bdk: Supervised version of Kohonen's self-organising maps

Description

Supervised version of self-organising maps for mapping high-dimensional spectra or patterns to 2D: the Bi-Directional Kohonen map. This is an alternating training of the X-space and the Y-space of the map, where for updating the X-space more weight is given to the features in Y, and vice versa. Weights start by default with values of (0.75, 0.25) and during training go to (0.5, 0.5). Prediction is done only using the X-space. For continuous Y, the Euclidean distance is used; for categorical Y the Tanimoto distance.

Usage

bdk(data, Y, grid=somgrid(), rlen = 100, alpha = c(0.05, 0.01), radius = quantile(nhbrdist, 0.67) * c(1, -1), xweight = 0.75, contin, toroidal = FALSE, n.hood, keep.data = TRUE)

Arguments

data

a matrix, with each row representing an object.

property that is to be modelled. In case of classification, Y is a matrix with exactly one '1' in each row indicating the class, and zeros elsewhere. For prediction of continuous properties, Y is a vector. A combination is possible, too, but one then should take care of appropriate scaling.

grid

a grid for the representatives: 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.

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 run from the given number to the negative value of that number; as soon as the neighbourhood gets smaller than one only the winning unit will be updated. The default is to start with a value that covers 2/3 of all unit-to-unit distances.

xweight

the initial weight given to the X map in the calculation of distances for updating Y, and to the Y map for updating X. This will linearly go to 0.5 during training. Defaults to 0.75.

contin

parameter indicating whether Y is continuous or categorical. The default is to check whether all row sums of Y equal 1: in that case contin is FALSE.

toroidal

if TRUE, the edges of the map are joined. Note that in a hexagonal toroidal map, the number of rows must be even.

n.hood

the shape of the neighbourhood, either "circular" or "square". The latter is the default for rectangular maps, the former for hexagonal maps.

keep.data

save data in return value.

Value

data: data matrix, only returned if keep.data == TRUE.
Y: Y, only returned if keep.data == TRUE.
contin: parameter indicating whether Y is continuous or categorical.
grid: the grid, an object of class "somgrid".
codes: list of two matrices, containing codebook vectors for X and Y, respectively.
changes: matrix containing two columns of mean average deviations from code vectors. Column 1 contains deviations used for updating Y; column 2 for updating X.
toroidal: whether a toroidal map is used.
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.
method: the type of som, here "bdk"

References

W.J. Melssen, R. Wehrens, and L.M.C. Buydens. Chemom. Intell. Lab. Syst., 83, 99-113 (2006).

Examples

Run this code

### Wine example
data(wines)
set.seed(7)

training <- sample(nrow(wines), 120)
Xtraining <- scale(wines[training,])
Xtest <- scale(wines[-training,],
               center = attr(Xtraining, "scaled:center"),
               scale = attr(Xtraining, "scaled:scale"))

bdk.wines <- bdk(Xtraining,
                 factor(wine.classes[training]),
                 grid = somgrid(5, 5, "hexagonal"))

bdk.prediction <- predict(bdk.wines, newdata=Xtest)
table(wine.classes[-training], bdk.prediction$prediction)

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