the parameters to pass to the trainSOM function to change its behavior and plot.somRes to plot the outputs of the algorithm.

## Author

Élise Maigné <elise.maigne@inrae.fr>
Jérome Mariette jerome.mariette@inrae.fr
Fabrice Rossi fabrice.rossi@apiacoa.org
Nathalie Vialaneix nathalie.vialaneix@inrae.fr

## Examples

# Run trainSOM algorithm on the iris data with 500 iterations
iris.som <- trainSOM(x.data=iris[,1:4])
iris.som
#>       Self-Organizing Map object...
#>          online learning, type: numeric
#>          5 x 5 grid with square topology
#>          neighbourhood type: gaussian
#>          distance type: euclidean
summary(iris.som)
#>
#> Summary
#>
#>       Class :  somRes
#>
#>       Self-Organizing Map object...
#>          online learning, type: numeric
#>          5 x 5 grid with square topology
#>          neighbourhood type: gaussian
#>          distance type: euclidean
#>
#>       Final energy     : 0.8543395
#>       Topographic error: 0
#>
#>       ANOVA                :
#>
#>         Degrees of freedom :  14
#>
#>                    F pvalue significativity
#> Sepal.Length  42.669      0             ***
#> Sepal.Width   18.012      0             ***
#> Petal.Length 295.589      0             ***
#> Petal.Width  160.906      0             ***
#>