R: Self- and super-organising maps

supersom {kohonen} | R Documentation

## Self- and super-organising maps

### Description

A supersom is an extension of self-organising maps (SOMs) to multiple data layers, possibly with different numbers and different types of variables (though equal numbers of objects). NAs are allowed. A weighted distance over all layers is calculated to determine the winning units during training. Functions `som` and `xyf` are simply wrappers for supersoms with one and two layers, respectively. Function `bdk` is deprecated.

### Usage

    som(X, ...)
    xyf(X, Y, ...)
    supersom(data, grid=somgrid(), rlen = 100, alpha = c(0.05, 0.01),
             radius = quantile(nhbrdist, 2/3),
             whatmap = NULL, user.weights = 1, maxNA.fraction = 0L,
             keep.data = TRUE, dist.fcts = NULL,
             mode = c("online", "batch", "pbatch"), cores = -1, init,
             normalizeDataLayers = TRUE)

### Arguments

`X, Y` | numerical data matrices, or factors. No `data.frame` objects are allowed - convert them to matrices first.
`data` | list of data matrices (numerical) of factors. If a vector is entered, it will be converted to a one-column matrix. No `data.frame` objectss are allowed.
`grid` | a grid for the codebook vectors: see `somgrid`.
`rlen` | the number of times the complete data set will be presented to the network.
`alpha` | learning rate, a vector of two numbers indicating the amount of change. Default is to decline linearly from 0.05 to 0.01 over `rlen` updates. Not used for the batch algorithm.
`radius` | the radius of the neighbourhood, either given as a single number or a vector (start, stop). If it is given as a single number the radius will change linearly from `radius` to zero; as soon as the neighbourhood gets smaller than one only the winning unit will be updated. Note that the default before version 3.0 was to run from `radius` to `-radius`. If nothing is supplied, the default is to start with a value that covers 2/3 of all unit-to-unit distances.
`whatmap` | What data layers to use. If unspecified all layers are used.
`user.weights` | the weights given to individual layers. This can be a single number (all layers have the same weight, the default), a vector of the same length as the `whatmap` argument, or a vector of the same length as the `data` argument. In xyf maps, this argument provides the same functionality as the now-deprecated `xweight` argument that was used prior to version 3.0.
`maxNA.fraction` | the maximal fraction of values that may be NA to prevent the row to be removed.
`keep.data` | if TRUE, return original data and mapping information. If FALSE, only return the trained map (in essence the codebook vectors).
`dist.fcts` | vector of distance functions to be used for the individual data layers, of the same length as the `data` argument, or the same length of the `whatmap` argument. If the length of this vector is one, the same distance will be used for all layers. Admissable values currently are "sumofsquares", "euclidean", "manhattan", and "tanimoto". Default is to use "sumofsquares" for continuous data, and "tanimoto" for factors.
`mode` | type of learning algorithm.
`cores` | number of cores to use in the "pbatch" learning mode. The default, -1, corresponds to using all available cores.
`init` | list of matrices, initial values for the codebook vectors. The list should have the same length as the data list, and corresponding numbers of variables (columns). Each list element should have a number of rows corresponding to the number of units in the map.
`normalizeDataLayers` | boolean, indicating whether `distance.weights` should be calculated (see details section). If `normalizeDataLayers == FALSE` the user weights are applied to the data immediately.
`...` | Further arguments for the `supersom` function presented to the `som` or `xyf` wrappers.

### Details

In order to avoid some layers to overwhelm others, simply because of the scale of the data points, the `supersom` function by default applies internal weights to balance this. The `user.weights` argument is applied on top of that: the result is that when a user specifies equal weights for all layers (the default), all layers contribute equally to the global distance measure. For large data sets (defined as containing more than 500 records), a sample of size 500 is used to calculate the mean distances in each data layer. If `normalizeDataLayers == FALSE` the user weights are applied directly to the data (`distance.weights` are set to 1).

Various definitions of the Tanimoto distance exist in the literature. The implementation here returns (for two binary vectors of length n) the fraction of cases in which the two vectors disagree. This is basically the Hamming distance divided by n - the incorrect naming is retained (for the moment) to guarantee backwards compatibility. If the vectors are not binary, they will be converted to binary strings (with 0.5 as the class boundary). This measure should not be used when variables are outside the range [0-1]; a check is done to make sure this is the case.

### Value

An object of class "kohonen" with components

`data` | data matrix, only returned if `keep.data == TRUE`.
`unit.classif` | winning units for all data objects, only returned if `keep.data == TRUE`.
`distances` | distances of objects to their corresponding winning unit, only returned if `keep.data == TRUE`.
`grid` | the grid, an object of class `somgrid`.
`codes` | a list of matrices containing codebook vectors.
`changes` | matrix of mean average deviations from code vectors; every map corresponds with one column.
`alpha, radius, user.weights, whatmap, maxNA.fraction` | input arguments presented to the function.
`distance.weights` | if `normalizeDataLayers` weights to equalize the influence of the individual data layers, else a vector of ones.
`dist.fcts` | distance functions corresponding to all layers of the data, not just the ones indicated by the whatmap argument.

### Author(s)

Ron Wehrens and Johannes Kruisselbrink

### References

R. Wehrens and L.M.C. Buydens, J. Stat. Softw. 21 (5), 2007; R. Wehrens and J. Kruisselbrink, submitted, 2017.

### See Also

`somgrid`, `plot.kohonen`, `predict.kohonen`, `map.kohonen`

### Examples

    data(wines)

    ## som
    som.wines <- som(scale(wines), grid = somgrid(5, 5, "hexagonal"))
    summary(som.wines)

    ## xyf
    xyf.wines <- xyf(scale(wines), vintages, grid = somgrid(5, 5, "hexagonal"))
    summary(xyf.wines)

    ## supersom example
    data(yeast)
    yeast.supersom <- supersom(yeast, somgrid(6, 6, "hexagonal"),
                               whatmap = c("alpha", "cdc15", "cdc28", "elu"),
                               maxNA.fraction = .5)

    plot(yeast.supersom, "changes")

    obj.classes <- as.integer(yeast$class)
    colors <- c("yellow", "green", "blue", "red", "orange")
    plot(yeast.supersom, type = "mapping", col = colors[obj.classes],
         pch = obj.classes, main = "yeast data")

[Package kohonen version 3.0.7 Index]