Umatrix-package
Description
The ESOM(emergent self organizing map) is an improvement of the regular SOM(self organizing map) which allows for toroid grids of neurons and is intended to be used in combination with the Umatrix. The set of neurons is referred to as weights within this package, as they represent the values within the high dimensional space. The neuron with smallest distance to a datapoint is called a Bestmatch and can be considered as projection of said datapoint. As the Umatrix is usually toroid, it is drawn four consecutive times to remove border effects. An island, or Imx, is a filter mask, which cuts out a subset of the Umatrix, which shows every point only a single time while avoiding border effects cutting through potential clusters. Finally the Pmatrix shows the density structures within the grid, by a set radius. It can be combined with the Umatrix resulting in the UStarMatrix, which is therefore a combination of density based structures as well as clearly divided ones.
References
Ultsch, A.: Data mining and knowledge discovery with emergent self-organizing feature maps for multivariate time series, In Oja, E. & Kaski, S. (Eds.), Kohonen maps, (1 ed., pp. 33-46), Elsevier, 1999.
Ultsch, A.: Maps for the visualization of high-dimensional data spaces, Proc. Workshop on Self organizing Maps (WSOM), pp. 225-230, Kyushu, Japan, 2003.
Ultsch, A.: U* C: Self-organized Clustering with Emergent Feature Maps, Lernen, Wissensentdeckung und Adaptivitaet (LWA), pp. 240-244, Saarbruecken, Germany, 2005.
Lotsch, J., Ultsch, A.: Exploiting the Structures of the U-Matrix, in Villmann, T., Schleif, F.-M., Kaden, M. & Lange, M. (eds.), Proc. Advances in Self-Organizing Maps and Learning Vector Quantization, pp. 249-257, Springer International Publishing, Mittweida, Germany, 2014.
Ultsch, A., Behnisch, M., Lotsch, J.: ESOM Visualizations for Quality Assessment in Clustering, In Merenyi, E., Mendenhall, J. M. & O'Driscoll, P. (Eds.), Advances in Self-Organizing Maps and Learning Vector Quantization: Proceedings of the 11th International Workshop WSOM 2016, pp. 39-48, Houston, Texas, USA, January 6-8, 2016, (10.1007/978-3-319-28518-4_3), Cham, Springer International Publishing, 2016.
Thrun, M. C., Lerch, F., Lotsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
Best matching units (BMU) of Hepta from FCPS (Fundamental Clustering Problem Suite)
Description
Best matching units (BMU) of an ESOM projection of the Hepta data set from FCPS (Fundamental Clustering Problem Suite) on an 80 x 40 planar grid of artifical neurons.
Usage
data("BMUHepta")Details
Size 212, Dimensions 3 (key, linecoordinates, columncoorditaes)
Classes 7, stored in Hepta$Cls
References
Ultsch A, Lotsch J: Machine-learned cluster identification in high-dimensional data. J Biomed Inform. 2017 Feb;66:95-104. doi: 10.1016/j.jbi.2016年12月01日1. Epub 2016 Dec 28.
Examples
data("BMUHepta")
str("BMUHepta")
Hepta from FCPS (Fundamental Clustering Problem Suite)
Description
Dataset with 7 easily seperable classes.
Usage
data("Hepta")Details
Size 212, Dimensions 3, stored in Hepta$Data
Classes 7, stored in Hepta$Cls
References
Ultsch, A.: U* C: Self-organized Clustering with Emergent Feature Maps, Lernen, Wissensentdeckung und Adaptivitaet (LWA), pp. 240-244, Saarbruecken, Germany, 2005.
Examples
data("Hepta")
str("Hepta")
Calculate the Delauny graph based radius
Description
Function to calculate the radius for data generation.
Usage
calculate_Delauny_radius(Data, BestMatches,
Columns = 80, Lines = 50, Toroid = TRUE)
Arguments
Data
Matrix of data (as submitted to Umatrix generation)
BestMatches
Array with positions of Bestmatches
Columns
Number of columns of the Umatrix
Lines
Number of columns of the Umatrix
Toroid
Whether a toroid Umatrx was used
Value
Returns a list of results.
neighbourDistances
Distances on the Umatrix neigborhood matrix.
RadiusByEM
Radius suggested by EM algorithm.
References
Ultsch A, Lotsch J: Machine-learned cluster identification in high-dimensional data. J Biomed Inform. 2017 Feb;66:95-104. doi: 10.1016/j.jbi.2016年12月01日1. Epub 2016 Dec 28.
Examples
## Not run:
data("Hepta")
data("HeptaBMU")
DelaunyHepta <- calculate_Delauny_radius(Data = Hepta$Data, BestMatches = HeptaBMU, Toroid = FALSE)
## End(Not run)Train an ESOM (emergent self organizing map) and project data
Description
The ESOM (emergent self organizing map) algorithm as defined by [Ultsch 1999]. A set of weigths(neurons) on a two-dimensional grid get trained to adapt the given datastructure. The weights will be used to project data on a two-dimensional space, by seeking the BestMatches for every datapoint.
Arguments
Data
Data that will be used for training and projection
Lines
Height of grid
Columns
Width of grid
Epochs
Number of Epochs the ESOM will run
Toroid
If TRUE, the grid will be toroid
NeighbourhoodFunction
Type of Neighbourhood; Possible values are: "cone", "mexicanhat" and "gauss"
StartLearningRate
Initial value for LearningRate
EndLearningRate
Final value for LearningRate
StartRadius
Start value for the Radius in which will be searched for neighbours
EndRadius
End value for the Radius in which will be searched for neighbours
NeighbourhoodCooling
Cooling method for radius; "linear" is the only available option at the moment
LearningRateCooling
Cooling method for LearningRate; "linear" is the only available option at the moment
shinyProgress
Generate progress output for shiny if Progress Object is given
ShiftToHighestDensity
If True, the Umatrix will be shifted so that the point with highest density will be at the center
InitMethod
name of the method that will be used to choose initializations Valid Inputs: "uni_min_max": uniform distribution with minimum and maximum from sampleData "norm_mean_std": normal distribuation based on mean and standard deviation of sampleData
Key
Vector of numeric keys matching the datapoints. Will be added to Bestmatches
UmatrixForEsom
If TRUE, Umatrix based on resulting ESOM is calculated and returned
Details
On a toroid grid, opposing borders are connected.
Value
List with
BestMatches
BestMatches of datapoints
Weights
Trained weights
Lines
Height of grid
Columns
Width of grid
Toroid
TRUE if grid is a toroid
JumpingDataPointsHist
Nr of DataPoints that jumped to a different BestMatch in every epoch
References
Kohonen, T., Self-organized formation of topologically correct feature maps. Biological cybernetics, 1982. 43(1): p. 59-69.
Ultsch, A., Data mining and knowledge discovery with emergent self-organizing feature maps for multivariate time series. Kohonen maps, 1999. 46: p. 33-46.
Examples
data('Hepta')
res=esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
Generative ESOM
Description
Function to generate new data with the same structure as the input data.
Usage
generate_data(Data, density_radius, Cls = NULL, gen_per_data = 10)
Arguments
Data
Matrix of data (as submitted to Umatrix generation)
density_radius
Numeric value of data generation radius
Cls
Classification of the data as a vector
gen_per_data
New isntances per original iunstance to be generated
Value
Returns a list of results.
original_data
The input data.
original_classes
The input classes.
generated_data
The generated data.
generated_classes
The generated classes.
References
Ultsch A, Lotsch J: Machine-learned cluster identification in high-dimensional data. J Biomed Inform. 2017 Feb;66:95-104. doi: 10.1016/j.jbi.2016年12月01日1. Epub 2016 Dec 28.
Examples
## Not run:
data("Hepta")
data("HeptaBMU")
HeptaData <- Hepta$Data
HeptaCls <y- Hepta$Cls
HeptaGenerated <- generate_data(HeptaData, 1, HeptaCls )
## End(Not run)GUI for manual classification
Description
This tool is a 'shiny' GUI that visualizes a given Umatrix and allows the user to select areas and mark them as clusters.
Arguments
Umatrix
Matrix of Umatrix Heights
BestMatches
Array with positions of Bestmatches
Cls
Classification of the Bestmatches
Imx
Matrix of an island that will be cut out of the Umatrix
Toroid
Are BestMatches placed on a toroid grid? TRUE by default
Value
A vector containing the selected class ids. The order is corresponding to the given Bestmatches
References
Thrun, M. C., Lerch, F., Loetsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
Examples
## Not run:
data("Hepta")
e = esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
cls = iClassification(e$Umatrix, e$BestMatches)
## End(Not run)iEsomTrain
Description
Trains the ESOM and shows the Umatrix.
Arguments
Data
Matrix of Data that will be used to learn. One DataPoint per row
BestMatches
Array with positions of Bestmatches
Cls
Classification of the Bestmatches as a vector
Key
Numeric vector of keys matching the Bestmatches
Toroid
Are BestMatches placed on a toroid grid? TRUE by default
Value
List with
Umatrix
matrix with height values of the umatrix
BestMatches
matrix containing the bestmatches
Lines
number of lines of the chosen ESOM
Columns
number of columns of the chosen ESOM
Epochs
number of epochs of the chosen ESOM
Weights
List of weights
Toroid
True if a toroid grid was used
EsomDetails
Further details describing the chosen ESOM parameters
JumpingDataPointsHist
Number of Datapoints that jumped to another neuron in each epoch
References
Thrun, M. C., Lerch, F., Loetsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
iUmapIsland
Description
The toroid Umatrix is usually drawn 4 times, so that connected areas on borders can be seen as a whole. An island is a manual cutout of such a tiled visualization, that is selected such that all connected areas stay intact. This 'shiny' tool allows the user to do this manually.
Arguments
Umatrix
Matrix of Umatrix Heights
BestMatches
Array with positions of BestMatches
Cls
Classification of the BestMatches
Value
Boolean Matrix that represents the island within the tiled Umatrix
References
Thrun, M. C., Lerch, F., Loetsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
Examples
## Not run:
data("Hepta")
e = esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
Imx = iUmapIsland(e$Umatrix, e$BestMatches)
plotMatrix(e$Umatrix, e$BestMatches, Imx = Imx$Imx)
## End(Not run)iUstarmatrix
Description
Calculates the Ustarmatrix by combining a Umatrix with a Pmatrix.
Arguments
Weights
Weights that were trained by the ESOM algorithm
Lines
Height of the used grid
Columns
Width of the used grid
Data
Matrix of Data that was used to train the ESOM. One datapoint per row
Imx
Island mask that will be cut out from displayed Umatrix
Cls
Classification of the Bestmatches
Toroid
Are weights placed on a toroid grid?
Value
Ustarmatrix
matrix with height values of the Ustarmatrix
References
Thrun, M. C., Lerch, F., Loetsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
plotMatrix
Description
Draws a plot based of given Umatrix or Pmatrix.
Arguments
Matrix
Umatrix or Pmatrix to be plotted
BestMatches
Positions of BestmMtches to be plotted onto the Umatrix
Cls
Class identifier for the BestMatches
ClsColors
Vector of colors that will be used to colorize the different classes
ColorStyle
If "Umatrix" the colors of a Umatrix (Blue -> Green -> Brown -> White) will be used; If "Pmatrix" the colors of a Pmatrix (White -> Yellow -> Red) will be used
Toroid
Should the Umatrix be drawn 4times?
BmSize
Integer between 0.1 and 5, magnification factor of the drawn BestMatch circles
DrawLegend
If TRUE, a color legend will be drawn next to the plot
FixedRatio
If TRUE, the plot will be drawn with a fixed ratio of x and y axis
CutoutPol
Only draws the area within given polygon
Nrlevels
Number of height levels that will be used within the Umatrix
TransparentContours
Use half transparent contours. Looks better but is slow
Imx
Mask to cut out an island. Every value should be either 1 (stays in) or 0 (gets cut out)
Clean
If TRUE axis, margins, ... surrounding the Umatrix image will be removed
RemoveOcean
If TRUE, the surrounding blue area around an island will be reduced as much as possible (while still maintaining a rectangular form)
TransparentOcean
If TRUE, the surrounding blue area around an island will be transparent
Title
A title that will be drawn above the plot
BestMatchesLabels
Vector of strings corresponding to the order of BestMatches which will be drawn on the plot as labels
BestMatchesShape
Numeric value of Shape that will be used. Responds to the usual shapes of ggplot
MarkDuplicatedBestMatches
If TRUE, BestMatches that are shown more than once within an island, will be marked
YellowCircle
If TRUE, a yellow circle is drawn around Bestmatches to distinct them better from background
Details
The heightScale (nrlevels) is set at the proportion of the 1 percent quantile against the 99 percent quantile of the matrix values.
Value
A 'ggplot' of a Matrix
References
Thrun, M. C., Lerch, F., Loetsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
Ultsch, A.: Maps for the visualization of high-dimensional data spaces, Proc. Workshop on Self organizing Maps (WSOM), pp. 225-230, Kyushu, Japan, 2003.
Siemon, H.P., Ultsch,A.: Kohonen Networks on Transputers: Implementation and Animation, in: Proceedings Intern. Neural Networks, Kluwer Academic Press, Paris, pp. 643-646, 1990.
Examples
data("Hepta")
e = esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
plotMatrix(e$Umatrix,e$BestMatches)
pmatrixForEsom
Description
Generates a Pmatrix based on the weights of an ESOM.
Arguments
Data
A [n,k] matrix containing the data
Weights
Weights stored as a list in a 2D matrix
Lines
Number of lines of the SOM that is described by weights
Columns
Number of columns of the SOM that is described by weights
Radius
The radius for measuring the density within the hypersphere
PlotIt
If set the Pmatrix will also be plotted
Toroid
Are BestMatches placed on a toroid grid? TRUE by default
Value
UstarMatrix
References
Ultsch, A.: Maps for the visualization of high-dimensional data spaces, Proc. Workshop on Self organizing Maps (WSOM), pp. 225-230, Kyushu, Japan, 2003.
Ultsch, A., Loetsch, J.: Computed ABC Analysis for Rational Selection of Most Informative Variables in Multivariate Data, PloS one, Vol. 10(6), pp. e0129767. doi 10.1371/journal.pone.0129767, 2015.
Thrun, M. C., Lerch, F., Loetsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
Examples
data("Hepta")
e = esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
Pmatrix = pmatrixForEsom(Hepta$Data,
e$Weights,
e$Lines,
e$Columns,
e$Toroid)
plotMatrix(Pmatrix, ColorStyle = "Pmatrix")
showMatrix3D
Description
Visualizes the matrix(Umatrix/Pmatrix) in an interactive window in 3D.
Arguments
Matrix
Matrix to be plotted
BestMatches
Positions of BestMatches to be plotted onto the matrix
Cls
Class identifier for the BestMatch at the given point
Imx
a mask (island) that will be used to cut out the Umatrix
Toroid
Should the Matrix be drawn 4 times (in a toroid view)
HeightScale
Optional. Scaling Factor for Mountain Height
BmSize
Size of drawn BestMatches
RemoveOcean
Remove as much area sourrounding an island as possible
ColorStyle
Either "Umatrix" or "Pmatrix" respectevily for their colors
ShowAxis
Draw an axis arround the drawn matrix
SmoothSlope
Try to increase the island size, to get smooth slopes around the island
ClsColors
Vector of colors that will be used for classes
FileName
Name for a stl file to write the Matrix to
Details
The heightScale is set at the proportion of the 1 percent quantile against the 99 percent quantile of the Matrix values.
References
Thrun, M. C., Lerch, F., Loetsch, J., Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision,Plzen, 2016.
Examples
## Not run:
data("Hepta")
e = esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
showMatrix3D(e$Umatrix)
## End(Not run)umatrixForEsom
Description
Calculate the Umatrix for given ESOM projection
Arguments
Weights
Weights from which the Umatrix will be calculated
Lines
Number of lines of the SOM that is described by weights
Columns
Number of columns of the SOM that is described by weights
Toroid
Boolean describing if the neural grid should be borderless
Value
Umatrix
References
Ultsch, A. and H.P. Siemon, Kohonen's Self Organizing Feature Maps for Exploratory Data Analysis. 1990.
Examples
data("Hepta")
e = esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
umatrix = umatrixForEsom(e$Weights,
Lines=e$Lines,
Columns=e$Columns,
Toroid=e$Toroid)
plotMatrix(umatrix,e$BestMatches)
ustarmatrixCalc
Description
The UStarMatrix is a combination of the Umatrix (average distance to neighbours) and Pmatrix (density in a point). It can be used to improve the Umatrix, if the dataset contains density based structures.
Arguments
Umatrix
A given Umatrix
Pmatrix
A density matrix
Value
UStarMatrix
References
Ultsch, A. U* C: Self-organized Clustering with Emergent Feature Maps. in Lernen, Wissensentdeckung und Adaptivitaet (LWA). 2005. Saarbruecken, Germany.
Examples
data("Hepta")
e = esomTrain(Hepta$Data, Key = 1:nrow(Hepta$Data))
Pmatrix = pmatrixForEsom(Hepta$Data,
e$Weights,
e$Lines,
e$Columns,
e$Toroid)
Ustarmatrix = ustarmatrixCalc(e$Umatrix, Pmatrix)
plotMatrix(Ustarmatrix, e$BestMatches)