Source document: https://docs-lawep.s3.us-east-2.amazonaws.com/1697800440304.pdf (Liberia)
Package ‘kohonen’ June 9, 2023 Version 3.0.12 Title Supervised and Unsupervised Self-Organising Maps Author Ron Wehrens and Johannes Kruisselbrink Maintainer Ron Wehrens <ron.wehrens@gmail.com> Description Functions to train self-organising maps (SOMs).

Also interrogation of the maps and pre- diction using trained maps are supported.

The name of the package refers to Teuvo Koho- nen, the inventor of the SOM.
License GPL (>= 2) Depends R (>= 2.10) Imports Rcpp (>= 0.12.12) LinkingTo Rcpp NeedsCompilation yes Repository CRAN Date/Publication 2023-06-09 08:40:02 UTC R topics documented: .

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26 27 kohonen-package Supervised and Unsupervised Self-Organising Maps Description Functions to train self-organising maps (SOMs).

Also interrogation of the maps and prediction using trained maps are supported.

The name of the package refers to Teuvo Kohonen, the inventor of the SOM.

Details The kohonen package implements several forms of self-organising maps (SOMs).
Online and batch training algorithms are available; batch training can also be done in parallel.

Multiple data layers may be presented to the training algorithm, with potentially different distance measures for each layer.

The overall distance is a weighted average of the layer distances.

Layers may be selected through the whatmap argument, or by providing a weight of zero.

The basic function is supersom; som is simply a wrapper for SOMs using just one layer (the classical form).
New data may be mapped to a trained SOM using the map.kohonen function.

Function predict.kohonen will map data to the SOM, and will return predictions (i.e., average values for winning units) for those layers that are not in the new data object.

Several visualisation methods are available in function plot.kohonen.
Index of help topics: check.whatmap classvec2classmat degelder expandMap getCodes kohonen-package layer.distances map.kohonen nir object.distances peppaPic plot.kohonen predict.kohonen summary.kohonen Check the validity of a whatmap argument Convert a classification vector into a matrix or the other way around.
Powder pattern data by Rene de Gelder Expand a self-organising map Extract codebook vectors from a kohonen object Supervised and Unsupervised Self-Organising Maps Assessing distances to winning units Map data to a supervised or unsupervised SOM Near-infrared data with temperature effects Calculate distances between object vectors in a SOM Synthetic image of a pepper plant with peppers Plot kohonen object Predict properties using a trained Kohonen map Summary and print methods for kohonen objects check.whatmap supersom tricolor unit.distances wines yeast Author(s) 3 Self- and super-organising maps Provides smooth unit colors for SOMs SOM-grid related functions Wine data Yeast cell-cycle data Ron Wehrens and Johannes Kruisselbrink Maintainer: Ron Wehrens <ron.wehrens@gmail.com> References R. Wehrens and J. Kruisselbrink: Flexible Self-Organising Maps in kohonen 3.0.
Journal of Statis- tical Software, 87, 7 (2018).

check.whatmap Check the validity of a whatmap argument Description Not meant to be called directly by the user.

Usage check.whatmap(x, whatmap) Arguments x whatmap Value A kohonen object, or a list of data matrices that can be used as input data for SOM functions.

An indication of a subset of the data; either by naming the elements, or giving indices.
If whatmap equals NULL, the selection of x is used if x is a kohonen object, or else no selection is performed.

Returns a numerical vector with the indices of the selected layers.

An invalid selection leads to an error.

Author(s) Ron Wehrens 4 classvec2classmat classvec2classmat Convert a classiﬁcation vector into a matrix or the other way around.
Description Functions toggle between a matrix representation, where class membership is indicated with one ’1’ and for the rest zeros at each row, and a factor.

The classiﬁcation matrix contains one column per class.

Conversion from a class matrix to a class vector assigns each row to the column with the highest value.

An optional argument can be used to assign only those objects that have a probability higher than a certain threshold (default is 0).
Usage classvec2classmat(yvec) classmat2classvec(ymat, threshold=0) Arguments yvec ymat class vector.

Usually a factor; if it is a vector of integer values, it will be con- verted to a factor.

class matrix: every column corresponds to a class.

threshold only classify into a class if the probability is larger than this threshold.

Value classvec2classmat returns the classiﬁcation matrix, where each column consists of zeros and ones; classmat2classvec returns a factor.
Author(s) Ron Wehrens See Also som,xyf,supersom Examples classes <- c(rep(1, 5), rep(2, 7), rep(3, 9)) classmat <- classvec2classmat(classes) classmat classmat2classvec(classmat) degelder 5 degelder Powder pattern data by Rene de Gelder Description X-ray powder patterns of 131 crystallographic structures, contributed by Rene de Gelder.
Usage data(degelder) Format This yields a list with three components: the ﬁrst component, ’"patterns"’, is a matrix of 131 rows and 441 variables, containing the powder patterns; the second component is "thetas", the 2theta val- ues at which intensities have been measured.

The ﬁnal component, ’"properties"’, gives information on the crystallographic properties of the structures.

Source Rene de Gelder, Institute of Molecules and Materials, Radboud University Nijmegen.
Examples ## Not run: data(degelder) mydata <- list(patterns = degelder$patterns, CellVol = log(degelder$properties[,"cell.vol"])) ## custom distance function require(Rcpp) sourceCpp(system.file("Distances", "wcc.cpp", package = "kohonen")) set.seed(7) powsom <- supersom(data = mydata, grid = somgrid(6, 4, "hexagonal"), dist.fcts = c("WCCd", "sumofsquares"), keep.data = TRUE) summary(powsom) ## End(Not run) 6 getCodes expandMap Expand a self-organising map Description Double the size of a map, imputing the codebookvectors of the new units by averiging their imme- diate neighbours.
Usage expandMap(kohobj) Arguments kohobj Value Object of class "kohonen") A new kohonen object, with a double size.
Author(s) Ron Wehrens Examples data(yeast) yeast.supersom <- supersom(yeast, somgrid(4, 4, "hexagonal"), whatmap = 3:6, maxNA.fraction = .5) yeast.supersom2 <- expandMap(yeast.supersom) yeast.supersom3 <- supersom(yeast, yeast.supersom2$grid, whatmap = 3:6, maxNA.fraction = .5, init = yeast.supersom2$codes[3:6]) getCodes Extract codebook vectors from a kohonen object Description Utility function for extracting codebook vectors.
These are present as a list element in a kohonen object, and themselves are a list as well, with one entry for each data layer.

This function returns either a list of codebook matrices (if more layers are selected), or just one matrix (if one layer is selected).

Usage getCodes(x, idx = 1:length(codes)) layer.distances Arguments x idx Value 7 An object of class kohonen.

Indices of the layer(s) for which codebook vectors are returned.
If idx is a single number, a matrix of codebook vectors; if it is a vector of numbers, a list of codebook matrices.

Author(s) Ron Wehrens See Also supersom Examples data(wines) set.seed(7) som.wines <- som(scale(wines), grid = somgrid(5, 5, "hexagonal")) dim(getCodes(som.wines)) layer.distances Assessing distances to winning units Description Given a trained SOM, distances of individual objects to their closest units may be calculated with function dist2WU.
Aggregation on the unit level is obtained through the function layer.distances.

The latter function is the workhorse for the "quality" plots in function plot.kohonen.

Usage layer.distances(kohobj, whatmap, data, classif = NULL) dist2WU(kohobj, whatmap, data, classif = NULL) Arguments kohobj whatmap data classif A trained kohonen object.

Data and mapping results should be included.

What layers to take into account - default is to consider all layers used in train- ing.

Also single layers may be chosen.


Note that although the underlying C code can also calculate results for any subset, currently subsets larger than one are forbidden.

Data to use - default is to use the data from the trained SOM.

Classiﬁcation vector, corresponding to the unit.classif element of a kohonen object.

It can also be provided explicitly.

8 Details map.kohonen The results will be weighted using both the user weights and distance weights.
Summing all the results for individual layers therefore would lead to the unit.classif vector of the kohonen object.

Value Function dist2WU returns a vector, representing for each object the distance to its winning unit.

Function layer.distances returns (as a vector) for each unit the average distance of objects for which it is the winning unit.

Author(s) Ron Wehrens See Also Quality plots from plot.kohonen.
Examples library(kohonen) data(wines) wines.sc <- scale(wines) set.seed(7) xyf.wines <- xyf(wines.sc, vintages, grid = somgrid(5, 5, "hexagonal")) dist2WU(xyf.wines, whatmap = 1) plot(xyf.wines, "quality", whatmap = 1) plot(xyf.wines, "property", property = layer.distances(xyf.wines, whatmap = 1)) map.kohonen Map data to a supervised or unsupervised SOM Description Map a data matrix onto a trained SOM.
Usage ## S3 method for class 'kohonen' map(x, newdata, whatmap = NULL, user.weights = NULL, maxNA.fraction = x$maxNA.fraction, ...) map.kohonen Arguments x newdata 9 An object of class kohonen.

list of data matrices (numerical) of factors, equal to the data argument of the supersom function.

No data.frame objects are allowed.

whatmap, user.weights, maxNA.fraction parameters that usually will be taken from the x object, but can be supplied by the user as well.
Note that it is not possible to change distance functions from the ones used in training the map.

See supersom for more information.

...

Currently ignored.

Value A list with elements unit.classif distances a vector of units that are closest to the objects in the data matrix.

distances of the objects to the closest units.

Distance measures are the same ones used in training the map.

whatmap, user.weights Values used for these arguments.
Author(s) Ron Wehrens See Also predict.kohonen, supersom Examples data(wines) set.seed(7) training <- sample(nrow(wines), 150) Xtraining <- scale(wines[training, ]) somnet <- som(Xtraining, somgrid(5, 5, "hexagonal")) map(somnet, scale(wines[-training, ], center=attr(Xtraining, "scaled:center"), scale=attr(Xtraining, "scaled:scale"))) nir Near-infrared data with temperature effects 10 nir Description A data object containing near-infrared spectra of ternary mixtures of ethanol, water and iso-propanol, measured at ﬁve different temperatures (30, 40, ..., 70 degrees Centigrade).
References F. Wulfert , W.Th.

Kok, A.K.

Smilde: Anal.

Chem.
1998, 1761-1767 Examples data(nir) set.seed(3) nirnet <- xyf(X = nir$spectra[nir$training,], Y = nir$composition[nir$training,], user.weights = c(3,1), grid = somgrid(6, 6, "hexagonal"), rlen=500) plot(nirnet, "counts", main="Counts") ## Focus on compound 2 (water): par(mfrow = c(1,2)) set.seed(13) nirnet <- xyf(X = nir$spectra[nir$training,], Y = nir$composition[nir$training, 2, drop = FALSE], grid = somgrid(6, 6, "hexagonal"), rlen=500) water.xyf <- predict(nirnet, newdata = nir$spectra[nir$training,], unit.predictions = getCodes(nirnet, 2), whatmap = 1)$prediction plot(nirnet, "property", property = water.xyf[[1]], main="Prediction of water content") ## Plot temperatures as circles symbols(nirnet$grid$pts[nirnet$unit.classif,] + matrix(rnorm(sum(nir$training)*2, sd=.1), ncol=2), circles = (nir$temperature[nir$training] - 20)/250, inches = FALSE, add = TRUE) ## Model temperatures set.seed(13) nirnet2 <- xyf(X = nir$spectra[nir$training,], Y = matrix(nir$temperature[nir$training], ncol = 1), user.weights = c(1,3), grid = somgrid(6, 6, "hexagonal"), rlen=500) temp.xyf <- predict(nirnet2, newdata = nir$spectra[nir$training,], unit.predictions = getCodes(nirnet2, 2), whatmap = 1)$prediction object.distances 11 plot(nirnet2, "property", property = temp.xyf[[1]], palette.name = rainbow, main="Prediction of temperatures") ## Plot concentrations of water as circles symbols(nirnet2$grid$pts[nirnet2$unit.classif,] + matrix(rnorm(sum(nir$training)*2, sd=.1), ncol=2), circles = 0.05 + 0.4 * nir$composition[nir$training,2], inches = FALSE, add = TRUE) object.distances Calculate distances between object vectors in a SOM Description This function calculates the distance between objects using the distance functions, weights and other attributes of a trained SOM.
This function is used in the calculation of the U matrix in function plot.kohonen using the type = "dist.neighbours" argument.

Usage object.distances(kohobj, type = c("data", "codes"), whatmap) Arguments kohobj type whatmap Value An object of class kohonen.

Whether to calculate distances between the data objects, or the codebook vec- tors.

What data layers to use.

If unspeciﬁed the data layers deﬁned in the kohonen object are used.

An object of class dist, which can be directly fed into (e.g.)
a hierarchical clustering.

Author(s) Ron Wehrens References R. Wehrens and J. Kruisselbrink, submitted, 2017.
See Also unit.distances, supersom 12 Examples data(wines) set.seed(7) sommap <- supersom(list(measurements = scale(wines), vintages = vintages), grid = somgrid(6, 4, "hexagonal")) obj.dists <- object.distances(sommap, type = "data") code.dists <- object.distances(sommap, type = "codes") peppaPic peppaPic Synthetic image of a pepper plant with peppers Description A data matrix with four columns representing a 600 by 800 image of a pepper plant.

Each row is a pixel in the image.


The ﬁrst column is the class label; the other columns contain the RGB values.

Usage data("peppaPic") Source http://dx.doi.org/10.4121/uuid:884958f5-b868-46e1-b3d8-a0b5d91b02c0 References This is image 10039 from a set of 10,500 images described in Barth R, IJsselmuiden J, Hemming J, and van Henten E (2017).

"Data Synthesis Methods for Semantic Segmentation in Agriculture.

A Capsicum annuum Dataset."

Submitted.


Examples data(peppaPic) head(peppaPic) ## show ground truth per pixel image(t(matrix(peppaPic[,1], 600, 800))[,600:1], col = rainbow(10)) plot.kohonen 13 plot.kohonen Plot kohonen object Description Plot objects of class kohonen.

Several types of plots are supported.
Usage ## S3 method for class 'kohonen' plot(x, type = c("codes", "changes", "counts", "dist.neighbours", "mapping", "property", "quality"), whatmap = NULL, classif = NULL, labels = NULL, pchs = NULL, main = NULL, palette.name = NULL, ncolors, bgcol = NULL, zlim = NULL, heatkey = TRUE, property, codeRendering = NULL, keepMargins = FALSE, heatkeywidth = .2, shape = c("round", "straight"), border = "black", na.color = "gray", ...) ## S3 method for class 'kohonen' identify(x, ...) add.cluster.boundaries(x, clustering, lwd = 5, ...) Arguments x type whatmap classif labels pchs main kohonen object.
type of plot.

(Wow!)

For a "codes" plot: what maps to show; for the "dist.neighbours" plot: what maps to take into account when calculating distances to neighbouring units.

classiﬁcation object, as returned by predict.kohonen, or vector of unit num- bers.

Only needed if type equals "mapping" and "counts".

labels to plot when type equals "mapping".

symbols to plot when type equals "mapping".

title of the plot.
title of the plot.

palette.name colors to use as unit background for "codes", "counts", "prediction", "property", and "quality" plotting types.

ncolors bgcol zlim heatkey number of colors to use for the unit backgrounds.

Default is 20 for continuous data, and the number of distinct values (if less than 20) for categorical data.

optional argument to colour the unit backgrounds for the "mapping" and "codes" plotting type.

Defaults to "gray" and "transparent" in both types, respectively.
optional range for color coding of unit backgrounds.

whether or not to generate a heatkey at the left side of the plot in the "property" and "counts" plotting types.

14 plot.kohonen property values to use with the "property" plotting type.

codeRendering How to show the codes.

Possible choices: "segments", "stars" and "lines".

keepMargins if FALSE (the default), restore the original graphical parameters after plotting the kohonen map.
If TRUE, one retains the map coordinate system so that one can add symbols to the plot, or map unit numbers using the identify function.

heatkeywidth width of the colour key; the default of 0.2 should work in most cases but in some cases, e.g.

when plotting multiple ﬁgures, it may need to be adjusted.

shape border na.color lwd, ... kind shape to be drawn: "round" (circle) or "straight".
Choosing "straight" pro- duces a map of squares when the grid is "rectangular", and produces a map of hexagons when the grid is "hexagonal".

color of the shape’s border.

background color matching NA - default "gray".

other graphical parameters.

clustering cluster labels of the map units.

Details Several different types of plots are supported: "changes" shows the mean distance to the closest codebook vector during training.

"codes" shows the codebook vectors.


"counts" shows the number of objects mapped to the individual units.

Empty units are depicted in gray.

"dist.neighbours" shows the sum of the distances to all immediate neighbours.

This kind of vi- sualisation is also known as a U-matrix plot.

Units near a class boundary can be expected to have higher average distances to their neighbours.

Only available for the "som" and "super- som" maps, for the moment.

"mapping" shows where objects are mapped.


It needs the "classif" argument, and a "labels" or "pchs" argument.

"property" properties of each unit can be calculated and shown in colour code.

It can be used to visualise the similarity of one particular object to all units in the map, to show the mean similarity of all units and the objects mapped to them, etcetera.

The parameter property contains the numerical values.

See examples below.
See examples below.

"quality" shows the mean distance of objects mapped to a unit to the codebook vector of that unit.

The smaller the distances, the better the objects are represented by the codebook vectors.

It is possible to visualize this for the complete set of layers used in training, or for individual layers only (using the whatmap argument).

Function identify.kohonen shows the number of a unit that is clicked on with the mouse.
The tolerance is calculated from the ratio of the plotting region and the user coordinates, so clicking at any place within a unit should work.

Function add.cluster.boundaries will add to an existing plot of a map thick lines, visualizing which units would be clustered together.

In toroidal maps, boundaries at the edges will only be shown on the top and right sides to avoid double boundaries.
plot.kohonen Value 15 Several types of plots return useful values (invisibly): the "counts", "dist.neighbours", and "quality" return vectors corresponding to the information visualized in the plot (unit background colours and heatkey).
Author(s) Ron Wehrens See Also som, supersom, xyf, predict.kohonen Examples data(wines) set.seed(7) kohmap <- xyf(scale(wines), vintages, grid = somgrid(5, 5, "hexagonal"), rlen=100) plot(kohmap, type="changes") counts <- plot(kohmap, type="counts", shape = "straight") ## show both sets of codebook vectors in the map par(mfrow = c(1,2)) plot(kohmap, type="codes", main = c("Codes X", "Codes Y")) par(mfrow = c(1,1)) similarities <- plot(kohmap, type="quality", palette.name = terrain.colors) plot(kohmap, type="mapping", labels = as.integer(vintages), col = as.integer(vintages), main = "mapping plot") ## add background colors to units according to their predicted class labels xyfpredictions <- classmat2classvec(getCodes(kohmap, 2)) bgcols <- c("gray", "pink", "lightgreen") plot(kohmap, type="mapping", col = as.integer(vintages), pchs = as.integer(vintages), bgcol = bgcols[as.integer(xyfpredictions)], main = "another mapping plot", shape = "straight", border = NA) ## Show 'component planes' set.seed(7) sommap <- som(scale(wines), grid = somgrid(6, 4, "hexagonal")) plot(sommap, type = "property", property = getCodes(sommap, 1)[,1], main = colnames(getCodes(sommap, 1))[1]) ## Show the U matrix Umat <- plot(sommap, type="dist.neighbours", main = "SOM neighbour distances") ## use hierarchical clustering to cluster the codebook vectors som.hc <- cutree(hclust(object.distances(sommap, "codes")), 5) add.cluster.boundaries(sommap, som.hc) 16 predict.kohonen ## and the same for rectangular maps set.seed(7) sommap <- som(scale(wines),grid = somgrid(6, 4, "rectangular")) plot(sommap, type="dist.neighbours", main = "SOM neighbour distances") ## use hierarchical clustering to cluster the codebook vectors som.hc <- cutree(hclust(object.distances(sommap, "codes")), 5) add.cluster.boundaries(sommap, som.hc) predict.kohonen Predict properties using a trained Kohonen map Description Map objects to a trained Kohonen map, and return for each object the desired property associ- ated with the corresponding winning unit.
These properties may be provided explicitly (argument unit.predictions) or implicitly (by providing trainingdata, that will be mapped to the SOM - the averages of the winning units for the trainingdata then will be used as unit.predictions).

If not given at all, the codebook vectors of the map will be used.
Usage ## S3 method for class 'kohonen' predict(object, newdata = NULL, unit.predictions = NULL, trainingdata = NULL, whatmap = NULL, threshold = 0, maxNA.fraction = object$maxNA.fraction, ...) Arguments object newdata Trained network, containing one or more information layers.

List of data matrices, or one single data matrix, for which predictions are to be made.

The data layers should match those in the trained map.

If not presented, the training data in the map will be used.
No data.frame objects are allowed.

unit.predictions trainingdata Explicit deﬁnition of the predictions for each unit.

Should be a list of matrices, vectors or factors, of the same length as object$codes.

List of data matrices, or one single data matrix, determining the mapping of the training data.

Normally, data stored in the kohonen object will be used for this, but one can also specify this argument explicitly.

Layers should match the trained map.


whatmap, maxNA.fraction parameters that usually will be taken from the x object, but can be supplied by the user as well.

See supersom for more information.

predict.kohonen threshold ...

Details Used in converting class predictions back into factors; see classmat2classvec.

Further arguments to be passed to map.kohonen, in particular user.weights.

If not provided will be taken from object.


17 The new data are mapped to the trained SOM using the layers indicated by the whatmap argu- ment.

The predictions correspond to the unit.predictions, normally corresponding to the aver- ages of the training data mapping to individual units.

If no unit.predictions are provided, the trainingdata will be used to calculate them - if trainingdata is not provided by the user and the kohonen object contains data, these will be used.
If no objects of the training data are mapping to a particular unit, the prediction for that unit will be NA.

Value Returns a list with components prediction predicted values for the properties of interest.

When multiple values are pre- dicted, this element is a list, otherwise a vector or a matrix.

unit.classif unit.predictions vector of unit numbers to which objects in the newdata object are mapped.

prediction values associated with map units.


Again, when multiple properties are predicted, this is a list.

the numbers of the data layers in the kohonen object used in the mapping on which the predictions are based.
whatmap Author(s) Ron Wehrens See Also som,xyf, supersom, map Examples data(wines) training <- sample(nrow(wines), 120) Xtraining <- scale(wines[training, ]) Xtest <- scale(wines[-training, ], center = attr(Xtraining, "scaled:center"), scale = attr(Xtraining, "scaled:scale")) trainingdata <- list(measurements = Xtraining, vintages = vintages[training]) testdata <- list(measurements = Xtest, vintages = vintages[-training]) mygrid = somgrid(5, 5, "hexagonal") som.wines <- supersom(trainingdata, grid = mygrid) 18 predict.kohonen ## ################################################################ ## Situation 0: obtain expected values for training data (all layers, ## also if not used in training) on the basis of the position in the map som.prediction <- predict(som.wines) ## ################################################################ ## Situation 1: obtain predictions for all layers used in training som.prediction <- predict(som.wines, newdata = testdata) table(vintages[-training], som.prediction$predictions[["vintages"]]) ## ################################################################ ## Situation 2: obtain predictions for the vintage based on the mapping ## of the sample characteristics only.
There are several ways of doing this: som.prediction <- predict(som.wines, newdata = testdata, whatmap = "measurements") table(vintages[-training], som.prediction$predictions[["vintages"]]) ## same, but now indicated implicitly som.prediction <- predict(som.wines, newdata = testdata[1]) table(vintages[-training], som.prediction$predictions[["vintages"]]) ## if no names are present in the list elements whatmap needs to be ## given explicitly; note that the order of the data layers needs to be ## consistent with the kohonen object som.prediction <- predict(som.wines, newdata = list(Xtest), whatmap = 1) table(vintages[-training], som.prediction$predictions[["vintages"]]) ## for xyf: explicitly indicate which layer is to be used for the mapping xyf.wines <- xyf(Xtraining, vintages[training], grid = mygrid) xyf.prediction <- predict(xyf.wines, Xtest, whatmap = 1) table(vintages[-training], xyf.prediction$predictions[[2]]) ## ############################################################### ## Situation 3: predictions for layers not present in the original ## data.
Training data need to be provided for those layers.
som.wines <- supersom(Xtraining, grid = mygrid) som.prediction <- predict(som.wines, newdata = testdata, trainingdata = trainingdata) table(vintages[-training], som.prediction$predictions[["vintages"]]) ## ################################################################ ## yeast examples, including NA values data(yeast) training.indices <- sample(nrow(yeast$alpha), 300) training <- rep(FALSE, nrow(yeast$alpha)) training[training.indices] <- TRUE ## unsupervised mapping, based on the alpha layer only.
Prediction ## for all layers including alpha summary.kohonen 19 yeast.som <- supersom(lapply(yeast, function(x) subset(x, training)), somgrid(4, 6, "hexagonal"), whatmap = "alpha", maxNA.fraction = .5) yeast.som.prediction <- predict(yeast.som, newdata = lapply(yeast, function(x) subset(x, !training))) table(yeast$class[!training], yeast.som.prediction$prediction[["class"]]) ## ################################################################ ## supervised mapping - creating the map is now based on both ## alpha and class, prediction for class based on the mapping of alpha.
yeast.som2 <- supersom(lapply(yeast, function(x) subset(x, training)), grid = somgrid(4, 6, "hexagonal"), whatmap = c("alpha", "class"), maxNA.fraction = .5) yeast.som2.prediction <- predict(yeast.som2, newdata = lapply(yeast, function(x) subset(x, !training)), whatmap = "alpha") table(yeast$class[!training], yeast.som2.prediction$prediction[["class"]]) summary.kohonen Summary and print methods for kohonen objects Description Summary and print methods for kohonen objects.
The print method shows the dimensions and the topology of the map; if information on the training data is included, the summary method addition- ally prints information on the size of the data, the distance functions used, and the mean distance of an object to its closest codebookvector, which is an indication of the quality of the mapping.

Usage ## S3 method for class 'kohonen' summary(object, ...) ## S3 method for class 'kohonen' print(x, ...) Arguments x, object ...
Author(s) Ron Wehrens a kohonen object Not used.

See Also som, xyf, supersom supersom 20 Examples data(wines) xyf.wines <- xyf(scale(wines), classvec2classmat(vintages), grid = somgrid(5, 5, "hexagonal")) xyf.wines summary(xyf.wines) supersom 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.
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, re- spectively.

Function nunits is a utility function returning the number of units in the map.
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) nunits(kohobj) Arguments X, Y data grid rlen alpha radius If a vector is entered, it will be numerical data matrices, or factors.

No data.frame objects are allowed - con- vert them to matrices ﬁrst.
list of data matrices (numerical) of factors.

converted to a one-column matrix.

No data.frame objectss are allowed.

a grid for the codebook vectors: see somgrid.

the number of times the complete data set will be presented to the network.

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.

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.

supersom whatmap user.weights 21 What data layers to use.

If unspeciﬁed all layers are used.

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 mode cores init 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 "tani- moto" for factors.

type of learning algorithm.

number of cores to use in the "pbatch" learning mode.

The default, -1, corre- sponds to using all available cores.

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 de- tails section).

If normalizeDataLayers == FALSE the user weights are applied to the data immediately.

an object of class kohonen.

Further arguments for the supersom function presented to the som or xyf wrap- pers.

kohobj ...

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.

22 Value An object of class "kohonen" with components supersom data unit.classif distances grid codes changes data matrix, only returned if keep.data == TRUE.

winning units for all data objects, only returned if keep.data == TRUE.

distances of objects to their corresponding winning unit, only returned if keep.data == TRUE.

the grid, an object of class somgrid.


a list of matrices containing codebook vectors.

matrix of mean average deviations from code vectors; every map corresponds with one column.

vector of row numbers with too many NA values (according to argument maxNA.fraction.

na.rows alpha, radius, user.weights, whatmap, maxNA.fraction distance.weights input arguments presented to the function.

if normalizeDataLayers weights to equalize the inﬂuence of the individual data layers, else a vector of ones.
distance functions corresponding to all layers of the data, not just the ones indi- cated by the whatmap argument.

dist.fcts 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) nunits(som.wines) ## xyf xyf.wines <- xyf(scale(wines), vintages, grid = somgrid(5, 5, "hexagonal")) summary(xyf.wines) ## supersom example data(yeast) tricolor 23 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") tricolor Provides smooth unit colors for SOMs Description Function provides colour values for SOM units in such a way that the colour changes smoothly in every direction.
Usage tricolor(grid, phis = c(0, 2 * pi/3, 4 * pi/3), offset = 0) Arguments grid phis offset Value An object of class somgrid, such as the grid element in a kohonen object.

A vector of three rotation angles.

Values for red, green and blue are given by the y-coordinate of the units after rotation with these three angles, respectively.

The default corresponds to (approximate) red colour of the middle unit in the top row, and pure green and blue colours in the bottom left and right units, respectively.
In case of a triangular map, the top unit is pure red.

Deﬁnes the minimal value in the RGB colour deﬁnition (default is 0).

By sup- plying a value in the range [0, .9], pastel-like colours are provided.

Returns a matrix with three columns corresponding to red, green and blue.

This can be used in the rgb function to provide colours for the units.
Author(s) Ron Wehrens See Also plot.kohonen 24 Examples unit.distances data(wines) som.wines <- som(wines, grid = somgrid(5, 5, "hexagonal")) colour1 <- tricolor(som.wines$grid) plot(som.wines, "mapping", bg = rgb(colour1)) colour2 <- tricolor(som.wines$grid, phi = c(pi/6, 0, -pi/6)) plot(som.wines, "mapping", bg = rgb(colour2)) colour3 <- tricolor(som.wines$grid, phi = c(pi/6, 0, -pi/6), offset = .5) plot(som.wines, "mapping", bg = rgb(colour3)) unit.distances SOM-grid related functions Description Function somgrid (modiﬁed from the version in the class package) sets up a grid of units, of a spec- iﬁed size and topology.
Distances between grid units are calculated by function unit.distances.

Usage somgrid(xdim = 8, ydim = 6, topo = c("rectangular", "hexagonal"), neighbourhood.fct = c("bubble", "gaussian"), toroidal = FALSE) unit.distances(grid, toroidal) Arguments xdim, ydim dimensions of the grid.

topo neighbourhood.fct choose between a hexagonal or rectangular topology.

choose between bubble and gaussian neighbourhoods when training a SOM.

logical, whether the grid is toroidal or not.


If not provided to the unit.distances function, the information in the grid object will be used.

an object of class somgrid.

toroidal grid Value Function somgrid returns an object of class "somgrid", with elements pts, and the input arguments to the function.

Function unit.distances returns a (symmetrical) matrix containing distances.

When grid$n.hood equals "circular", Euclidean distances are used; for grid$n.hood is "square" maximum distances.
For toroidal maps (joined at the edges) distances are calculated for the shortest path.
Author(s) Ron Wehrens 25 wines Examples mygrid <- somgrid(5, 5, "hexagonal") fakesom <- list(grid = mygrid) class(fakesom) <- "kohonen" par(mfrow = c(2,1)) dists <- unit.distances(mygrid) plot(fakesom, type="property", property = dists[1,], main="Distances to unit 1", zlim=c(0,6), palette = rainbow, ncolors = 7) dists <- unit.distances(mygrid, toroidal=TRUE) plot(fakesom, type="property", property = dists[1,], main="Distances to unit 1 (toroidal)", zlim=c(0,6), palette = rainbow, ncolors = 7) wines Wine data Description A data frame containing 177 rows and thirteen columns; object vintages contains the class labels.
These data are the results of chemical analyses of wines grown in the same region in Italy (Pied- mont) but derived from three different cultivars: Nebbiolo, Barberas and Grignolino grapes.

The wine from the Nebbiolo grape is called Barolo.

The data contain the quantities of several con- stituents found in each of the three types of wines, as well as some spectroscopic variables.

Usage data(wines) Source http://kdd.ics.uci.edu References M. Forina, C. Armanino, M. Castino and M. Ubigli.
Vitis, 25:189-201 (1986) 26 yeast yeast Yeast cell-cycle data Description Microarray cell-cycle data for 800 yeast genes, arrested with six different methods, arranged in a list.

Additional class information is present as well.

Usage data(yeast) References P. Spellman et al., Mol.

Biol.
Cell 9, 3273-3297 (1998) Index ∗ classif check.whatmap, 3 classvec2classmat, 4 expandMap, 6 map.kohonen, 8 object.distances, 11 plot.kohonen, 13 predict.kohonen, 16 summary.kohonen, 19 supersom, 20 tricolor, 23 unit.distances, 24 ∗ cluster layer.distances, 7 ∗ datasets degelder, 5 nir, 10 peppaPic, 12 wines, 25 yeast, 26 ∗ manip getCodes, 6 layer.distances, 7 ∗ package kohonen-package, 2 identify.kohonen (plot.kohonen), 13 kohonen (kohonen-package), 2 kohonen-package, 2 layer.distances, 7 map, 17 map (map.kohonen), 8 map.kohonen, 8, 22 nir, 10 nunits (supersom), 20 object.distances, 11 peppaPic, 12 plot.kohonen, 8, 13, 22, 23 predict.kohonen, 9, 15, 16, 22 print.kohonen (summary.kohonen), 19 som, 4, 15, 17, 19 som (supersom), 20 somgrid (unit.distances), 24 summary.kohonen, 19 supersom, 4, 7, 9, 11, 15–17, 19, 20 add.cluster.boundaries (plot.kohonen), 13 check.whatmap, 3 classmat2classvec, 17 classmat2classvec (classvec2classmat), 4 classvec2classmat, 4 degelder, 5 dist2WU (layer.distances), 7 expandMap, 6 getCodes, 6 27 tricolor, 23 unit.distances, 11, 24 vintages (wines), 25 wines, 25 xyf, 4, 15, 17, 19 xyf (supersom), 20 yeast, 26