Type:	Package
Title:	Visualizations of High-Dimensional Data
Version:	1.3.3
Date:	2025-01-26
Maintainer:	Michael Thrun <m.thrun@gmx.net>
Description:	Gives access to data visualisation methods that are relevant from the data scientist's point of view. The flagship idea of 'DataVisualizations' is the mirrored density plot (MD-plot) for either classified or non-classified multivariate data published in Thrun, M.C. et al.: "Analyzing the Fine Structure of Distributions" (2020), PLoS ONE, <doi:10.1371/journal.pone.0238835>. The MD-plot outperforms the box-and-whisker diagram (box plot), violin plot and bean plot and geom_violin plot of ggplot2. Furthermore, a collection of various visualization methods for univariate data is provided. In the case of exploratory data analysis, 'DataVisualizations' makes it possible to inspect the distribution of each feature of a dataset visually through a combination of four methods. One of these methods is the Pareto density estimation (PDE) of the probability density function (pdf). Additionally, visualizations of the distribution of distances using PDE, the scatter-density plot using PDE for two variables as well as the Shepard density plot and the Bland-Altman plot are presented here. Pertaining to classified high-dimensional data, a number of visualizations are described, such as f.ex. the heat map and silhouette plot. A political map of the world or Germany can be visualized with the additional information defined by a classification of countries or regions. By extending the political map further, an uncomplicated function for a Choropleth map can be used which is useful for measurements across a geographic area. For categorical features, the Pie charts, slope charts and fan plots, improved by the ABC analysis, become usable. More detailed explanations are found in the book by Thrun, M.C.: "Projection-Based Clustering through Self-Organization and Swarm Intelligence" (2018) <doi:10.1007/978-3-658-20540-9>.
License:	GPL-3
Imports:	Rcpp (≥ 0.12.12), ggplot2, sp, pracma, reshape2
Suggests:	plyr, MBA, ggmap, plotrix, rworldmap, rgl, ABCanalysis, choroplethr, R6, parallelDist, knitr (≥ 1.12), rmarkdown (≥ 0.9), vioplot, ggExtra, plotly, htmlwidgets, diptest, moments, signal, ggrepel, MASS, ROCit, ScatterDensity (≥ 0.0.3), colorspace, viridis, gridExtra
LinkingTo:	Rcpp, RcppArmadillo
Depends:	R (≥ 3.5)
LazyLoad:	yes
LazyData:	TRUE
LazyDataCompression:	xz
URL:	https://www.deepbionics.org/
VignetteBuilder:	knitr
BugReports:	https://github.com/Mthrun/DataVisualizations/issues
NeedsCompilation:	yes
Packaged:	2025-01-26 14:22:15 UTC; MCT
Author:	Michael Thrun [aut, cre, cph], Felix Pape [aut, rev], Onno Hansen-Goos [ctr, ctb], Quirin Stier [ctb, rev], Hamza Tayyab [ctr, ctb], Luca Brinkmann [ctr, ctb], Dirk Eddelbuettel [ctr], Craig Varrichio [ctr], Alfred Ultsch [dtc, ctb, ctr]
Repository:	CRAN
Date/Publication:	2025-01-26 15:10:02 UTC

Visualizations of High-Dimensional Data

Description

Gives access to data visualisation methods that are relevant from the data scientist's point of view. The flagship idea of 'DataVisualizations' is the mirrored density plot (MD-plot) for either classified or non-classified multivariate data published in Thrun, M.C. et al.: "Analyzing the Fine Structure of Distributions" (2020), PLoS ONE, <DOI:10.1371/journal.pone.0238835>. The MD-plot outperforms the box-and-whisker diagram (box plot), violin plot and bean plot and geom_violin plot of ggplot2. Furthermore, a collection of various visualization methods for univariate data is provided. In the case of exploratory data analysis, 'DataVisualizations' makes it possible to inspect the distribution of each feature of a dataset visually through a combination of four methods. One of these methods is the Pareto density estimation (PDE) of the probability density function (pdf). Additionally, visualizations of the distribution of distances using PDE, the scatter-density plot using PDE for two variables as well as the Shepard density plot and the Bland-Altman plot are presented here. Pertaining to classified high-dimensional data, a number of visualizations are described, such as f.ex. the heat map and silhouette plot. A political map of the world or Germany can be visualized with the additional information defined by a classification of countries or regions. By extending the political map further, an uncomplicated function for a Choropleth map can be used which is useful for measurements across a geographic area. For categorical features, the Pie charts, slope charts and fan plots, improved by the ABC analysis, become usable. More detailed explanations are found in the book by Thrun, M.C.: "Projection-Based Clustering through Self-Organization and Swarm Intelligence" (2018) <DOI:10.1007/978-3-658-20540-9>.

Details

For a brief introduction to DataVisualizations please see the vignette A Quick Tour in Data Visualizations.

Please see https://www.deepbionics.org/. Depending on the context please cite either [Thrun, 2018] regarding visualizations in the context of clustering or [Thrun/Ultsch, 2018] for other visualizations.

For the Mirrored Density Plot (MD plot) please cite [Thrun et al., 2020] and see the extensive vignette in https://md-plot.readthedocs.io/en/latest/index.html. The MD plot is also available in Python https://pypi.org/project/md-plot/

Index of help topics:

ABCbarplot              Barplot with Sorted Data Colored by ABCanalysis
AccountingInformation_PrimeStandard_Q3_2019
                        Accounting Information in the Prime Standard in
                        Q3 in 2019 (AI_PS_Q3_2019)
BimodalityAmplitude     Bimodality Amplitude
CCDFplot                plot Complementary Cumulative Distribution
                        Function (CCDF) in Log/Log uses ecdf, CCDF(x) =
                        1-cdf(x)
ChoroplethPostalCodesAndAGS_Germany
                        Postal Codes and AGS of Germany for a
                        Choropleth Map
Choroplethmap           Plots the Choropleth Map
ClassBarPlot            ClassBarPlot
ClassBoxplot            Creates Boxplot plot for all classes
ClassErrorbar           ClassErrorbar
ClassMDplot             Class MDplot for Data w.r.t. all classes
ClassPDEplot            PDE Plot for all classes
ClassPDEplotMaxLikeli   Create PDE plot for all classes with maximum
                        likelihood
Classplot               Classplot
CombineCols             Combine vectors of various lengths
CombineRows             Combine matrices of various lengths
Crosstable              Crosstable plot
DataVisualizations-package
                        Visualizations of High-Dimensional Data
DefaultColorSequence    Default color sequence for plots
DensityContour          Contour plot of densities
DensityScatter          Scatter plot with densities
DrawWorldWithCls        Plot a classificated world map
DualaxisClassplot       Dualaxis Classplot
DualaxisLinechart       DualaxisLinechart
Fanplot                 The fan plot
FundamentalData_Q1_2018
                        Fundamental Data of the 1st Quarter in 2018
GoogleMapsCoordinates   Google Maps with marked coordinates
Heatmap                 Heatmap for Clustering
HeatmapColors           Default color sequence for plots
ITS                     Income Tax Share
InspectBoxplots         Inspect Boxplots
InspectCorrelation      Inspect the Correlation
InspectDistances        Inspection of Distance-Distribution
InspectScatterplots     Pairwise scatterplots and optimal histograms
InspectStandardization
                        QQplot of Data versus Normalized Data
InspectVariable         Visualization of Distribution of one variable
JitterUniqueValues      Jitters Unique Values
Lsun3D                  Lsun3D inspired by FCPS [Thrun/Ultsch, 2020]
                        introduced in [Thrun, 2018]
MAplot                  Minus versus Add plot
MDplot                  Mirrored Density plot (MD-plot)
MDplot4multiplevectors
                        Mirrored Density plot (MD-plot)for Multiple
                        Vectors
MTY                     Muncipal Income Tax Yield
Meanrobust              Robust Empirical Mean Estimation
Multiplot               Plot multiple ggplots objects in one panel
OptimalNoBins           Optimal Number Of Bins
PDEnormrobust           PDEnormrobust
PDEplot                 PDE plot
ParetoDensityEstimation
                        Pareto Density Estimation V3
ParetoRadius            ParetoRadius for distributions
Piechart                The pie chart
Pixelmatrix             Plot of a Pixel Matrix
Plot3D                  3D plot of points
PlotGraph2D             PlotGraph2D
PlotMissingvalues       Plot of the Amount Of Missing Values
PlotProductratio        Product-Ratio Plot
PmatrixColormap         P-Matrix colors
QQplot                  QQplot with a Linear Fit
ROC                     ROC plot
RobustNorm_BackTrafo    Transforms the Robust Normalization back
RobustNormalization     RobustNormalization
ShepardDensityScatter   Shepard PDE scatter
Sheparddiagram          Draws a Shepard Diagram
SignedLog               Signed Log
Silhouetteplot          Silhouette plot of classified data.
Slopechart              Slope Chart
StatPDEdensity          Pareto Density Estimation
Stdrobust               Standard Deviation Robust
Worldmap                plots a world map by country codes
categoricalVariable     A categorical Feature.
estimateDensity2D       estimateDensity2D
stat_pde_density        Calculate Pareto density estimation for ggplot2
                        plots
world_country_polygons
                        world_country_polygons
zplot                   Plotting for 3 dimensional data

Author(s)

Michael Thrun, Felix Pape, Onno Hansen-Goos, Alfred Ultsch

Maintainer: Michael Thrun <m.thrun@gmx.net>

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Thrun et al., 2020] Thrun, M. C., Gehlert, T. & Ultsch, A.: Analyzing the Fine Structure of Distributions, PLoS ONE, Vol. 15(10), pp. 1-66, DOI 10.1371/journal.pone.0238835, 2020.

Examples

data("Lsun3D")
Data=Lsun3D$Data

Pixelmatrix(Data)



InspectDistances(as.matrix(dist(Data)))


MAlist=MAplot(ITS,MTY)

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
#clear cluster structure
plot(Data[,1:2],col=Cls)
#However, the silhouette plot does not indicate a very good clustering in cluster 1 and 2

Silhouetteplot(Data,Cls = Cls)


Heatmap(as.matrix(dist(Data)),Cls = Cls)

Barplot with Sorted Data Colored by ABCanalysis

Description

This plot can be read like a scree plot for PCA. It allowed to select the most important values visually.

Usage

ABCbarplot(Data,

Colors=DataVisualizations::DefaultColorSequence[1:3],

main,xlab,ylab="Value")

Arguments

Details

ABC analysis is explained in ABCanalysis. The visualization is based on ggplot2.

Value

List V of

Author(s)

Michael Thrun

References

Ultsch. A ., Lotsch 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.

See Also

ABCanalysis

Examples

data('FundamentalData_Q1_2018')
Data=as.matrix(FundamentalData_Q1_2018$Data)
Data[!is.finite(Data)]=0
results=prcomp(Data)
main="Scree plot with Class A of the Most-Important Eigenvalues"
plotlist = ABCbarplot(results$sdev,ylab='Eigenvalues',main=main)
plotlist$ggobject

Accounting Information in the Prime Standard in Q3 in 2019 (AI_PS_Q3_2019)

Description

Accounting Information of 261 companies traded in the Frankfurt stock exchange in the German Prime standard.

Usage

data("AccountingInformation_PrimeStandard_Q3_2019")

Format

A list with of three objects

Key

[1:n] Key of the 261 obeservations

Data

[1:n,1:d] numeric matrix of 261 observations on the 45 variables describing the accounting information

Cls

[1:n] a numeric vector of k clusters of the clustering performend in [Thrun/Ultsch, 2019]

Details

Detailed data description can be found in [Thrun/Ultsch, 2019].

Source

Yahoo Finance

References

[Thrun/Ultsch, 2019] Thrun, M. C., & Ultsch, A.: Stock Selection via Knowledge Discovery using Swarm Intelligence with Emergence, IEEE Intelligent Systems, Vol. under review, pp., 2019.

Examples

data(AccountingInformation_PrimeStandard_Q3_2019)

str(AI_PS_Q3_2019)
dim(AI_PS_Q3_2019$Data)

Bimodality Amplitude

Description

Computes the Bimodality Amplitude of [Zhang et al., 2003]

Usage

BimodalityAmplitude(x, PlotIt=FALSE)

Arguments

Details

This function calculates the Bimodality Ampltiude of a data vector. This is a measure of the proportion of bimodality and the existence of bimodality. The value lies between zero and one (that is: [0,1]) where the value of zero implies that the data is unimodal and the value of one implies the data is two point masses.

Note

function was rewritten after the flow of a function of Sathish Deevi because the original function was incorrect.

Author(s)

Michael Thrun

References

Zhang, C., Mapes, B., & Soden, B.: Bimodality in tropical water vapour, Quarterly Journal of the Royal Meteorological Society, Vol. 129(594), pp. 2847-2866, 2003.

Examples

#Example 1
data<-c(rnorm(299,0,1),rnorm(299,5,1))
BimodalityAmplitude(data,TRUE)

#Example 2
dist1<-rnorm(2100,5,2)
dist2<-dist1+11
data<-c(dist1,dist2)

BimodalityAmplitude(data,TRUE)

#Example 3
dist1<-rnorm(210,-15,1)
dist2<-rep(dist1,3)+30
data<-c(dist1,dist2)

BimodalityAmplitude(data,TRUE)

#Example 4
data<-runif(1000,-15,1)

BimodalityAmplitude(data,TRUE)

plot Complementary Cumulative Distribution Function (CCDF) in Log/Log uses ecdf, CCDF(x) = 1-cdf(x)

Description

plot Complementary Cumulative Distribution Function (CCDF) in Log/Log uses ecdf, CCDF(x) = 1-cdf(x)

Arguments

Value

V$CCDFuniqX,V$CCDFuniqY CCDFuniqY= 1-cdf(CCDFuniqX), such that plot(CCDFuniqX,CCDFuniqY)...)

Author(s)

Michael Thrun

Postal Codes and AGS of Germany for a Choropleth Map

Description

Zip Codes and Community Identification Number of Germany which can be used in a Choropleth Map.

Usage

data("ChoroplethPostalCodesAndAGS_Germany")

Format

A data frame with 8702 observations on the following 4 variables.

PLZ

German postal codes/zip codes

Cls

Clustering aggregated of germany postal codes by MTY and ITS features

AGS

It is the 'Amtlicher Gemeindeschluessel' (Community Identification Number) of German municipalities

Names

Names of municipalities

Details

CLS are the the labels of a MTS versus ITS Bayesian classification showing two main groups of low quota ('1') and high quota ('2') municipalities. Additionally, outliers are manually classified into two separated groups called sponsors ('3') and promoted ('4'). In the Bayesian Classification non classified data have the label '0'. If a 'AGS' code of a 'PLZ' was unclear than the label is 'NaN'.

Source

Generated for [Thrun/Ultsch, 2018] using the approach of [Ultsch/Behnisch, 2017].

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch/Behnisch, 2017] Ultsch, A., Behnisch, M.: Effects of the payout system of income taxes to municipalities in Germany, Applied Geography, Vol. 81, pp. 21-31, 2017.

Examples

data(ChoroplethPostalCodesAndAGS_Germany)
str(ChoroplethPostalCodesAndAGS_Germany)

Plots the Choropleth Map

Description

A thematic map with areas colored in proportion to the measurement of the statistical variable being displayed on the map. A political map geneated by this function was used in the conference talk of the publication [Thrun/Ultsch, 2018].

Usage

Choroplethmap(Counts, PostalCodes, NumberOfBins = 0,

 Breaks4Intervals, percentiles = c(0.5, 0.95), 
 
 digits = 0, PostalCodesShapes, PlotIt = TRUE,

 DiscreteColors, HighColorContinuous = "red",

 LowColorContinuous = "deepskyblue1", NAcolor = "grey",

 ReferenceMap = FALSE, main = "Political Map of Germany",

 legend = "Range of values", Silent = TRUE)

Arguments

Details

This wrapper for the choroplethr enables to visualize a political map easily in the case of german zip codes based on given counts and postal codes. Other postal codes are in principle usable.

Value

List of

Note

You could read https://www.r-bloggers.com/2016/05/case-study-mapping-german-zip-codes-in-r/, if you want to change the map (PostalCodesShapes shape object).

Author(s)

Michael Thrun

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

See Also

Google choroplethr package.

Examples

#If you download the package from CRAN
## Not run: 
# 1. Step: Downlaod the shape file from the website 
# https://github.com/Mthrun/DataVisualizations/blob/master/data/GermanPostalCodesShapes.rda
# 2. Step: load it from the local path od the downloaded file with
load(file='GermanPostalCodesShapes.rda')

## End(Not run)

# If you download the package from GitHub, you can omit the two steps above.
# Then, do not use the 'PostalCodesShapes' input parameter

#Many postal codes are required to see a structure
#Exemplary two postal codes in the upper left corner of the map

## Not run: 
out=Choroplethmap(c(4,8,5,4),

c('49838', '26817', '49838', '26817'),

NumberOfBins=2,PlotIt=FALSE,
 PostalCodesShapes=GermanPostalCodesShapes)

out$chorR6obj$render()

## End(Not run)
#bins are only presented in the map if the have values within
## Not run: 
out=Choroplethmap(c(4,8,5,4),c('49838', '26817',

 '49838', '26817'),NumberOfBins=5,
 
 Breaks4Intervals=c(1,2,3,5,10),PlotIt=FALSE,
 PostalCodesShapes=GermanPostalCodesShapes)


out$chorR6obj$render()

## End(Not run)
# Result of [Thrun/Ultsch, 2018]
# Slightly misuse the function for visualizing a political map 
# resulting out of a clustering

## Not run: 
data('ChoroplethPostalCodesAndAGS_Germany')
res=Choroplethmap(as.numeric(ChoroplethPostalCodesAndAGS_Germany$Cls)+1,

ChoroplethPostalCodesAndAGS_Germany$PLZ,NumberOfBins = 2,

Breaks4Intervals = c(0,1,2,3,4,5,6),digits = 1,ReferenceMap = F,

DiscreteColors = c('white','green','blue','red','magenta'),

main = 'Classification of German Postal Codes based on Income Tax Share and Yield',

legend = 'ITS vs MTY Classification in 2010',NAcolor = 'black',PlotIt=FALSE,
 PostalCodesShapes=GermanPostalCodesShapes)


#takes time to process
res$chorR6obj$render()

## End(Not run)

ClassBarPlot

Description

Represent values for each class and instance as bar plot with optional error deviation, e.g., mean values of features depending on class with standard deviation.

Usage

ClassBarPlot(Values, Cls, Deviation, Names, ClassColors,

            ylab = "Values", xlab = "Instances", PlotIt = TRUE)

Arguments

Value

ggplot2 object

Author(s)

Quirin Stier

Examples

# Compute means and counts
tmpVar1 <- aggregate(Sepal.Length ~ Species, 

data = iris, FUN = function(x) c(mean = mean(x), n = length(x)))


tmpVar2 <- aggregate(Sepal.Width ~ Species, 

data = iris, FUN = function(x) c(mean = mean(x), n = length(x)))


tmpVar3 <- aggregate(Petal.Length ~ Species, 

data = iris, FUN = function(x) c(mean = mean(x), n = length(x)))


tmpVar4 <- aggregate(Petal.Width ~ Species, 

data = iris, FUN = function(x) c(mean = mean(x), n = length(x)))

# Extract mean and count
tmpVar1_mean <- tmpVar1$Sepal.Length[, "mean"]
tmpVar2_mean <- tmpVar2$Sepal.Width[, "mean"]
tmpVar3_mean <- tmpVar3$Petal.Length[, "mean"]
tmpVar4_mean <- tmpVar4$Petal.Width[, "mean"]

# Compute standard deviations
tmpVar5 <- aggregate(Sepal.Length ~ Species, data = iris, FUN = sd)
tmpVar6 <- aggregate(Sepal.Width ~ Species, data = iris, FUN = sd)
tmpVar7 <- aggregate(Petal.Length ~ Species, data = iris, FUN = sd)
tmpVar8 <- aggregate(Petal.Width ~ Species, data = iris, FUN = sd)

# Combine results
Values <- c(tmpVar1_mean, tmpVar2_mean, tmpVar3_mean, tmpVar4_mean)
Class <- rep(1:3, 4)
Deviation <- c(tmpVar5$Sepal.Length, tmpVar6$Sepal.Width, tmpVar7$Petal.Length, tmpVar8$Petal.Width)
  
  if(length(Values) == length(Class)){
    ClassBarPlot(Values = Values, Cls = Class, Deviation = Deviation)
  }
  

Creates Boxplot plot for all classes

Description

Boxplot the data for all classes

Usage

ClassBoxplot(Data, Cls,  ColorSequence = DataVisualizations::DefaultColorSequence,

 ClassNames = NULL,All=FALSE, PlotLegend = TRUE,

 main = 'Boxplot per Class', xlab = 'Classes', ylab = 'Range of Data')

Arguments

Value

A List of

in mode invisible

Author(s)

Michael Thrun, Felix Pape

Examples

data(ITS)
#please download package from cran
#model=AdaptGauss::AdaptGauss(ITS)
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))

DataVisualizations::ClassBoxplot(ITS,Classification)$ggobject

ClassErrorbar

Description

Plots ClassErrorbars at Xvalue positions for one or more than one classes with user means and defined whiskers

Usage

ClassErrorbar(Xvalues, Ymatrix, Cls, ClassNames, ClassCols, ClassShape, 

MeanFun = median, SDfun, JitterPosition = 0.5,

main = "Error bar plot", xlab, ylab, WhiskerWidth = 7, Whisker_lwd = 1, BW = TRUE)

Arguments

Details

If k=1, e.g., one method is used, d=m and Cls=rep(1,m). All vector [1:k] assume the occurance of the classes in Cls as ordered with increasing value.

Statistics are provided in long table format with the column names Xvalues, Mean, SD and Method. The method column specifies the names of the k classes.

If Xvalues is a character vector (see example), ggplot2 automatically sets the position on the x-axis. Otherwise specific numeric positions can be set. This allowes also for plotting a smooth line over the average (see example).

Value

List with

Author(s)

Michael Thrun

Examples

data('FundamentalData_Q1_2018')
Data=as.matrix(FundamentalData_Q1_2018$Data)
Cls = FundamentalData_Q1_2018$Cls
Class1Data = matrix(NA, nrow = nrow(Data), ncol = 2)
Class2Data = matrix(NA, nrow = nrow(Data), ncol = 2)
Class1Data[which(Cls==1), ] = Data[which(Cls==1), c("TotalAssets", "TotalLiabilities")]
Class2Data[which(Cls==2), ] = Data[which(Cls==2), c("TotalAssets", "TotalLiabilities")]
YMatrix = cbind(Class1Data, 
                Class2Data)

#Option 1: character vector
ClassErrorbar(c("TotalRevenue","GrossProfit"), 
         YMatrix, c
		 (1,1,2,2), 
         ClassNames=c("Class 1", "Class 2"), 
         main="ClassErrorbar of Q1 2018 for total revenue and gross profit",
         xlab="GrossProfit/TotalRevenue", 
         ylab="Median +- std", 
         WhiskerWidth = 1)
		 
#Option 2: numerical vector
ClassErrorbar(c(1,2), 
		 YMatrix,
		 c(1,1,2,2), 
         ClassNames=c("Class 1", "Class 2"), 
         main="ClassErrorbar of Q1 2018 for total revenue and gross profit",
         xlab="GrossProfit/TotalRevenue", 
         ylab="Median +- std", 
         WhiskerWidth = 1)

#Option 3: numerical vector + line
## Not run: 
#arbitrary data
Y_someOtherData=cbind(YMatrix,YMatrix,
YMatrix,YMatrix)
some_values=c(2,3,4,5,6,8,9,10)
ClassErrorbar(some_values, 
		 Y_someOtherData,
		 c(1,1,2,2), 
         ClassNames=c("Class 1", "Class 2"), 
         main="ClassErrorbar of Q1 2018 for total revenue and gross profit",
         xlab="GrossProfit/TotalRevenue", 
         ylab="Median +- std", 
         WhiskerWidth = 1)$ggobj+
geom_smooth(method="auto", se=F, fullrange=F, level=0.95)

## End(Not run)

Class MDplot for Data w.r.t. all classes

Description

Creates a Mirrored-Density plot w.r.t. to each class of a numerical vector of data.

Usage

ClassMDplot(Data, Cls, ColorSequence = DataVisualizations::DefaultColorSequence,

                         ClassNames = NULL, PlotLegend = TRUE,Ordering = "Columnwise",
                         
                         main = 'MDplot for each Class',
                         
                         xlab = 'Classes', ylab = 'PDE of Data per Class',
                         
                         Fill = 'darkblue', MinimalAmoutOfData=40,
                         
                         MinimalAmoutOfUniqueData=12,SampleSize=1e+05,...)

Arguments

Details

Further examples for the ClassMDplot can be found in https://md-plot.readthedocs.io/en/latest/application/example_application.html.

The Cls vector is reordered from lowest to highest number. The ClassNames vector and ColorSequence vectors are matched by this ordering of Cls, i.e. the lowest number gets the first color or class name.

Value

A List of

in mode invisible

Note

Function is still experimental because ColorSequence does not work yet, because we are unable to specify the colors in ggplot2. If someone knows a solution, please mail the maintainer of the package. Similar issue for PlotLegend.

Author(s)

Michael Thrun, Felix Pape

References

Thrun, M. C., Breuer, L., & Ultsch, A. : Knowledge discovery from low-frequency stream nitrate concentrations: hydrology and biology contributions, Proc. European Conference on Data Analysis (ECDA), Paderborn, Germany, 2018.

See Also

https://md-plot.readthedocs.io/en/latest/application/example_application.html

MDplot https://pypi.org/project/md-plot/

Examples

data(ITS)

#shortcut for example if AdaptGauss not installed
Classification = kmeans(ITS, centers = 2)$cluster

#better approach
#please download package from cran
#model=AdaptGauss::AdaptGauss(ITS)
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))
ClassNames=c(1,2)
names(ClassNames)=c("Insert name \n of Class 1","Insert name \n  of Class 2")
ClassMDplot(ITS,Classification,ClassNames = ClassNames)

PDE Plot for all classes

Description

PDEplot the data for all classes, weights the pdf with priors

Usage

ClassPDEplot(Data, Cls, ColorSequence,

 ColorSymbSequence, PlotLegend = 1,

 SameKernelsAndRadius = 0, xlim, ylim, ...)

Arguments

Value

Kernels of the Pareto density estimation in mode invisible

Author(s)

Michael Thrun

Examples

data(ITS)
#please download package from cran
#model=AdaptGauss::AdaptGauss(ITS)
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))

DataVisualizations::ClassPDEplot(ITS,Classification)$ggobject

Create PDE plot for all classes with maximum likelihood

Description

PDEplot the data for allclasses, weight the Plot with 1 (= maximum likelihood)

Usage

ClassPDEplotMaxLikeli(Data, Cls, ColorSequence = DataVisualizations::DefaultColorSequence,

 ClassNames, PlotLegend = TRUE, MinAnzKernels = 0,PlotNorm,

 main = "Pareto Density Estimation (PDE)",

 xlab = "Data", ylab = "ParetoDensity", xlim, ylim, lwd=1, ...)

Arguments

Value

Author(s)

Felix Pape

References

Aubert, A. H., Thrun, M. C., Breuer, L., & Ultsch, A. : Knowledge discovery from high-frequency stream nitrate concentrations: hydrology and biology contributions, Scientific reports, Nature, Vol. 6(31536), pp. doi 10.1038/srep31536, 2016.

Examples

data(ITS)
#model=AdaptGauss::AdaptGauss(ITS)
##please download package from cran
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))

DataVisualizations::ClassPDEplotMaxLikeli(ITS,Classification)$ggobject

Classplot

Description

Allows to plot one time series or feauture with a classification as a labeled scatter plot with a line. The colors are the labels defined by the classification.

Usage

Classplot(X, Y, Cls, Plotter,Names = NULL, na.rm = FALSE, 

xlab = "X", ylab = "Y", main = "Class Plot", Colors = NULL,

Size = 8,PointBorderCol="black",

LineColor = NULL, LineWidth = 1, LineType  = NULL, 

Showgrid  = TRUE, pch,  AnnotateIt = FALSE, SaveIt = FALSE, 

Nudge_x_Names = 0, Nudge_y_Names = 0, Legend = "", SmallClassesOnTop = TRUE,

...)

Arguments

Details

The mapping of colors to the labels of Cls is consecutive, i.e., the label with the smallest value in Cls gets the first color in Colors. The Colors are plotted in order from label with the highest number of points to the label with the lowest number of points beeing on top.

Default is "plotly" if Names are NULL. However, ggplot2 is preferable in case that Names parameter is used because overlapping text labels are avoided. In that case the default is "ggplot". Note that ggplot2 options are currently slightly restricted.

For example, the function is usefull to see if temporal clustering has time dependent variations and for Hidden Markov Models (see Mthrun/RHmm on GitHub).

Value

plotly object or ggplot2 objected depending on Plotter

Author(s)

Michael Thrun

See Also

DualaxisClassplot

Examples

data(Lsun3D)
Classplot(Lsun3D$Data[,1],Lsun3D$Data[,2],Lsun3D$Cls)

#ggplot 2 with different symbols
  Classplot(
    Lsun3D$Data[, 1],
    Lsun3D$Data[, 2],
    Lsun3D$Cls,
    Plotter = "ggplot2",
    Size = 3,
    pch = Lsun3D$Cls + 5
  )

#plotly with line
data(Lsun3D)
Classplot(Lsun3D$Data[,1],Lsun3D$Data[,2],Lsun3D$Cls,
LineType="-",LineColor = "green")

#ggplot2 with annotations
data(Lsun3D)
ind=sample(1:nrow(Lsun3D$Data),20)
Classplot(Lsun3D$Data[ind,1],Lsun3D$Data[ind,2],Lsun3D$Cls[ind],
Names = rownames(Lsun3D$Data)[ind],Size =1,
Plotter = "ggplot2",AnnotateIt = TRUE)



#ggplot2 with labels and legend per class
data(Lsun3D)
Classplot(Lsun3D$Data[,1],Lsun3D$Data[,2],Lsun3D$Cls,
Names = paste0("C",Lsun3D$Cls),Size =2,Legend ="Classes")

Combine vectors of various lengths

Description

Combine arbitrary vectors of data, filling in missing rows with NaN

Usage

CombineCols(...,na.rm=FALSE)

Arguments

Details

Robust alternative to cbind that fills missing values with nan instead of extending length of vector by duplicating elements

Value

matrix of dimensionality of n x d with n beeing the length of the longest vector and d the number of vectors given as input

Note

special application by MCT of rowr cbind.fill which is now not on CRAN anymore

Author(s)

Craig Varrichio

See Also

CombineRows

Examples

CombineCols(c(1,2,3),c(1),c(2,3))

Combine matrices of various lengths

Description

Combine arbitrary matrices of data, filling in missing columns with NaN

Usage

CombineRows(...,na.rm=FALSE)

Arguments

Details

Robust alternative to rbind that fills missing values with #NaN, tries to match given column names if matrices are inserted otherwise fills up the missing columns at the end.

The first argument has to be a matrix. It is assumed that this matrix has to be filled up and other arguments or not of bigger size than d columns. Otherwiese the further elements stored in columns >d are ignored.

Value

matrix of dimensionality of n x d with n beeing the number of rows of the first argument and d the number columns of the first argument given as input

Author(s)

Michael Thrun

See Also

CombineRows

Examples

matrix_pattern=cbind(c(1,2,3),c(4,5,6),c(7,8,9))

CombineRows(matrix_pattern,c(1),c(2,3))


CombineRows(matrix_pattern,cbind(c(1,2,3),c(4,5,6)))

Crosstable plot

Description

Presents a heatmap with values and a cross table of given Data matrix of two features and a bin width or percentualized values. In this approach the bin width is fixes. A more general way to approach this is the kernel density estimation plot of PDEscatter.

Usage

Crosstable(Data, xbins = seq(0, 100, 5), ybins = xbins, 

NormalizationFactor = 1, PlotIt = TRUE, main='Cross Table',

PlotText=TRUE,TextDigits=0,TextProbs=c(0.05,0.95))

Arguments

Details

The interval in each bin is closed to the left and opened to the right. The cross table can be seen as a two-dimensional histogram. The idea to add histograms to the table is taken from [Charpentier. 2014].

Value

The cross table in invisible mode which depicts the number of values (frequency) in an specific range with regard to two features.

The first feature is on the x-axis (left to right), and the second on y-axis (top to bottom) contrary to the plot where it is bottom to top.

Note

For non percentiled values the PlotText part does not seem always to work, but I currently dont know why the text does not always overlap with the heatmap.

Author(s)

Michael Thrun

References

[Charpentier. 2014] Charpentier, Arthur, ed. Computational actuarial science with R. CRC Press, 2014.

See Also

table, image, PDEscatter

Examples

data(ITS)
data(MTY)
#simple but not a good transformation
Data=(cbind(ITS/max(ITS),MTY/max(MTY)))*100
#choice for bins could be better
Crosstable(Data)

Default color sequence for plots

Description

Defines the default color sequence for plots made within the Projections package.

Usage

data("DefaultColorSequence")

Format

A vector with 562 different strings describing colors for plots.

Contour plot of densities

Description

Density estimation (PDE) [Ultsch, 2005] or "SDH" [Eilers/Goeman, 2004] used for a density contour plot.

Usage

DensityContour(X,Y, DensityEstimation="SDH", 

SampleSize, na.rm=FALSE,PlotIt=TRUE,
                              
NrOfContourLines=20,Plotter='ggplot', DrawTopView = TRUE,
                              
xlab, ylab, main="DensityContour",
                              
xlim, ylim, Legendlab_ggplot="value",

AddString2lab="",NoBinsOrPareto=NULL,...)

Arguments

Details

The DensityContour function generates the density of the xy data as a z coordinate. Afterwards xyz will be plotted either as a contour plot or a 3d plot. It assumens that the cases of x and y are mapped to each other meaning that a cbind(x,y) operation is allowed. This function plots the Density on top of a scatterplot. Variances of x and y should not differ by extreme numbers, otherwise calculate the percentiles on both first. If DrawTopView=FALSE only the plotly option is currently available. If another option is chosen, the method switches automatically there.

PlotIt=FALSE is usefull if one likes to perform adjustements like axis scaling prior to plotting with ggplot2 or plotly.

Value

List of:

Note

MT contributed with several adjustments

Author(s)

Felix Pape

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, (Ultsch, A. & Huellermeier, E. Eds., 10.1007/978-3-658-20540-9), Doctoral dissertation, Heidelberg, Springer, ISBN: 978-3658205393, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, In Baier, D. & Werrnecke, K. D. (Eds.), Innovations in classification, data science, and information systems, (Vol. 27, pp. 91-100), Berlin, Germany, Springer, 2005.

[Eilers/Goeman, 2004] Eilers, P. H., & Goeman, J. J.: Enhancing scatterplots with smoothed densities, Bioinformatics, Vol. 20(5), pp. 623-628. 2004.

Examples

#taken from [Thrun/Ultsch, 2018]
data("ITS")
data("MTY")
Inds=which(ITS<900&MTY<8000)
plot(ITS[Inds],MTY[Inds],main='Bimodality is not visible in normal scatter plot')

DensityContour(ITS[Inds],MTY[Inds],DensityEstimation="SDH",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='Smoothed Densities histogram indicates Bimodality' )

DensityContour(ITS[Inds],MTY[Inds],DensityEstimation="PDE",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='PDE indicates Bimodality' )

Scatter plot with densities

Description

Density estimation is performed by (PDE) [Ultsch, 2005] or "SDH" [Eilers/Goeman, 2004] and visualized in a density scatter plot [Brinkmann et al., 2023] in which the points are colored by their density.

Usage

DensityScatter(X,Y,DensityEstimation="SDH",

Type="DDCAL", Plotter = "native",Marginals = FALSE,

SampleSize,na.rm=FALSE, xlab, ylab, 

main="DensityScatter", AddString2lab="",
                        
xlim, ylim,NoBinsOrPareto=NULL,...)

Arguments

Details

The DensityScatter function generates the density of the xy data as a z coordinate. Afterwards xy points will be plotted as a scatter plot, where the z values defines the coloring of the xy points. It assumens that the cases of x and y are mapped to each other meaning that a cbind(x,y) operation is allowed. This function plots the Density on top of a scatterplot. Variances of x and y should not differ by extreme numbers, otherwise calculate the percentiles on both first.

Value

List of:

Note

MT contributed with several adjustments

Author(s)

Felix Pape

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, (Ultsch, A. & Huellermeier, E. Eds., 10.1007/978-3-658-20540-9), Doctoral dissertation, Heidelberg, Springer, ISBN: 978-3658205393, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, In Baier, D. & Werrnecke, K. D. (Eds.), Innovations in classification, data science, and information systems, (Vol. 27, pp. 91-100), Berlin, Germany, Springer, 2005.

[Eilers/Goeman, 2004] Eilers, P. H., & Goeman, J. J.: Enhancing scatterplots with smoothed densities, Bioinformatics, Vol. 20(5), pp. 623-628. 2004

[Lux/Rinderle-Ma, 2023] Lux, M. & Rinderle-Ma, S.: DDCAL: Evenly Distributing Data into Low Variance Clusters Based on Iterative Feature Scaling, Journal of Classification vol. 40, pp. 106-144, 2023.

[Brinkmann et al., 2023] Brinkmann, L., Stier, Q., & Thrun, M. C.: Computing Sensitive Color Transitions for the Identification of Two-Dimensional Structures, Proc. Data Science, Statistics & Visualisation (DSSV) and the European Conference on Data Analysis (ECDA), p.109, Antwerp, Belgium, July 5-7, 2023.

Examples

#taken from [Thrun/Ultsch, 2018]
data("ITS")
data("MTY")
Inds=which(ITS<900&MTY<8000)
plot(ITS[Inds],MTY[Inds],main='Bimodality is not visible in normal scatter plot')

DensityScatter(ITS[Inds],MTY[Inds],DensityEstimation="SDH",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='Smoothed Densities histogram indicates Bimodality' )

DensityScatter(ITS[Inds],MTY[Inds],DensityEstimation="PDE",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='PDE indicates Bimodality' )

Plot a classificated world map

Description

This function plots a world map where the single countries get colored differently by using a classification

Arguments

Value

a plot

Author(s)

Florian Lerch

Dualaxis Classplot

Description

Allows to plot two time series or features with one or two classification(a) as labeled scatter plots. The colors are the labels defined by the classification. Usefull to see if temporal clustering has time dependent variations and for Hidden Markov Models (see Mthrun/RHmm on GitHub).

Usage

DualaxisClassplot(X, Y1, Y2, Cls1,

Cls2, xlab = "X", y1lab = "Y1", y2lab = "Y2",

main = "Dual Axis Class Plot", Colors, Showgrid = TRUE, SaveIt = FALSE)

Arguments

Value

plotly object

Author(s)

Michael Thrun

See Also

Classplot

Examples

##ToDo

DualaxisLinechart

Description

A line chart with dual axisSS

Usage

DualaxisLinechart(X, Y1, Y2, xlab = "X", 

y1lab = "Y1", y2lab = "Y2", main = "Dual Axis Line Chart",

cols = c("black", "blue"),Overlaying="y", SaveIt = FALSE)

Arguments

Details

enables to visualize to lines in one plot overlaying them using ploty (e.g. two time series with two ranges of values)

Value

plotly object

Author(s)

Michael Thrun

Examples

#subplot renames the numbering of subsequent plots
y1=runif(100,0,1)
y2=rnorm(100,m=5,s=1)
DualaxisLinechart(1:100, y1, y2,main="Random Time series")


y1=runif(100,0,1)
y2=(1:100*3+4)*runif(100,0,1)
p1=DualaxisLinechart(1:100, y1, y2,main="Random Time series",Overlaying="y2")

y3=1:100*(-2)+4
y4=rnorm(100,m=0,s=2)
p2=DualaxisLinechart(1:100, y3, y4,main="Random Time series",Overlaying="y4")
plotly::subplot(p1,p2)

The fan plot

Description

The better alternative to the pie chart represents amount of values given in data.

Usage

Fanplot(Datavector,Names,Labels,MaxNumberOfSlices,main='',col,
MaxPercentage=FALSE,ShrinkPies=0.05,Rline=1.1, lwd=2,LabelCols="black",...)

Arguments

Details

A normal pie plot is dificult to interpret for a human observer, because humans are not trained well to observe angles [Gohil, 2015, p. 102]. Therefore, the fan plot is used. As proposed in [Gohil 2015] the fan.plot() of the plotrix package is used to solve this problem. If Number of Slices is higher than MaxNumberOfSlices then ABCanalysis is applied (see [Ultsch/Lotsch, 2015]) and group A chosen. If Number of Slices in group A is higher than MaxNumberOfSlices, then the most important ones out of group A are chosen. If MaxNumberOfSlices is higher than Slices in group A, additional slices are shown depending on the percentage (from high to low).

Color sequence is automatically shortened to the MaxNumberOfSlices used in the fan plot.

Value

silent output by calling invisible of a list with

Author(s)

Michael Thrun

References

[Gohil, 2015] Gohil, Atmajitsinh. R data Visualization cookbook. Packt Publishing Ltd, 2015.

[Ultsch/Lotsch, 2015] Ultsch. A ., Lotsch 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.

See Also

fan.plot Piechart

Examples

data(categoricalVariable)
Fanplot(categoricalVariable)

Fundamental Data of the 1st Quarter in 2018

Description

This dataset was extracted out of Yahoo finance and was investigated in [Thrun et al., 2019] and clustered in [Thrun, 2019].

Usage

data("FundamentalData_Q1_2018")

Format

The format is: List of 3 $ Data :'data.frame': 269 obs. of 45 variables: ..$ TotalRevenue : num [1:269] 3779000 78225 48220 63726 3084 ... ..$ CostofRevenue : num [1:269] 2348000 60835 26174 35203 882 ... ..$ GrossProfit : num [1:269] 1431000 17390 22046 28523 2202 ... ..$ SellingGeneralandAdministrative : num [1:269] 459000 NaN 15162 17072 2005 ... ..$ Others : num [1:269] -3000 10272 -52 3131 1784 ... ..$ TotalOperatingExpenses : num [1:269] 2872000 73833 41284 56787 5081 ... ..$ OperatingIncomeorLoss : num [1:269] 907000 4392 6936 6939 -1997 ... ..$ TotalOtherIncomeDIVxpensesNet : num [1:269] -28000 -344 1 -210 -240 ... ..$ EarningsBeforeInterestandTaxes : num [1:269] 907000 4392 6936 6939 -1997 ... ..$ InterestExpense : num [1:269] -20000 -415 NaN -243 -238 ... ..$ IncomeBeforeTax : num [1:269] 879000 4048 6937 6729 -2237 ... ..$ IncomeTaxExpense : num [1:269] 233000 1365 2188 1896 7 ... ..$ NetIncomeFromContinuingOps : num [1:269] 646000 2683 4749 4833 -2244 ... ..$ NetIncome_x : num [1:269] 644000 2817 4645 4833 -2244 ... ..$ NetIncome : num [1:269] 644000 2817 4645 4833 -2244 ... ..$ CashAndCashEquivalents : num [1:269] 926000 29047 45911 94859 11217 ... ..$ NetReceivables : num [1:269] 2527000 46171 20774 151952 2774 ... ..$ Inventory : num [1:269] 2011000 471 NaN 10572 8924 ... ..$ TotalCurrentAssets : num [1:269] 5674000 80224 68061 267187 25989 ... ..$ LongTermInvestments : num [1:269] 234000 450 NaN 4155 872 ... ..$ PropertyPlantandEquipment : num [1:269] 4216000 14561 3093 32247 7073 ... ..$ IntangibleAssets : num [1:269] 78000 40706 3975 6169 125 ... ..$ OtherAssets : num [1:269] 810000 8224 1091 2978 13310 ... ..$ DeferredLongTermAssetCharges : num [1:269] 759000 684 1091 784 1405 ... ..$ TotalAssets : num [1:269] 11262000 167807 83155 351220 47369 ... ..$ AccountsPayable : num [1:269] 1442000 10567 1698 17316 1386 ... ..$ ShortDIVurrentLongTermDebt : num [1:269] 1275000 30192 NaN 26668 917 ... ..$ OtherCurrentLiabilities : num [1:269] 1064000 36942 22781 92297 2659 ... ..$ TotalCurrentLiabilities : num [1:269] 2577000 54430 24479 114210 4299 ... ..$ OtherLiabilities : num [1:269] 1795000 19435 6876 29347 2018 ... ..$ TotalLiabilities : num [1:269] 5576000 97136 31355 165628 6980 ... ..$ CommonStock : num [1:269] 198000 14946 5198 15250 28644 ... ..$ RetainedEarnings : num [1:269] NaN 44030 34767 40374 -8965 ... ..$ TreasuryStock : num [1:269] 5455000 11686 NaN 129968 20710 ... ..$ OtherStockholderEquity : num [1:269] 5455000 11686 NaN 129968 20710 ... ..$ TotalStockholderEquity : num [1:269] 5653000 70662 51212 185592 40389 ... ..$ NetTangibleAssets : num [1:269] 5325000 6314 40302 140939 40264 ... ..$ Depreciation : num [1:269] 156000 2728 331 1381 410 ... ..$ AdjustmentsToNetIncome : num [1:269] 216000 1911 116 2912 39 ... ..$ ChangesInOtherOperatingActivities : num [1:269] -20000 -2174 -829 NaN 428 ... ..$ TotalCashFlowFromOperatingActivities : num [1:269] 452000 7349 4274 -8241 -1367 ... ..$ CapitalExpenditures : num [1:269] -88000 -966 -1778 -2067 -155 ... ..$ TotalCashFlowsFromInvestingActivities: num [1:269] 30000 -879 -1766 -2746 -484 ... ..$ TotalCashFlowsFromFinancingActivities: num [1:269] -789000 -6660 -21867 -961 -204 ... ..$ ChangeInCashandCashEquivalents : num [1:269] -306000 -215 2508 -11842 -2062 ... $ Names: chr [1:269, 1:6] "1COV" "A1OS" "AAD" "AAG" ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:6] "Key" "ISIN" "Company" "Sector" ... $ Cls : num [1:269] 1 1 1 1 2 1 1 1 3 1 ...

Details

Stocks are selected by the German Prime standard accoridingly to the "Names" data frame. Fundamental Data with missing values is stored in "Data". The rownames of "Data" have the same Key as the first row of "Names" which is the trading symbol. "Cls" provides the clustering as a numerical vector of 1:k classes performed by Databionic Swarm in [Thrun, 2019].

Source

Yahoo finance

References

Thrun, M. C., : Knowledge Discovery in Quarterly Financial Data of Stocks Based on the Prime Standard using a Hybrid of a Swarm with SOM, in Verleysen, M. (Ed.), European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), Vol. 27, pp. 397-402, Ciaco, ISBN: 978-287-587-065-0, Bruges, Belgium, 2019.

[Thrun et al., 2019] Thrun, M. C., Gehlert, Tino, & Ultsch, A. : Analyzing the Fine Structure of Distributions, arXiv:1908.06081, 2019.

Examples

data(FundamentalData_Q1_2018)
## maybe str(FundamentalData_Q1_2018) ; plot(FundamentalData_Q1_2018) ...

Google Maps with marked coordinates

Description

Google Maps with marked coordinates.

Usage

GoogleMapsCoordinates(Longitude,Latitude,Cls=rep(1,length(Longitude)),
zoom=3,location= c(mean(Longitude),mean(Latitude)),stroke=1.7,size=6,sequence)

Arguments

Details

This plot was used in [Thrun, 2018, p. 135].

Value

ggobject()

Note

requires an Internet connection, requires an API key of Google. See ?ggmap::register_google for details.

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.

Heatmap for Clustering

Description

Heatmap of Distances of Data sorted by Cls. Clustering algorithms provide a Classifcation of data, where the labels are defined as a numeric vector Cls. Then, a typical cluster-respectively group structure is displayed by the Heatmap function. At the margin of the heatmap a dendrogram can be shown, if hierarchical cluster algorithms are used [Wilkinson,2009]. Here the dendrogram has to be shown separately and only the heatmap itself is displayed

Usage

Heatmap(DataOrDistances,Cls,method='euclidean',

LowLim=0,HiLim,LineWidth=0.5,Clabel="Cluster No.")

Arguments

Details

"Cluster heatmaps are commonly used in biology and related fields to reveal hierarchical clusters in data matrices. Heatmaps visualize a data matrix by drawing a rectangular grid corresponding to rows and columns in the matrix and coloring the cells by their values in the data matrix. In their most basic form, heatmaps have been used for over a century [Wilkinson, 2012]. In addition to coloring cells, cluster heatmaps reorder the rows and/or columns of the matrix based on the results of hierarchical clustering. (...) . Cluster heatmaps have high data density, allowing them to compact large amounts of information into a small space [Weinstein, 2008]", [Engle, 2017].

The procedure can be adapted to distance matrices [Thrun, 2018]. Then, the color scale is chosen such that pixels of low distances have blue and teal colors, pixels of middle distances yellow colors, and pixels of high distances have orange and red colors [Thrun, 2018]. The distances are ordered by the clustering and the clusters are divided by black lines. A clustering is valid if the intra-cluster distances are distinctively smaller that inter-cluster distances in the heatmap [Thrun, 2018]. For another example, please see [Thrun, 2018] (Fig. 3.7, p. 31).

Value

object of ggplot2

Author(s)

Michael Thrun

References

[Wilkinson,2009] Wilkinson, L., & Friendly, M.: The history of the cluster heat map, The American Statistician, Vol. 63(2), pp. 179-184. 2009.

[Engle et al., 2017] Engle, S., Whalen, S., Joshi, A., & Pollard, K. S.: Unboxing cluster heatmaps, BMC bioinformatics, Vol. 18(2), pp. 63. 2017.

[Weinstein, 2008] Weinstein, J. N.: A postgenomic visual icon, Science, Vol. 319(5871), pp. 1772-1773. 2008.

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

See Also

Pixelmatrix

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data

#Data
Heatmap(Data,Cls = Cls)

#Distances
Heatmap(as.matrix(dist(Data)),Cls = Cls)

Default color sequence for plots

Description

Defines the default color sequence for plots made with PixelMatrixPlot

Usage

data("HeatmapColors")

Format

A vector with different strings describing colors for this plot.

Income Tax Share

Description

Numerical vector of length 11194. details in [Ultsch/Behnisch, 2017; Thrun/Ultsch, 2018].

Usage

data("ITS")

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch/Behnisch, 2017] Ultsch, A., Behnisch, M.: Effects of the payout system of income taxes to municipalities in Germany, Applied Geography, Vol. 81, pp. 21-31, 2017.

Examples

data(ITS)
str(ITS)

Inspect Boxplots

Description

Enables to inspect the boxplots for multiple variables in ggplot2 syntax. Each boxplot also has a point for the mean of the variable.

Usage

InspectBoxplots(Data, Names,Means=TRUE)

Arguments

Value

The ggplot object of the boxplots

Author(s)

Felix Pape

Examples

x <- cbind(A = rnorm(200, 1, 3), B = rnorm(100, -2, 5))
InspectBoxplots(x)

Inspect the Correlation

Description

Inspects the correlation between two given features using density scatter plots.

Usage

InspectCorrelation(X, Y, DensityEstimation = "SDH",

CorMethod = "spearman", na.rm = TRUE,

SampleSize = round(sqrt(5e+08), -3),

NrOfContourLines = 20, Plotter = "native",

DrawTopView = T, xlab, ylab,

main = "Spearman correlation coef.:", xlim, ylim, 

Legendlab_ggplot = "value", ...)

Arguments

Details

Example shows that features with high correlation coefficient do not correlate because of bimodality.

Value

plotting handler

Author(s)

Michael Thrun

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

See Also

DensityScatter

Examples

data(ITS)
data(MTY)
Inds=which(ITS<900&MTY<8000)

InspectCorrelation(ITS[Inds],MTY[Inds])

Inspection of Distance-Distribution

Description

Visualizes the distances between objects in the data matrix

Usage

InspectDistances(DataOrDistances,method= "euclidean",sampleSize = 50000,...)

Arguments

Details

For an interpretation of the distribution analysis of the distance please read [Thrun, 2018, p. 27, 185].

Note

uses InspectVariable

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.

Examples

data("Lsun3D")
Data=Lsun3D$Data

InspectDistances(as.matrix(dist(Data)))

Pairwise scatterplots and optimal histograms

Description

Pairwise scatterplots and optimal histograms of all features stored as columns of data are plotted

Usage

InspectScatterplots(Data,Names=colnames(Data))

Arguments

Details

For two features, PDEscatter function should be used to isnpect modalities [Thrun/Ultsch, 2018]. For many features the function takes too lang. In such a case this function can be used. See [Thrun/Ultsch, 2018] for optimal histogram description.

Author(s)

Michael Thrun

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A.: Effects of the payout system of income taxes to municipalities in Germany, 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Vol. accepted, Foundation of the Cracow University of Economics, Zakopane, Poland, 2018.

Examples

Data=cbind(rnorm(100, mean = 2, sd = 3  ),rnorm(100,mean = 0, sd = 1),rnorm(100,mean = 6, sd = 0.5))
#InspectScatterplots(Data)

QQplot of Data versus Normalized Data

Description

Allows to inspect if standardization of data makes sense

Usage

InspectStandardization(Data, TransData, xug = -3, xog = 3, xlab = "Normal", yDataLab =

"Data", yTransDataLab = "Trasformated Data", Symbol4Gerade = "red", main = "", ...)

Arguments

Details

...

Value

plot

Author(s)

Michael Thrun

References

Michael, J. R.: The stabilized probability plot, Biometrika, Vol. 70(1), pp. 11-17, 1983.

Visualization of Distribution of one variable

Description

Enables distribution inspection by visualization as described in [Thrun, 2018] and for example used in

Usage

InspectVariable(Feature, Name, i = 1, xlim, ylim,

 sampleSize =1e+05, main)
 

Arguments

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

Examples

data("ITS")
InspectVariable(ITS,Name='Income in EUR',main='ITS')

Jitters Unique Values

Description

Jitters Unique Values for Visualizations

Usage

JitterUniqueValues(Data, Npoints = 20,

min = 0.99999, max = 1.00001)

Arguments

Details

min and max are either multiplied or added to data depending on the range of values. If Npoints==2, then only two values per unique of Data is jittered otherwise additional values are generated.Npoints==1 does not jitter the values but gives the unique values back.

Value

vector of DataJitter[1:(m+Npoints-1)] jittered values

Author(s)

Michael Thrun

See Also

used for example in MDplot

Examples

data=c(rep(1,10),rep(0,10),rep(100,10))

JitterUniqueValues(data,Npoints=1)

JitterUniqueValues(data,Npoints=2)

DataJitter=JitterUniqueValues(data,Npoints=20)

Lsun3D inspired by FCPS [Thrun/Ultsch, 2020] introduced in [Thrun, 2018]

Description

Clearly defined clusters, different variances. Detailed description of dataset and its clustering challenge is provided in [Thrun/Ultsch, 2020].

Usage

data("Lsun3D")

Details

Size 404, Dimensions 3

Dataset defines discontinuites, where the clusters have different variances. Three main clusters, and four outliers (in cluster 4). For a more detailed description see [Thrun, 2018].

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Clustering Benchmark Datasets Exploiting the Fundamental Clustering Problems, Data in Brief, Vol. 30(C), pp. 105501, doi:10.1016/j.dib.2020.105501, 2020.

Examples

data(Lsun3D)
str(Lsun3D)
Cls=Lsun3D$Cls
Data=Lsun3D$Data

Minus versus Add plot

Description

Bland-Altman plot [Altman/Bland, 1983].

Usage

MAplot(X,Y,islog=TRUE,LoA=FALSE,CI=FALSE,

densityplot=FALSE,main,xlab,ylab,

Cls,lwd=2,ylim=NULL,...)

Arguments

Details

Bland-Altman plot [Altman/Bland, 1983] for visual representation of genomic data or in order to decorrelate data.

"The limits of agreement (LoA) are defined as the mean difference +- 1.96 SD of differences. If these limits do not exceed the maximum allowed difference between methods (the differences within mean +- 1.96 SD are not clinically important), the two methods are considered to be in agreement and may be used interchangeably." cited as in URL. Please note, that the underyling assumption is the normal distribution of the differences. Input argument LoA=TRUE shows the mean of the difference in blue and +- 1.96 SD in green. Input argument CI=TRUE shows the mean of the difference in blue and the confidence intervall as red dashed lines similar to the cited URL.

In case of densityplot=FALSE, the function Classplot is always called with Plotter="native". Then, the input argument "Colors"" of points can only be set in Classplot if "Cls"" is given in this function, otherwise the points are always black. The input argument "Size"" sets the size of points in Classplot.

Value

Author(s)

Michael Thrun

References

[Altman/Bland, 1983] Altman D.G., Bland J.M.: Measurement in medicine: the analysis of method comparison studies, The Statistician, Vol. 32, p. 307-317, doi:10.2307/2987937, 1983.

https://www.medcalc.org/manual/bland-altman-plot.php

[Stockl et al., 2004] Stockl, D., Rodriguez Cabaleiro, D., Van Uytfanghe, K., & Thienpont, L. M.: Interpreting method comparison studies by use of the Bland-Altman plot: reflecting the importance of sample size by incorporating confidence limits and predefined error limits in the graphic, Clinical chemistry, Vol. 50(11), pp. 2216-2218. 2004.

Examples

data("ITS")
data("MTY")
MAlist=MAplot(ITS,MTY)

Mirrored Density plot (MD-plot)

Description

This function creates a MD-plot for each variable of the data matrix. The MD-plot is a visualization for a boxplot-like shape of the PDF published in [Thrun et al., 2020] with the default ordering by shape. It is an improvement of violin or so-called bean plots and posses advantages in comparison to the conventional well-known box plot [Thrun et al., 2020].

A complete guide about the MDplot can be found in https://md-plot.readthedocs.io/en/latest/index.html.

Usage

MDplot(Data, Names, Ordering='Default', Scaling="None",

Fill='darkblue', RobustGaussian=TRUE, GaussianColor='magenta',

Gaussian_lwd=1.5, BoxPlot=FALSE,BoxColor='darkred', 

MDscaling='width', LineColor='black', LineSize=0.01,

QuantityThreshold=50, UniqueValuesThreshold=12,

SampleSize=5e+05,SizeOfJitteredPoints=1,OnlyPlotOutput=TRUE,

main="MD-plot",ylab="Range of values in which PDE is estimated",

BW=FALSE,ForceNames=FALSE)

Arguments

Details

In short, the MD-plot can be described as a PDE optimized violin plot. The Pareto Density Estimation (PDE) is an approach to estimate the probability density function (pdf) [Ultsch, 2005].

The MD-plot is in the process of beeing peer-reviewed [Thrun/Ultsch, 2019].

Statistical testing is performed with dip.test and agostino.test.

For the paramter Ordering the following options are possible:

Default

Ordering of plots by convex/concav/unimodal/nonunimodal shapes using statistical criteria. In this case the signal is required.

Columnwise

Ordering of plots by the order of columns of Data.

AsIs

Synonym of Columnwise: Ordering of plots by the order of columns of Data.

Alphabetical

Ordering of plots by the order of columns of Data sorted in alphabetical order by column names.

Average

Ordering of plots by the order of columns of Data sorted in order of increasing column-wise average

Bimodal

Ordering of plots by the order of columns of Data sorted in order of decreasing bimodality amplitude[Zhang et al., 2003]

Variance

Ordering of plots by the order of columns of Data sorted in order of increasing inter-quartile range

Statistics

Ordering of plots depending on the logarithm of the p-vlaues of statistical testing. In this case the packages moments, diptest and signal are required.

For the paramter Scaling the following options are possible:

None

No Scaling of data is done.

Percentalize

Data is scaled between zero and 100.

CompleteRobust

Data is first robustly scaled between zero and 1, then centered to zero and outliers are capped by a robustly formula described in RobustNormalization.

Robust

Data is robustly scaled between zero and 1 by a formula described in the RobustNormalization.

Log

Data is transformed with a sgined log allowing for negative values to be transformed with a logarithm of base 10, please see SignedLog for details.

Value

In the default case of OnlyPlotOutput==TRUE: The ggplot object of the MD-plot.

Otherwise for OnlyPlotOutput==FALSE: A list of

Note that the package ggExtra is not necessarily required but if given the feature names are automatically rotated.

Note

1.) One would assume that in the first of the two following cases ggplot2 only adjusts the plotting region but:

MDplot(MTY)+ylim(c(0,7000)) is equal to MDplot(MTY[MTY<7000]).

This means in both cases the data is clipped and AFTERWARDS the density estimation is performed.

2.) Because of a (sometimes) strange behavior of either ggplot2 or reshape2, numerical column names are changed to character by adding 'C_' which can disabled using ForceNames=TRUE.

3.) Columnnames will be automatically deblanked and cleaned. To force specific columnnames the input Names can be used in combination with ForceNames=TRUE. However, this can result in plotting errors or other strange behavior.

4.) Overlaying MD-plots with robustly estimated gaussians seldomly will yield magenta (or other GaussianColor) lines overlaying more than the violin plot they should overlay, because the width of the two plots is not the same (but I am unable to set it strictly in ggplot). In such a case just call the function again.

Author(s)

Michael Thrun, Felix Pape contributed with the idea to use ggplot2 as the basic framework.

References

[Thrun et al., 2020] Thrun, M. C., Gehlert, T. & Ultsch, A.: Analyzing the Fine Structure of Distributions, PLoS ONE, Vol. 15(10), pp. 1-66, DOI 10.1371/journal.pone.0238835, 2020.

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Zhang et al., 2003] Zhang, C., Mapes, B., & Soden, B.: Bimodality in tropical water vapour, Quarterly Journalof the Royal Meteorological Society, 129(594), 2847-2866, 2003.

See Also

https://md-plot.readthedocs.io/en/latest/index.html

ClassMDplot

https://pypi.org/project/md-plot/

Examples

x = cbind(
    A = runif(2000, 1, 5),
    B = c(rnorm(1000, 0, 1), rnorm(1000, 2.6, 1)),
    C = c(rnorm(2000, 2.5, 1)),
    D = rpois(2000, 5)
  )
MDplot(x)

Mirrored Density plot (MD-plot)for Multiple Vectors

Description

This function creates a MD-plot for multiple numerical vectors of various lenghts. The MD-plot is a visualization for a boxplot-like Shape of the PDF published in [Thrun et al., 2020]. It is an improvement of violin or so-called bean plots and posses advantages in comparison to the conventional well-known box plot [Thrun et al., 2020].

Usage

MDplot4multiplevectors(..., Names, Ordering = 'Columnwise',
Scaling = "None", Fill = 'darkblue', RobustGaussian = TRUE,

GaussianColor = 'magenta', Gaussian_lwd = 1.5, BoxPlot = FALSE,

BoxColor = 'darkred', MDscaling = 'width', LineSize = 0.01,

LineColor = 'black', QuantityThreshold = 40, UniqueValuesThreshold = 12,

SampleSize = 5e+05, SizeOfJitteredPoints = 1, OnlyPlotOutput = TRUE)

Arguments

Details

Please see MDplot for details.

Value

In the default case of OnlyPlotOutput==TRUE: The ggplot object of the MD-plot.

Otherwise for OnlyPlotOutput==FALSE: A list of

Note that the package ggExtra is not necessarily required but if given the feauture names are automatically rotated.

Note

cbind.fill is internally used from the depricated R package rowr of Craig Varrichio.

Author(s)

Michael Thrun.

References

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Thrun et al., 2020] Thrun, M. C., Gehlert, T. & Ultsch, A.: Analyzing the Fine Structure of Distributions, PLoS ONE, Vol. 15(10), pp. 1-66, DOI 10.1371/journal.pone.0238835, 2020.

See Also

ClassMDplot MDplot https://pypi.org/project/md-plot/

Examples

MDplot4multiplevectors(runif(20000, 1, 5),c(rnorm(20000,0,1),

rnorm(20000,2.6,1)),c(rnorm(2000,2.5,1)),rpois(25000,5),

Names=c('A','B','C','D'))

V=list(runif(20000, 1, 5),c(rnorm(20000,0,1),

rnorm(20000,2.6,1)),c(rnorm(2000,2.5,1)),rpois(25000,5))


MDplot4multiplevectors(V,Names=c('A','B','C','D'))

Muncipal Income Tax Yield

Description

Numerical vector of length 11194. details in [Ultsch/Behnisch, 2017; Thrun/Ultsch, 2018].

Usage

data("MTY")

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch/Behnisch, 2017] Ultsch, A., Behnisch, M.: Effects of the payout system of income taxes to municipalities in Germany, Applied Geography, Vol. 81, pp. 21-31, 2017.

Examples

data(MTY)
str(MTY)

Robust Empirical Mean Estimation

Description

If the input is a matrix the mean value will be compute for every column.

Usage

Meanrobust(x, p=10,na.rm=TRUE)

Arguments

Author(s)

Zornitsa Manolova

See Also

mean

Plot multiple ggplots objects in one panel

Description

ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)
For example, if the layout is specified as the matrix(c(1,2,3,3), nrow=2, byrow=TRUE), then plot 1 will go in the upper left, 2 will go in the upper right, and 3 will go all the way across the bottom.

Usage

Multiplot(..., Plotlist=NULL, ColNo=1, LayoutMat,Plotter =
                    "native")

Arguments

Value

List with Plotlist

Author(s)

Winston Chang

Examples

data(Lsun3D)
Data=Lsun3D$Data
Cls=Lsun3D$Cls
obj1=Classplot(Data[,1],Data[,2],Cls=Cls,Plotter="ggplot",Size=3,main="Top plot")
obj2=Classplot(Data[,2],Data[,3],Cls=Cls,Plotter="ggplot",Size=3,main="Middle plot")
obj3=Classplot(Data[,1],Data[,3],Cls=Cls,Plotter="ggplot",Size=3,main="Bottom plot")
V=Multiplot(obj1,obj2,obj3)

Optimal Number Of Bins

Description

Optimal Number Of Bins is a kernel density estimation for fixed intervals.

Calculation of the optimal number of bins for a histogram.

Usage

OptimalNoBins(Data)

Arguments

Details

The bin width ist defined with bw=3.49*stdrobust(1/(n)^1/3)

Value

optNrOfBins The best possible number of bins. Not less than 10 though

Note

This the second version of the function prior available in AdaptGauss

Author(s)

Alfred Ultsch, Michael Thrun

References

David W. Scott Jerome P. Keating: A Primer on Density Estimation for the Great Home Run Race of 98, STATS 25, 1999, pp 16-22.

See Also

ParetoRadius

Examples

Data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)

optNrOfBins = OptimalNoBins(Data)

minData = min(Data,na.rm = TRUE)

maxData = max(Data,na.rm = TRUE)

i = maxData-minData

optBreaks = seq(minData, maxData, i/optNrOfBins) # bins in fixed intervals 

hist(Data, breaks=optBreaks)

PDEnormrobust

Description

This functions plots ParetoDensityEsrtimation (PDE) and robustly estimated Gaussian with empirical Mean and Variance

Usage

PDEnormrobust(Data,xlab='PDE',ylab,main='PDEnormrobust',
                          PlotSymbolPDE='blue',
                          PlotSymbolGauss= 'magenta',PlotIt=TRUE,
                          Mark2Sigma=FALSE,Mark3Sigma=FALSE,
                          p_mean=10,p_sd=25,...)

Arguments

Details

Within Mark2Sigma 95 percent of data should be contained if distribution is Gaussian

Within Mark3Sigma 99 percent of data should be contained if distribution is Gaussian

The 3sgima rule is usually defined as M+-3SD containing 99.7 percent of data but to simplify, the input parameter name is called Mark3Sigma instead Mark2comma576Sigma, the same reason applies to the output parameter Sigma3.

Value

Author(s)

Michael Thrun

Examples

data(MTY)

PDEnormrobust(unname(MTY))

PDE plot

Description

This function plots the Pareto probability density estimation (PDE), uses PDEstimationForGauss and ParetoRadius.

Usage

PDEplot(Data, paretoRadius = 0, weight = 1, kernels = NULL,

                 LogPlot = F, PlotIt = TRUE, title =
                 "ParetoDensityEstimation(PDE)", color = "blue",
				 
                 xpoints = FALSE, xlim, ylim, xlab, ylab =
                 "PDE", ggPlot = ggplot(), sampleSize = 2e+05, lwd = 2)
				 

Arguments

Value

Author(s)

Michael Thrun

References

Ultsch, A.: Pareto Density Estimation: A Density Estimation for Knowledge Discovery, Baier D., Wernecke K.D. (Eds), In Innovations in Classification, Data Science, and Information Systems - Proceedings 27th Annual Conference of the German Classification Society (GfKL) 2003, Berlin, Heidelberg, Springer, pp, 91-100, 2005.

Examples

x <- rnorm(1000, mean = 0.5, sd = 0.5)
y <- rnorm(750, mean = -0.5, sd = 0.75)
plt <- PDEplot(x, color = "red")$ggPlot
plt <- PDEplot(y, color = "blue", ggPlot = plt)$ggPlot

# Second Example
#  ggplotObj=ggplot()
#  for(i in 1:length(Variables))
#     ggplotObj=PDEplot(Data[,i],ggPlot = ggplotObj)$ggPlot

Pareto Density Estimation V3

Description

This function estimates the Pareto Density for the distribution of one variable. In the default setting the functions estimates internally the appropriate number and position of kernels to estimate the density properly. However, the user can set the kernels manually. In this case density will only be estimated only around these values even if data exists outside the range of kernels or the internally estimated paretoRadius does not contain all datapoints between each kernel. See example for details.

Usage

ParetoDensityEstimation(Data, paretoRadius, kernels = NULL,
  MinAnzKernels = 100,PlotIt=FALSE,Silent=FALSE)

Arguments

Details

Pareto Density Estimation (PDE) is a method for the estimation of probability density functions using hyperspheres. The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. It is shown, that Pareto Density is the best estimate for clusters of Gaussian structure. The method is shown to be robust when cluster overlap and when the variances differ across clusters. This is the best density estimation to judge Gaussian Mixtures of the data see [Ultsch 2003].

If input argument kernels is set manually the output arguments paretoDensity_internal and kernels_internal provide the internally estimated density and kernels. Otherwise these arguments are NULL. The function provides a message if range of kernels and range of data does not overlap completly.

Typically it is not advisable to set paretoRadius manually. However in specific cases, the function ParetoRadius is used prior to calling this function. In such cases the input argument can use a priorly estimated paretoRadius.

Value

List With

kernels

[1:m] numeric vector. data values at with Pareto Density is measured.

paretoDensity

[1:m] numeric vector containing the determined density by paretoRadius.

paretoRadius

numeric value of defining the radius

kernels_internal

Either NULL or internally estimated [1:p] numeric vector of kernels if input argument kernels was set by the user

paretoDensity_internal

Either NULL or internally estimated density if input argument kernels was set by the user

Note

This the second version of the function prior available in AdaptGauss

Author(s)

Michael Thrun

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

See Also

ParetoRadius

PDEplot

MDplot

Examples

   
   #kernels are estimated internally
   data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)
   pdeVal        <- ParetoDensityEstimation(data)
   plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
   yaxs='i',xlab='Data',ylab='PDE')
   
   ##data exist outside of the range kernels
   kernels=seq(from=-3,to=3,by=0.01) 
   pdeVal        <- ParetoDensityEstimation(data,  kernels=kernels)
   plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
   yaxs='i',xlab='Data',ylab='PDE')
   
   #data exists in-between kernels that is not measured
   pdeVal$paretoRadius#0.42
   kernels=seq(from=-8,to=8,by=1)
   pdeVal        <- ParetoDensityEstimation(data,  kernels=kernels)
   plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
   yaxs='i',xlab='Data',ylab='PDE')
   
   

ParetoRadius for distributions

Description

Calculation of the ParetoRadius i.e. the 18 percentiles of all mutual Euclidian distances in data.

Usage

ParetoRadius(Data, maximumNrSamples = 10000,
  plotDistancePercentiles = FALSE)

Arguments

Details

The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. ParetoRadius() is a kernel density estimation for variable intervals. It works only on Data without missing values (NA) or NaN. In other cases, please use ParetoDensityEstimation directly.

Value

numeric value, the Pareto radius.

Note

This the second version of the function prior available in AdaptGauss.

For larger datasets the quantile_c() function is used instead of quantile in R which was programmed by Dirk Eddelbuettel on Jun 6 and taken by the author from https://github.com/RcppCore/Rcpp/issues/967.

Author(s)

Michael Thrun

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

See Also

ParetoDensityEstimation, OptimalNoBins

The pie chart

Description

the pie chart represents amount of values given in data.

Usage

Piechart(Datavector,Names,Labels,MaxNumberOfSlices,
main='',col,Rline=1,...)

Arguments

Details

If Number of Slices is higher than MaxNumberOfSlices then ABCanalysis is applied (see [Ultsch/Lotsch, 2015]) and group A chosen. If Number of Slices in group A is higher than MaxNumberOfSlices, then the most important ones out of group A are chosen. If MaxNumberOfSlices is higher than Slices in group A, additional slices are shown depending on the percentage (from high to low). Parameters of visualization a set as in [Schwabish, 2014] defined.

Color sequence is automatically shortened to the MaxNumberOfSlices used in the pie chart.

Value

silent output by calling invisible of a list with

Note

You see in the example below that a pie chart does not visualize such data well contrary to the fanPlot.

Author(s)

Michael Thrun

References

[Schwabish, 2014] Schwabish, Jonathan A. An Economist's Guide to Visualizing Data. Journal of Economic Perspectives, 28 (1): 209-34. DOI: 10.1257/jep.28.1.209, 2014.

[Ultsch/Lotsch, 2015] Ultsch. A ., Lotsch 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.

Examples

data(categoricalVariable)
Piechart(categoricalVariable)

Plot of a Pixel Matrix

Description

Plots Data matrix as a pixel coulour image.

Usage

Pixelmatrix(Data, XNames, LowLim, HiLim,

YNames, main,FillNotFiniteWithHighestValue=FALSE) 

Arguments

Details

Low values are shown in blue and green, middle values in yellow and high values in orange and red.

Author(s)

Michael Thrun, Felix Pape

Examples

data("Lsun3D")
Data=Lsun3D$Data

Pixelmatrix(Data)

3D plot of points

Description

A wrapper for Data with systematic clustering colors for either a 2D (x,y) or 3D (x,y,z) plot combined with a classification

Usage

Plot3D(Data,Cls,UniqueColors,

size=2,na.rm=FALSE,Plotter3D="rgl",...)

Arguments

Details

For geom_point only size and na.rm is available as further arguments.

Note

Uses either geom_point for 2D or plot3d for 3D or plot_ly

Author(s)

Michael Thrun

References

RGL vignette in https://cran.r-project.org/package=rgl

Examples

#Spin3D similar output

data(Lsun3D)
Plot3D(Lsun3D$Data,Lsun3D$Cls,type='s',radius=0.1,box=FALSE,aspect=TRUE)
rgl::grid3d(c("x", "y", "z"))


#Projected Points with Classification
Data=cbind(runif(500,min=-3,max=3),rnorm(500))

# Classification
Cls=ifelse(Data[,1]>0,1,2)
Plot3D(Data,Cls,UniqueColors = DataVisualizations::DefaultColorSequence[c(1,3)],size=2)

## Not run: 
#Points with Non-Overlapping Labels
#require(ggrepel)
Data=cbind(runif(30,min=-1,max=1),rnorm(30,0,0.5))
Names=paste0('VeryLongName',1:30)
ggobj=Plot3D(Data)
ggobj +  geom_text_repel(aes(label=Names), size=3)

## End(Not run)

PlotGraph2D

Description

plots a neighborhood graph in two dimensions given the 2D coordinates of the points

Usage

PlotGraph2D(AdjacencyMatrix, Points, Cls, Colors, xlab = "X", ylab = "Y", xlim,
ylim, Plotter = "native", LineColor = "grey", pch = 20, lwd = 0.1, main = "",
mainSize)

Arguments

Details

The points are the vertices of the graph. the adjacency matrix defines the edges. Via adjacency matrix various graphs, like from deldir package, can be used.

Value

native plot or plotly object depending on input argument Plotter

Author(s)

Michael Thrun

References

Lecture of Knowledge Discovery II

See Also

pch

Examples

N=10
x=runif(N)
y=runif(N)
Euklid=as.matrix(dist(cbind(x,y)))
Radius=quantile(as.vector(Euklid),0.5)
RKugelGraphAdjMatrix = matrix(0, ncol = N, nrow = N)
for (i in 1:N) {
  RInd = which(Euklid[i, ] <= Radius, arr.ind = TRUE)
  RKugelGraphAdjMatrix[i, RInd] = 1
}
PlotGraph2D(RKugelGraphAdjMatrix,cbind(x,y))

Plot of the Amount Of Missing Values

Description

Percentage of missing values per feature are visualized as a bar plot.

Usage

PlotMissingvalues(Data,Names,

WhichDefineMissing=c('NA','NaN','DUMMY','.',' '),

PlotIt=TRUE,

xlab='Amount Of Missing Values in Percent',

xlim=c(0,100),...)

Arguments

Value

plots not finite and missing values as a bar plot for each feature d and returns with invisible the amount of missing values as a vector. Works even with character variables, but WhichDefineMissing cannot be changed at the current version. Please make a suggestion on GitHub how to improve this.

Note

Does not work with the tibble format, in such a case please call as.data.frame(as.matrix(Data))

Author(s)

Michael Thrun

Examples

data("ITS")
data("MTY")

PlotMissingvalues(cbind(ITS,MTY),Names=c('ITS','MTY'))

Product-Ratio Plot

Description

The product-ratio plot as defined in [Tukey, 1977, p. 594].

Usage

PlotProductratio(X, Y, na.rm = FALSE, 

main='Product Ratio Analysis',xlab = "Log of Ratio",ylab = "Root of Product", ...)

Arguments

Details

In the case where there are many instances of very small values, but a small number of very large ones, this plot is usefull [Tukey, 1977, p. 615].

Value

matrix[1:n,2] with sqrt(x*y) and log(x/y) as the two columns

Author(s)

Michael Thrun

References

[Tukey, 1977] Tukey, J. W.: Exploratory data analysis, United States Addison-Wesley Publishing Company, ISBN: 0-201-07616-0, 1977.

Examples

#Beware: The data does no fit ne requirements for this approach
data('ITS')
data(MTY)
PlotProductratio(ITS,MTY)

P-Matrix colors

Description

Defines the default color sequence for plots made with PDEscatter

Usage

data("PmatrixColormap")

Format

Returns the vectors for a (heat) colormap.

QQplot with a Linear Fit

Description

Qantile-quantile plot with a linear fit

Usage

QQplot(X,Y,Type=8,NoQuantiles=10000,xlab, ylab,col="red",main='',
lwd=3,pch=20,subplot=FALSE,...)

Arguments

Details

Output is the evaluation of a linear (regression) fit of lm called 'line' and a quantile quantile plot (QQplot). Per default 10.000 quantiles are chosen, but in the case of very large data vectors one can reduce the quantiles for faster computation. The 100 percentiles used for the regression line are of darker blue than the quantiles chosen by the user.

Value

List with

Author(s)

Michael Thrun

References

Michael, J. R.: The stabilized probability plot, Biometrika, Vol. 70(1), pp. 11-17, 1983.

Examples

data(MTY)
NormalDistribution=rnorm(50000)
QQplot(NormalDistribution,MTY)

ROC plot

Description

Receiver operating characteristic curve

Usage

ROC(Data, Cls, Names, Colors)

Arguments

Value

Author(s)

Quirin Stier

Examples

Data = runif(1000,0,1)
Cls  = sample(c(0,1), 1000, replace = TRUE)
ROC(Data, Cls)

Transforms the Robust Normalization back

Description

Transforms the Robust Normalization back if Capped=FALSE

Usage

RobustNorm_BackTrafo(TransformedData,

MinX,Denom,Center=0)

Arguments

Details

For details see RobustNormalization

Value

[1:n,1:d] Data matrix

Author(s)

Michael Thrun

See Also

RobustNormalization

Examples

data(Lsun3D)
Data = Lsun3D$Data
TransList = RobustNormalization(Data, Centered = TRUE, WithBackTransformation = TRUE)

Lsun3DData = RobustNorm_BackTrafo(TransList$TransformedData,
                                 TransList$MinX,
                                 TransList$Denom,
                                 TransList$Center)

sum(Lsun3DData - Data) #<e-15

RobustNormalization

Description

RobustNormalization as described in [Milligan/Cooper, 1988].

Usage

RobustNormalization(Data,Centered=FALSE,Capped=FALSE,

na.rm=TRUE,WithBackTransformation=FALSE,

pmin=0.01,pmax=0.99) 

Arguments

Details

Normalizes features either between -1 to 1 (Centered=TRUE) or 0-1 (Centered=TRUE) without changing the distribution of a feature itself. For a more precise description please read [Thrun, 2018, p.17].

"[The] scaling of the inputs determines the effective scaling of the weights in the last layer of a MLP with BP neural netowrk, it can have a large effect on the quality of the final solution. At the outset it is best to standardize all inputs to have mean zero and standard deviation 1 [(or at least the range under 1)]. This ensures all inputs are treated equally in the regularization prozess, and allows to choose a meaningful range for the random starting weights."[Friedman et al., 2012]

Value

if WithBackTransformation=FALSE: TransformedData[1:n,1:d] i.e., normalized data matrix of n cases and d features

if WithBackTransformation=TRUE: List with

Author(s)

Michael Thrun

References

[Milligan/Cooper, 1988] Milligan, G. W., & Cooper, M. C.: A study of standardization of variables in cluster analysis, Journal of Classification, Vol. 5(2), pp. 181-204. 1988.

[Friedman et al., 2012] Friedman, J., Hastie, T., & Tibshirani, R.: The Elements of Statistical Learning, (Second ed. Vol. 1), Springer series in statistics New York, NY, USA:, ISBN, 2012.

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

See Also

RobustNorm_BackTrafo

Examples

Scaled = RobustNormalization(rnorm(1000, 2, 100), Capped = TRUE)
hist(Scaled)

m = cbind(c(1, 2, 3), c(2, 6, 4))
List = RobustNormalization(m, FALSE, FALSE, FALSE, TRUE)
TransformedData = List$TransformedData

mback = RobustNorm_BackTrafo(TransformedData, List$MinX, List$Denom, List$Center)

sum(m - mback)

Shepard PDE scatter

Description

Draws ein Shepard Diagram (scatterplot of distances) with an two-dimensional PDE density estimation .

Usage

ShepardDensityScatter(InputDists, OutputDists, Plotter= "native", Type = "DDCAL",
DensityEstimation="SDH", Marginals = FALSE, xlab='Input Distances',
ylab='Output Distances',main='ProjectionMethod', sampleSize=500000)

Arguments

Details

Introduced and described in [Thrun, 2018, p. 63] with examples in [Thrun, 2018, p. 71-72]

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20540-9, Heidelberg, 2018.

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
InputDist=as.matrix(dist(Data))
res = stats::cmdscale(d = InputDist, k = 2, eig = TRUE, 
        add = FALSE, x.ret = FALSE)

ProjectedPoints = as.matrix(res$points)
ShepardDensityScatter(InputDist,as.matrix(dist(ProjectedPoints)),main = 'MDS')
ShepardDensityScatter(InputDist[1:100,1:100],

as.matrix(dist(ProjectedPoints))[1:100,1:100],main = 'MDS')

Draws a Shepard Diagram

Description

This function plots a Shepard diagram which is a scatter plot of InputDist and OutputDist

Usage

Sheparddiagram(InputDists, OutputDists, xlab = "Input Distances",

                 ylab= "Output Distances", fancy = F,

				 main = "ProjectionMethod", gPlot = ggplot())

Arguments

Value

ggplot2 object containing the plot.

Author(s)

Michael Thrun

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
InputDist=as.matrix(dist(Data))
res = stats::cmdscale(d = InputDist, k = 2, eig = TRUE, 
        add = FALSE, x.ret = FALSE)
ProjectedPoints = as.matrix(res$points)


Sheparddiagram(InputDist,as.matrix(dist(ProjectedPoints)),main = 'MDS')

Signed Log

Description

Computes the Signed Log if Data

Usage

SignedLog(Data,Base="Ten")

Arguments

Details

A neat transformation for data, it it has a better representation on the log scale.

Value

Transformed Data

Note

Number Selections for Base for 2,10, "Two" or "Ten" add 1 to every datapoint as defined in the lectures.

Author(s)

Michael Thrun

References

Prof. Dr. habil. A. Ultsch, Lectures in Knowledge Discovery, 2014.

See Also

log

Examples

# sampling is done
# because otherwise the example takes too long
# in the CRAN check
data('ITS')
ind=sample(length(ITS),1000)

MDplot(SignedLog(cbind(ITS[ind],MTY[ind])*(-1),Base = "Ten"))

Silhouette plot of classified data.

Description

Silhouette plot of cluster silhouettes for the n-by-d data matrix Data or distance matrix where the clusters are defined in the vector Cls.

Usage

Silhouetteplot(DataOrDistances, Cls, method='euclidean',

PlotIt=TRUE,...)

Arguments

Details

"The Silhouette plot is a common unsupervised index for visual evaluation of a clustering [L. R. Kaufman/Rousseeuw, 2005] [introduced in [Rousseeuw, 1987]]. A reasonable clustering is characterized by a silhouette width of greater than 0.5, and an average width below 0.2 should be interpreted as indicating a lack of any substantial cluster structure [Everitt et al., 2001, p. 105]. However, it is evident that silhouette scores assume clusters that are spherical or Gaussian in shape [Herrmann, 2011, pp. 91-92]" [Thrun, 2018, p. 29].

Value

Author(s)

Onno Hansen-Goos, Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.

[Rousseeuw, 1987] Rousseeuw, Peter J.: Silhouettes: a Graphical Aid to the Interpretation and Validation of Cluster Analysis, Computational and Applied Mathematics, 20, p.53-65, 1987.

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
#clear cluster structure
plot(Data[,1:2],col=Cls)
#However, the silhouette plot does not indicate a very good clustering in cluster 1 and 2
Silhouetteplot(Data,Cls = Cls,main='Silhouetteplot')

Slope Chart

Description

ABC analysis improved slope chart

Usage

Slopechart(FirstDatavector,

SecondDatavector,

Names,

Labels,

MaxNumberOfSlices,

TopLabels=c('FirstDatavector','SecondDatavector'),

main='Comparision of Descending Frequency')

Arguments

Details

still experimental.

Value

silent output by calling invisible of a list with

Author(s)

Michael Thrun

References

[Gohil, 2015] Gohil, Atmajitsinh. R data Visualization cookbook. Packt Publishing Ltd, 2015.

See Also

Piechart, Fanplot

Examples

## will follow

Pareto Density Estimation

Description

Density Estimation for ggplot with a clear model behind it.

Format

The format is: Classes 'StatPDEdensity', 'Stat', 'ggproto' <ggproto object: Class StatPDEdensity, Stat> aesthetics: function compute_group: function compute_layer: function compute_panel: function default_aes: uneval extra_params: na.rm finish_layer: function non_missing_aes: parameters: function required_aes: x y retransform: TRUE setup_data: function setup_params: function super: <ggproto object: Class Stat>

Details

PDE was published in [Ultsch, 2005], short explanation in [Thrun, Ultsch 2018] and the PDE optimized violin plot was published in [Thrun et al., 2018].

References

[Ultsch,2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Thrun, Ultsch 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Thrun et al, 2018] Thrun, M. C., Pape, F., & Ultsch, A. : Benchmarking Cluster Analysis Methods using PDE-Optimized Violin Plots, Proc. European Conference on Data Analysis (ECDA), accepted, Paderborn, Germany, 2018.

Standard Deviation Robust

Description

Robust empirical estimation for standard deviation.NaNs are ignored.

Usage

Stdrobust(x, lowInnerPercentile=25,na.rm=TRUE)

Arguments

Value

Author(s)

Zornitsa Manolova

See Also

sd quantile

plots a world map by country codes

Description

The Worldmap function is used in [Thrun, 2018].

Usage

Worldmap(CountryCodes, Cls, Colors, 

MissingCountryColor = grDevices::gray(0.8), ...)

Arguments

Value

List of

Author(s)

Michae Thrun

References

Used in

[Thrun, 2018] Thrun, M. C. : Cluster Analysis of the World Gross-Domestic Product Based on Emergent Self-Organization of a Swarm, 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Foundation of the Cracow University of Economics, Zakopane, Poland, accepted, 2018.

Source for shapefile: - package maptoops and

Originally 'mappinghacks.com/data/TM_WORLD_BORDERS_SIMPL-0.2.zip', now available from https://github.com/nasa/World-Wind-Java/tree/master/WorldWind/testData/shapefiles

Examples

# data from [Thrun, 2018]
Cls=c(1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 
1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 
2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 2L, 2L, 2L, 1L, 
2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 
2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 
2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L
)
Codes=c("AFG", "AGO", "ALB", "ARG", "ATG", "AUS", "AUT", "BDI", "BEL", 
"BEN", "BFA", "BGD", "BGR", "BHR", "BHS", "BLZ", "BMU", "BOL", 
"BRA", "BRB", "BRN", "BTN", "BWA", "CAF", "CAN", "CH2", "CHE", 
"CHL", "CHN", "CIV", "CMR", "COG", "COL", "COM", "CPV", "CRI", 
"CUB", "CYP", "DJI", "DMA", "DNK", "DOM", "DZA", "ECU", "EGY", 
"ESP", "ETH", "FIN", "FJI", "FRA", "FSM", "GAB", "GBR", "GER", 
"GHA", "GIN", "GMB", "GNB", "GNQ", "GRC", "GRD", "GTM", "GUY", 
"HKG", "HND", "HTI", "HUN", "IDN", "IND", "IRL", "IRN", "IRQ", 
"ISL", "ISR", "ITA", "JAM", "JOR", "JPN", "KEN", "KHM", "KIR", 
"KNA", "KOR", "LAO", "LBN", "LBR", "LCA", "LKA", "LSO", "LUX", 
"MAC", "MAR", "MDG", "MDV", "MEX", "MHL", "MLI", "MLT", "MNG", 
"MOZ", "MRT", "MUS", "MWI", "MYS", "NAM", "NER", "NGA", "NIC", 
"NLD", "NOR", "NPL", "NZL", "OMN", "PAK", "PAN", "PER", "PHL", 
"PLW", "PNG", "POL", "PRI", "PRT", "PRY", "ROM", "RWA", "SDN", 
"SEN", "SGP", "SLB", "SLE", "SLV", "SOM", "STP", "SUR", "SWE", 
"SWZ", "SYC", "SYR", "TCD", "TGO", "THA", "TON", "TTO", "TUN", 
"TUR", "TWN", "TZA", "UGA", "URY", "USA", "VCT", "VEN", "VNM", 
"VUT", "WSM", "ZAF", "ZAR", "ZMB", "ZWE")
Worldmap(Codes,Cls)

A categorical Feature.

Description

Character vector of length 391029 with five different labels.

Usage

data("categoricalVariable")

Examples

data(categoricalVariable)
unique(categoricalVariable)

estimateDensity2D

Description

Estimates densities for two-dimensional data with the given estimation type

Usage

estimateDensity2D(X, Y, DensityEstimation = "SDH",

SampleSize, na.rm = FALSE, NoBinsOrPareto = NULL)

Arguments

Details

Each two-dimensional data point is defined by its corresponding X and Y value.

Value

List V with

Author(s)

Luca Brinkman and Michael Thrun

References

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, In Baier, D. & Werrnecke, K. D. (Eds.), Innovations in classification, data science, and information systems, (Vol. 27, pp. 91-100), Berlin, Germany, Springer, 2005.

[Eilers/Goeman, 2004] Eilers, P. H., & Goeman, J. J.: Enhancing scatterplots with smoothed densities, Bioinformatics, Vol. 20(5), pp. 623-628. 2004

Examples

X=runif(100)
Y=rnorm(100)
#V=estimateDensity2D(X,Y)

Calculate Pareto density estimation for ggplot2 plots

Description

This function enables to replace the default density estimation for ggplot2 plots with the Pareto density estimation [Ultsch, 2005]. It is used for the PDE-Optimized violin plot published in [Thrun et al, 2018].

Usage

stat_pde_density(mapping = NULL, data = NULL,
geom = "violin", bounds = bounds, 
position = "dodge", ..., 
                    trim = TRUE, scale =
                    "area", na.rm = FALSE, 
                    show.legend = NA, 
                    inherit.aes = TRUE)

Arguments

Details

Pareto Density Estimation (PDE) is a method for the estimation of probability density functions using hyperspheres. The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. It is shown, that Pareto Density is the best estimate for clusters of Gaussian structure. The method is shown to be robust when cluster overlap and when the variances differ across clusters.

Author(s)

Felix Pape

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Thrun et al, 2018] Thrun, M. C., Pape, F., & Ultsch, A.: Benchmarking Cluster Analysis Methods using PDE-Optimized Violin Plots, Proc. European Conference on Data Analysis (ECDA), accepted, Paderborn, Germany, 2018.

See Also

stat_density

Examples

miris <- reshape2::melt(iris)

ggplot2::ggplot(miris, 

mapping = ggplot2::aes(y = .data$value, x = .data$variable)) +

ggplot2::geom_violin(stat = "PDEdensity")

world_country_polygons

Description

world_country_polygons shapefile

Usage

data("world_country_polygons")

Format

world_country_polygons stores data objects using classes defined in the sp package or inheriting from those classes updated to sp Y= 1.4 and rgdal >= 1.5.

Since DataVisualization Version 1.2.1 it stores now a CRS objects with a comment containing an WKT2 CRS representation, thanks to a suggestion of Roger Bivand.

Details

Note that the rebuilt CRS object contains a revised version of the input Proj4 string as well as the WKT2 string, and may be used with both older and newer versions of sp. See maptools package for further details. Also note that since sp >= 2.0 maptools and rgdal were deprecated without change to the workflow. See terra for an alternative to maptools.

Author(s)

Hamza Tayyab, Michael Thrun

Source

maptools package

References

maptools package

Examples

data(world_country_polygons)
str(world_country_polygons)

Plotting for 3 dimensional data

Description

Plots z above xy plane as 3D mountain or 2D contourlines

Usage

zplot(x, y, z, DrawTopView = TRUE, NrOfContourLines = 20,

                 TwoDplotter = "native", xlim, ylim)

Arguments

Value

If the plotting backend does support it, this will return a handle for the generated plot.

Author(s)

Felix pape

Examples

## Not run: 
data("Lsun3D")
Data=Lsun3D$Data
if(exists("zplot", where = asNamespace("DataVisualizations")))
      DataVisualizations::zplot(Data[,1],Data[,2],Data[,3])

## End(Not run)