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 prediction using trained maps are supported. The name of the package refers to Teuvo Kohonen, the inventor of the SOM.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends: R (≥ 2.10)
Imports: Rcpp (≥ 0.12.12)
LinkingTo: Rcpp
NeedsCompilation: yes
Packaged: 2023-06-09 07:22:08 UTC; ron
Repository: CRAN
Date/Publication: 2023-06-09 08:40:02 UTC

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           Check the validity of a whatmap argument
classvec2classmat       Convert a classification vector into a matrix
                        or the other way around.
degelder                Powder pattern data by Rene de Gelder
expandMap               Expand a self-organising map
getCodes                Extract codebook vectors from a kohonen object
kohonen-package         Supervised and Unsupervised Self-Organising
                        Maps
layer.distances         Assessing distances to winning units
map.kohonen             Map data to a supervised or unsupervised SOM
nir                     Near-infrared data with temperature effects
object.distances        Calculate distances between object vectors in a
                        SOM
peppaPic                Synthetic image of a pepper plant with peppers
plot.kohonen            Plot kohonen object
predict.kohonen         Predict properties using a trained Kohonen map
summary.kohonen         Summary and print methods for kohonen objects
supersom                Self- and super-organising maps
tricolor                Provides smooth unit colors for SOMs
unit.distances          SOM-grid related functions
wines                   Wine data
yeast                   Yeast cell-cycle data

Author(s)

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 Statistical Software, 87, 7 (2018).

Check the validity of a whatmap argument

Description

Not meant to be called directly by the user.

Usage

check.whatmap(x, whatmap)

Arguments

x

A kohonen object, or a list of data matrices that can be used as input data for SOM functions.

whatmap

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.

Value

Returns a numerical vector with the indices of the selected layers. An invalid selection leads to an error.

Author(s)

Ron Wehrens

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

class vector. Usually a factor; if it is a vector of integer values, it will be converted to a factor.

ymat

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)

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 values 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)

Expand a self-organising map

Description

Double the size of a map, imputing the codebookvectors of the new units by averiging their immediate neighbours.

Usage

expandMap(kohobj)

Arguments

kohobj

Object of class "kohonen")

Value

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])

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))

Arguments

x

An object of class kohonen.

idx

Indices of the layer(s) for which codebook vectors are returned.

Value

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))

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

A trained kohonen object. Data and mapping results should be included.

whatmap

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

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

classif

Classification vector, corresponding to the unit.classif element of a kohonen object. It can also be provided explicitly.

Details

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 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, ...)

Arguments

x

An object of class kohonen.

newdata

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

a vector of units that are closest to the objects in the data matrix.

distances

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")))

Near-infrared data with temperature effects

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

  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)

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

An object of class kohonen.

type

Whether to calculate distances between the data objects, or the codebook vectors.

whatmap

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

Value

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

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")

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 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

kohonen object.

type

type of plot. (Wow!)

whatmap

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.

classif

classification object, as returned by predict.kohonen, or vector of unit numbers. Only needed if type equals "mapping" and "counts".

labels

labels to plot when type equals "mapping".

pchs

symbols to plot when type equals "mapping".

main

title of the plot.

palette.name

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

ncolors

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.

bgcol

optional argument to colour the unit backgrounds for the "mapping" and "codes" plotting type. Defaults to "gray" and "transparent" in both types, respectively.

zlim

optional range for color coding of unit backgrounds.

heatkey

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

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

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

border

color of the shape's border.

na.color

background color matching NA - default "gray".

lwd, ...

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 visualisation 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 "supersom" 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.

"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.

Value

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)

## 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 properties using a trained Kohonen map

Description

Map objects to a trained Kohonen map, and return for each object the desired property associated 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

Trained network, containing one or more information layers.

newdata

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

Explicit definition of the predictions for each unit. Should be a list of matrices, vectors or factors, of the same length as object$codes.

trainingdata

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.

threshold

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.

Details

The new data are mapped to the trained SOM using the layers indicated by the whatmap argument. The predictions correspond to the unit.predictions, normally corresponding to the averages 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 predicted, this element is a list, otherwise a vector or a matrix.

unit.classif

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

unit.predictions

prediction values associated with map units. Again, when multiple properties are predicted, this is a list.

whatmap

the numbers of the data layers in the kohonen object used in the mapping on which the predictions are based.

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)

## ################################################################
## 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
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 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 additionally 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

a kohonen object

...

Not used.

Author(s)

Ron Wehrens

See Also

som, xyf, supersom

Examples

data(wines)
xyf.wines <- xyf(scale(wines), classvec2classmat(vintages),
                 grid = somgrid(5, 5, "hexagonal"))
xyf.wines
summary(xyf.wines)

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 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

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.

kohobj

an object of class kohonen.

...

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.

na.rows

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

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)
nunits(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")

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

An object of class somgrid, such as the grid element in a kohonen object.

phis

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.

offset

Defines the minimal value in the RGB colour definition (default is 0). By supplying a value in the range [0, .9], pastel-like colours are provided.

Value

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

Examples

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))

SOM-grid related functions

Description

Function somgrid (modified from the version in the class package) sets up a grid of units, of a specified 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

choose between a hexagonal or rectangular topology.

neighbourhood.fct

choose between bubble and gaussian neighbourhoods when training a SOM.

toroidal

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.

grid

an object of class somgrid.

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

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)

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 (Piedmont) 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 constituents 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)

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)

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