, Felix Pape [aut,
rev], Luca Brinkman [aut], Quirin Stier [aut]
| Title: | Density Estimation and Visualization of 2D Scatter Plots |
|---|---|
| Description: | The user has the option to utilize the two-dimensional density estimation techniques called smoothed density published by Eilers and Goeman (2004) <doi:10.1093/bioinformatics/btg454>, and pareto density which was evaluated for univariate data by Thrun, Gehlert and Ultsch, 2020 <doi:10.1371/journal.pone.0238835>. Moreover, it provides visualizations of the density estimation in the form of two-dimensional scatter plots in which the points are color-coded based on increasing density. Colors are defined by the one-dimensional clustering technique called 1D distribution cluster algorithm (DDCAL) published by Lux and Rinderle-Ma (2023) <doi:10.1007/s00357-022-09428-6>. |
| Authors: | Michael Thrun [aut, cre, cph]
, Felix Pape [aut,
rev], Luca Brinkman [aut], Quirin Stier [aut]
|
| Maintainer: | Michael Thrun <[email protected]> |
| License: | GPL-3 |
| Version: | 0.0.4 |
| Built: | 2024-11-02 06:39:50 UTC |
| Source: | CRAN |
The user has the option to utilize the two-dimensional density estimation techniques called smoothed density published by Eilers and Goeman (2004) <doi:10.1093/bioinformatics/btg454>, and pareto density which was evaluated for univariate data by Thrun, Gehlert and Ultsch, 2020 <doi:10.1371/journal.pone.0238835>. Moreover, it provides visualizations of the density estimation in the form of two-dimensional scatter plots in which the points are color-coded based on increasing density. Colors are defined by the one-dimensional clustering technique called 1D distribution cluster algorithm (DDCAL) published by Lux and Rinderle-Ma (2023) <doi:10.1007/s00357-022-09428-6>.
The DESCRIPTION file:
| Package: | ScatterDensity |
| Type: | Package |
| Title: | Density Estimation and Visualization of 2D Scatter Plots |
| Version: | 0.0.4 |
| Date: | 2023-10-09 |
| Authors@R: | c(person("Michael", "Thrun", email= "[email protected]",role=c("aut","cre","cph"), comment = c(ORCID = "0000-0001-9542-5543")),person("Felix", "Pape",role=c("aut","rev")),person("Luca","Brinkman",role=c("aut")),person("Quirin", "Stier",role=c("aut"), comment = c(ORCID = "0000-0002-7896-4737"))) |
| Maintainer: | Michael Thrun <[email protected]> |
| Description: | The user has the option to utilize the two-dimensional density estimation techniques called smoothed density published by Eilers and Goeman (2004) <doi:10.1093/bioinformatics/btg454>, and pareto density which was evaluated for univariate data by Thrun, Gehlert and Ultsch, 2020 <doi:10.1371/journal.pone.0238835>. Moreover, it provides visualizations of the density estimation in the form of two-dimensional scatter plots in which the points are color-coded based on increasing density. Colors are defined by the one-dimensional clustering technique called 1D distribution cluster algorithm (DDCAL) published by Lux and Rinderle-Ma (2023) <doi:10.1007/s00357-022-09428-6>. |
| LazyLoad: | yes |
| Imports: | Rcpp, pracma |
| Suggests: | DataVisualizations, ggplot2, ggExtra, plotly, FCPS, parallelDist, secr, ClusterR |
| Depends: | methods, R (>= 2.10) |
| LinkingTo: | Rcpp, RcppArmadillo |
| NeedsCompilation: | yes |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| URL: | https://www.deepbionics.org/ |
| BugReports: | https://github.com/Mthrun/ScatterDensity/issues |
| Packaged: | 2023-10-09 14:19:26 UTC; MCT |
| Author: | Michael Thrun [aut, cre, cph] (<https://orcid.org/0000-0001-9542-5543>), Felix Pape [aut, rev], Luca Brinkman [aut], Quirin Stier [aut] (<https://orcid.org/0000-0002-7896-4737>) |
| Repository: | CRAN |
| Date/Publication: | 2023-10-09 14:40:03 UTC |
Index of help topics:
DDCAL Density Distribution Cluster Algorithm of [Lux
and Rinderle-Ma, 2023].
DensityScatter.DDCAL Scatter density plot [Brinkmann et al., 2023]
PDEscatter Scatter Density Plot
PointsInPolygon PointsInPolygon
PolygonGate PolygonGate
ScatterDensity-package
Density Estimation and Visualization of 2D
Scatter Plots
SmoothedDensitiesXY Smoothed Densities X with Y
inPSphere2D 2D data points in Pareto Sphere
Michael Thrun [aut, cre, cph] (<https://orcid.org/0000-0001-9542-5543>), Felix Pape [aut, rev], Luca Brinkman [aut], Quirin Stier [aut] (<https://orcid.org/0000-0002-7896-4737>)
Maintainer: Michael Thrun <[email protected]>
#Todo#Todo
DDCAL is a clustering-algorithm for one-dimensional data, which heuristically finds clusters to evenly distribute the data points in low variance clusters.
DDCAL(data, nClusters, minBoundary = 0.1, maxBoundary = 0.45, numSimulations = 20, csTolerance = 0.45, csToleranceIncrease = 0.5)DDCAL(data, nClusters, minBoundary = 0.1, maxBoundary = 0.45, numSimulations = 20, csTolerance = 0.45, csToleranceIncrease = 0.5)
data |
[1:n] Numeric vector, with the data values |
nClusters |
Scalar, number of clusters to be found |
minBoundary |
Scalar, in the range (0,1), gives the lower boundary (in percent), for the simulation. Default is 0.1 |
maxBoundary |
Scalar, in the range (0,1), gives the upper boundary (in percent), for the simulation. Default is 0.45 |
numSimulations |
Scalar, number of simulations/iterations of the algorithm |
csTolerance |
Scalar, in the range (0,1). Gives cluster size tolerance factor. The necessary cluster size is defined by (dataSize/nClusters - dataSize/nClusters * csTolerance). Default is 0.45 |
csToleranceIncrease |
Scalar, in the range (0,1), gives the procentual increase of the csTolerance-factor, if some clusters did not reach the necessary size. Default is 0.5 |
DDCAL creates a evenly spaced division of the min-max-normalized data from minBoundary to maxBoundary. Those divisions will be used as boundaries. The first initial clusters will be the data from min(data) to minBoundary and maxBoundary to max(data). The clusters will be extended to neighboring points, as long as the standard deviations of the clusters will be reduced. A potential clusters will be used, if they have the necessary size, given as (dataSize/nClusters - dataSize/nClusters * csTolerance). If both clusters can be used, the left cluster (which is the cluster from min(data) to minBoundary or above) is preferred. If no clusters can be found with the necessary size, then the csTolerance-factor and with it the necessary cluster size will be lowered. If a clusters is used, the next boundaries are found, which are not in the already existing clusters and the procedure is repeated with the not already clustered data, until all points are assigned to clusters.
If a matrix is given as input data, the first column of the matrix will be used as data for the clustering
Non-finite values will not be clustered, but instead will get the cluster label NaN.
The algorithm is not garantueed to produce the given number of clusters, given in nClusters. The found number of clusters can be lower, depending on the data and input parameters.
labels |
[1:n] Numeric vector, containing the labels for the input data points |
Luca Brinkmann
[Lux and Rinderle-Ma, 2023] Lux, M., Rinderle-Ma, S.: DDCAL: Evenly Distributing Data into Low Variance Clusters Based on Iterative Feature Scaling; Springer Journal of Classification, Vol. 40, pp. 106-144, DOI: doi:10.1007/s00357-022-09428-6, 2023.
# Load data if(requireNamespace("FCPS")){ data(EngyTime, package = "FCPS") engyTimeData = EngyTime$Data c1 = engyTimeData[,1] c2 = engyTimeData[,2] }else{ c1 = rnorm(n=4000) c2 = rnorm(n=4000,1,2) } # Calculate Densities densities = SmoothedDensitiesXY(c1,c2)$Densities # Use DDCAL to cluster the densities labels = DDCAL(densities, 9) # Plot Densities according to labels my_colors = c("#000066", "#3333CC", "#9999FF", "#00FFFF", "#66FF33", "#FFFF00", "#FF9900", "#FF0000", "#990000") labels = as.factor(labels) df = data.frame(c1, c2, labels) if(requireNamespace("ggplot2")){ ggplot2::ggplot(df, ggplot2::aes(c1, c2, color = labels)) + ggplot2::geom_point() + ggplot2::scale_color_manual(values = my_colors) }# Load data if(requireNamespace("FCPS")){ data(EngyTime, package = "FCPS") engyTimeData = EngyTime$Data c1 = engyTimeData[,1] c2 = engyTimeData[,2] }else{ c1 = rnorm(n=4000) c2 = rnorm(n=4000,1,2) } # Calculate Densities densities = SmoothedDensitiesXY(c1,c2)$Densities # Use DDCAL to cluster the densities labels = DDCAL(densities, 9) # Plot Densities according to labels my_colors = c("#000066", "#3333CC", "#9999FF", "#00FFFF", "#66FF33", "#FFFF00", "#FF9900", "#FF0000", "#990000") labels = as.factor(labels) df = data.frame(c1, c2, labels) if(requireNamespace("ggplot2")){ ggplot2::ggplot(df, ggplot2::aes(c1, c2, color = labels)) + ggplot2::geom_point() + ggplot2::scale_color_manual(values = my_colors) }
Density estimation (PDE) [Ultsch, 2005] or "SDH" [Eilers/Goeman, 2004] used for a scatter density plot, with clustering of densities with DDCAL [Lux/Rinderle-Ma, 2023] proposed by [Brinkmann et al., 2023].
DensityScatter.DDCAL(X, Y, nClusters = 12, Plotter = "native", SDHorPDE = TRUE, PDEsample = 5000, Marginals = FALSE, na.rm=TRUE, pch = 10, Size = 1, xlab="x", ylab="y", main = "",lwd = 2, xlim=NULL,ylim=NULL,Polygon,BW = TRUE,Silent = FALSE, ...)DensityScatter.DDCAL(X, Y, nClusters = 12, Plotter = "native", SDHorPDE = TRUE, PDEsample = 5000, Marginals = FALSE, na.rm=TRUE, pch = 10, Size = 1, xlab="x", ylab="y", main = "",lwd = 2, xlim=NULL,ylim=NULL,Polygon,BW = TRUE,Silent = FALSE, ...)
X |
Numeric vector [1:n], first feature (for x axis values) |
Y |
Numeric vector [1:n], second feature (for y axis values) |
nClusters |
Integer defining the number of clusters (colors) used for finding a hard color transition. |
Plotter |
(Optional) String, name of the plotting backend to use. Possible values are: " |
SDHorPDE |
(Optional) Boolean, if TRUE SDH is used to calculate density, if FALSE PDE is used |
PDEsample |
(Optional) Scalar, Sample size for PDE and/or for ggplot2 plotting. Default is 5000 |
Marginals |
(Optional) Boolean, if TRUE the marginal distributions of X and Y will be plotted together with the 2D density of X and Y. Default is FALSE |
na.rm |
(Optional) Boolean, if TRUE non finite values will be removed |
pch |
(Optional) Scalar or character. Indicates the shape of data points, see |
Size |
(Optional) Scalar, size of data points in plot, default is 1 |
xlab |
String, title of the x axis. Default: "X", see |
ylab |
String, title of the y axis. Default: "Y", see |
main |
(Optional) Character, title of the plot. [1:2] |
lwd |
(Optional) Scalar, thickness of the lines used for the marginal distributions (only needed if |
xlim |
(Optional) numerical vector, min and max of x values to be plottet |
ylim |
(Optional) numerical vector, min and max of y values to be plottet |
Polygon |
(Optional) [1:p,1:2] numeric matrix that defines for x and y coordinates a polygon in magenta |
BW |
(Optional) Boolean, if TRUE ggplot2 will use a white background, if FALSE the typical ggplot2 backgournd is used. Not needed if " |
Silent |
(Optional) Boolean, if TRUE no messages will be printed, default is FALSE |
... |
Further plot arguments |
The DensityScatter.DDCAL function generates the density of the xy data as a z coordinate. Afterwards xyz will be plotted as a contour plot. It assumens that the cases of x and y are mapped to each other meaning that a cbind(x,y) operation is allowed.
The colors for the densities in the contour plot are calculated with DDCAL, which produces clusters to evenly distribute the densities in low variance clusters.
In the case of "native" as Plotter, the handle returns NULL because the basic R functon plot() is used
If "ggplot2" as Plotter is used, the ggobj is returned
Support for plotly will be implemented later
Luca Brinkmann, Michael Thrun
[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.
# Create two bimodial distributions x1=rnorm(n = 7500,mean = 0,sd = 1) y1=rnorm(n = 7500,mean = 0,sd = 1) x2=rnorm(n = 7500,mean = 2.5,sd = 1) y2=rnorm(n = 7500,mean = 2.5,sd = 1) x=c(x1,x2) y=c(y1,y2) DensityScatter.DDCAL(x, y, Marginals = TRUE)# Create two bimodial distributions x1=rnorm(n = 7500,mean = 0,sd = 1) y1=rnorm(n = 7500,mean = 0,sd = 1) x2=rnorm(n = 7500,mean = 2.5,sd = 1) y2=rnorm(n = 7500,mean = 2.5,sd = 1) x=c(x1,x2) y=c(y1,y2) DensityScatter.DDCAL(x, y, Marginals = TRUE)
This function determines the 2D data points inside a ParetoSphere with ParetoRadius.
inPSphere2D(data, paretoRadius=NULL)inPSphere2D(data, paretoRadius=NULL)
data |
numeric matrix of data. |
paretoRadius |
numeric value. radius of P-spheres. If not given, calculate by the function 'paretoRad' |
numeric vector with the number of data points inside a P-sphere with ParetoRadius.
Felix Pape
Concept of Pareto density estimation (PDE) proposed for univsariate data by [Ultsch, 2005] and comparet to varius density estimation techniques by [Thrun et al., 2020] for univariate data is here applied for a scatter density plot. It was also applied in [Thrun and Ultsch, 2018] to bivariate data, but is not yet compared to other techniques.
PDEscatter(x,y,SampleSize, na.rm=FALSE,PlotIt=TRUE,ParetoRadius,sampleParetoRadius, NrOfContourLines=20,Plotter='native', DrawTopView = TRUE, xlab="X", ylab="Y", main="PDEscatter", xlim, ylim, Legendlab_ggplot="value")PDEscatter(x,y,SampleSize, na.rm=FALSE,PlotIt=TRUE,ParetoRadius,sampleParetoRadius, NrOfContourLines=20,Plotter='native', DrawTopView = TRUE, xlab="X", ylab="Y", main="PDEscatter", xlim, ylim, Legendlab_ggplot="value")
x |
Numeric vector [1:n], first feature (for x axis values) |
y |
Numeric vector [1:n], second feature (for y axis values) |
SampleSize |
Numeric m, positiv scalar, maximum size of the sample used for calculation. High values increase runtime significantly. The default is that no sample is drawn |
na.rm |
Function may not work with non finite values. If these cases should be automatically removed, set parameter TRUE |
ParetoRadius |
Numeric, positiv scalar, the Pareto Radius. If omitted (or 0), calculate by paretoRad. |
sampleParetoRadius |
Numeric, positiv scalar, maximum size of the sample used for estimation of "kernel", should be significantly lower than SampleSize because requires distance computations which is memory expensive |
PlotIt |
|
NrOfContourLines |
Numeric, number of contour lines to be drawn. 20 by default. |
Plotter |
String, name of the plotting backend to use. Possible values are: " |
DrawTopView |
Boolean, True means contur is drawn, otherwise a 3D plot is drawn. Default: TRUE |
xlab |
String, title of the x axis. Default: "X", see |
ylab |
String, title of the y axis. Default: "Y", see |
main |
string, the same as "main" in |
xlim |
see |
ylim |
see |
Legendlab_ggplot |
String, in case of |
The PDEscatter 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 PDE 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.
The method was succesfully used in [Thrun, 2018; Thrun/Ultsch 2018].
PlotIt=FALSE is usefull if one likes to perform adjustements like axis scaling prior to plotting with ggplot2 or plotly. In the case of "native"" the handle returns NULL because the basic R functon plot() is used
List of:
X |
Numeric vector [1:m],m<=n, first feature used in the plot or the kernels used |
Y |
Numeric vector [1:m],m<=n, second feature used in the plot or the kernels used |
Densities |
Numeric vector [1:m],m<=n, Number of points within the ParetoRadius of each point, i.e. density information |
Matrix3D |
1:n,1:3] marix of x,y and density information |
ParetoRadius |
ParetoRadius used for PDEscatter |
Handle |
Handle of the plot object. Information-string if native R plot is used. |
MT contributed with several adjustments
Felix Pape
[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.
[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 doi:10.1371/journal.pone.0238835, 2020.
#taken from [Thrun/Ultsch, 2018] if(requireNamespace("DataVisualizations")){ data("ITS",package = "DataVisualizations") data("MTY",package = "DataVisualizations") Inds=which(ITS<900&MTY<8000) plot(ITS[Inds],MTY[Inds],main='Bimodality is not visible in normal scatter plot') PDEscatter(ITS[Inds],MTY[Inds],xlab = 'ITS in EUR', ylab ='MTY in EUR' ,main='Pareto Density Estimation indicates Bimodality' ) }#taken from [Thrun/Ultsch, 2018] if(requireNamespace("DataVisualizations")){ data("ITS",package = "DataVisualizations") data("MTY",package = "DataVisualizations") Inds=which(ITS<900&MTY<8000) plot(ITS[Inds],MTY[Inds],main='Bimodality is not visible in normal scatter plot') PDEscatter(ITS[Inds],MTY[Inds],xlab = 'ITS in EUR', ylab ='MTY in EUR' ,main='Pareto Density Estimation indicates Bimodality' ) }
Defines a Cls based on points in a given polygon.
PointsInPolygon(Points, Polygon, PlotIt = FALSE, ...)PointsInPolygon(Points, Polygon, PlotIt = FALSE, ...)
Points |
[1:n,1:2] xy cartesian coordinates of a projection |
Polygon |
Numerical matrix of 2 columns defining a closed polygon |
PlotIt |
TRUE: Plots marked points |
... |
Further Plotting Arguments,xlab etc used in |
We assume that polygon is closed, i.e., that the last point connects to the fist point
Numerical classification vector Cls with 1 = outside polygon and 2 = inside polygon
Michael Thrun
XY=cbind(runif(80,min = -1,max = 1),rnorm(80)) #closed polygon polymat <- cbind(x = c(0,1,1,0), y = c(0,0,1,1)) #takes sometimes more than 5 sec Cls=PointsInPolygon(XY,polymat,PlotIt = TRUE)XY=cbind(runif(80,min = -1,max = 1),rnorm(80)) #closed polygon polymat <- cbind(x = c(0,1,1,0), y = c(0,0,1,1)) #takes sometimes more than 5 sec Cls=PointsInPolygon(XY,polymat,PlotIt = TRUE)
A specific Gate defined by xy coordinates that result in a closed polygon is applied to the flowcytometry data.
PolygonGate(Data, Polygon, GateVars, PlotIt = FALSE, PlotSampleSize = 1000)PolygonGate(Data, Polygon, GateVars, PlotIt = FALSE, PlotSampleSize = 1000)
Data |
numerical matrix n x d |
Polygon |
numerical marix of two columns defining the coordiantes of the polygon. polygon assumed to be closed, i.e.,last coordinate connects to first coordinate. |
GateVars |
vector, either column index in Data of X and Y coordinates of gate or its variable names as string |
PlotIt |
if TRUE: plots a sample of data in the two selected variables and marks point inside the gate as yellow and outside as magenta |
PlotSampleSize |
size pof the plottet sample |
Gates are alwaxs two dimensional, i.e., require two filters, although all dimensions of data are filted by the gates. Only high-dimensional points inside the polygon (gate) are given back
list of
DataInGate |
m x d numerical matrix with m<=n of data points inside the gate |
InGateInd |
index of length m for the datapoints in original matrix |
if GateVars is not found a text is given back which will state this issue
Michael Thrun
Data <- matrix(runif(1000), ncol = 10) colnames(Data)=paste0("GateVar",1:ncol(Data)) poly <- cbind(x = c(0.2,0.5,0.8), y = c(0.2,0.8,0.2)) #set PlotIt TRUE for understanding the example #Select index V=PolygonGate(Data,poly,c(5,8),PlotIt=FALSE,100) #select var name V=PolygonGate(Data,poly,c("GateVar5","GateVar8"),PlotIt=FALSE,100)Data <- matrix(runif(1000), ncol = 10) colnames(Data)=paste0("GateVar",1:ncol(Data)) poly <- cbind(x = c(0.2,0.5,0.8), y = c(0.2,0.8,0.2)) #set PlotIt TRUE for understanding the example #Select index V=PolygonGate(Data,poly,c(5,8),PlotIt=FALSE,100) #select var name V=PolygonGate(Data,poly,c("GateVar5","GateVar8"),PlotIt=FALSE,100)
Density is the smothed histogram density at [X,Y] of [Eilers/Goeman, 2004]
SmoothedDensitiesXY(X, Y, nbins, lambda, Xkernels, Ykernels, PlotIt = FALSE)SmoothedDensitiesXY(X, Y, nbins, lambda, Xkernels, Ykernels, PlotIt = FALSE)
X |
Numeric vector [1:n], first feature (for x axis values) |
Y |
Numeric vector [1:n], second feature (for y axis values), nbins= nxy => the nr of bins in x and y is nxy nbins = c(nx,ny) => the nr of bins in x is nx and for y is ny |
nbins |
number of bins, nbins =200 (default) |
lambda |
smoothing factor used by the density estimator or c() default: lambda = 20 which roughly means that the smoothing is over 20 bins around a given point. |
Xkernels |
bin kernels in x direction are given |
Ykernels |
bin kernels y direction are given |
PlotIt |
FALSE: no plotting, TRUE: simple plot |
lambda has to chosen by the user and is a sensitive parameter.
List of:
Densities |
numeric vector [1:n] is the smothed density in 3D |
Xkernels |
numeric vector [1:nx], nx defined by |
Ykernels |
numeric vector [1:ny], nx defined by |
hist_F_2D |
matrix [1:nx,1:ny] beeing the smoothed 2D histogram |
ind |
an index such that |
Michael Thrun
[Eilers/Goeman, 2004] Eilers, P. H., & Goeman, J. J.: Enhancing scatterplots with smoothed densities, Bioinformatics, Vol. 20(5), pp. 623-628.DOI: doi:10.1093/bioinformatics/btg454, 2004.
if(requireNamespace("DataVisualizations")){ data("ITS",package = "DataVisualizations") data("MTY",package = "DataVisualizations") Inds=which(ITS<900&MTY<8000) V=SmoothedDensitiesXY(ITS[Inds],MTY[Inds]) }else{ #sample random data ITS=rnorm(1000) MTY=rnorm(1000) V=SmoothedDensitiesXY(ITS,MTY) }if(requireNamespace("DataVisualizations")){ data("ITS",package = "DataVisualizations") data("MTY",package = "DataVisualizations") Inds=which(ITS<900&MTY<8000) V=SmoothedDensitiesXY(ITS[Inds],MTY[Inds]) }else{ #sample random data ITS=rnorm(1000) MTY=rnorm(1000) V=SmoothedDensitiesXY(ITS,MTY) }