= (Data,
XKernel, YKernel,
ContinuousDataPDE,
GridDensity,
Means, Covariances, Weights,
MainAxesAngle,
Colors, Cls,
Camera = ,
AxNames = ("X", "Y"),
Source = "F1", Debug = ){
# DESCRIPTION1
# Compares the continuous density plot of a dataset with the density
# distribution defined by one or more gaussians (GMM; Mean, Cov, Weights).
# The datapoints from the dataset have the density assigned by the GMM
# component with the the highest probability (class assignment must be given
# and is not computed here).
#
# INPUT
# Data[1:n, 1:2] Numeric matrix with n observations and 2
# features.
# XKernel[1:x] Numeric vector defining domain of x axis.
# YKernel[1:x] Numeric vector defining domain of y axis.
# GridDensity[1:x, 1:x] Numeric matrix PDF for a GMM with one or more
# Gaussians on a Grid defined by the vectors XKernel
# and YKernel.
# Means List with l [1:2] numerical vector defining
# the means of the l GMM components.
# Covariances List with l [1:2, 1:2] numerical matrices
# defining the covariance matrices of the l GMM
# components.
# Weights[1:l] Numerical vector with weights for each GMM
# component.
# MainAxesAngle[1:4] Numeric vector with 1st and 2nd main axes
# of a 2D ellipsoid and the respective angles
# measured to the first unit vector c(0,1).
# Colors[1:n] Numerical vector of size n containing the
# colors of each observation.
# Cls[1:n] Numerical vector of size n containing the
# classes of each observation.
# Camera List of attributes concerning the camera
# angle for plotly visualizations.
# ShowScatter Boolean (Default=TRUE). T: Show Data
# Scatter with empirical estimated density.
# F: Do not show nothing.
# ShowMarkers Boolean (Default=TRUE). T: Show main axes
# of the GMM ellipsoid/circle.
# AxNames Character vector with names for each
# dimension ax of 2D plot.
# Source (Default = "F1"). Character indicating plot
# source. Important attribute for plotly in
# shiny in order to keep control of specific
# panels.
# Debug Boolean (Default=FALSE). T: Show developer
# information and warnings in terminal.
# F: Show nothing.
#
# OUTPUT
# plotOut Plotly object containing plot for direct visualization.
#
# DETAILS
# Uses a density estimation (discretized computation on grid) to display
# a continuous density plot on domain defined by XKernel and YKernel of the
# whole empircal data distribution.
# The density of the GMM components is computed via an multivariate gaussian
# formula.
# The datapoints take the density of the GMM components with highest
# probability to take the specific datapoint. This computation must be done
# outside of this routine (give the Cls/Class/Labels as parameter).
# Parameter Camera is important for shiny to let the view fixed during
# continuous updates of the interactive visualization (Shiny App). The Source
# is important to separate between multiple visualizations in the Shiny App.
#
# Author: QMS 15.12.2021
((Data)){
("Parameter Data is missing. Returning.")
()
}{
(!(Data)){
("Parameter Data is not of type matrix. Returning.")
()
} ((Data)[2] != 2){
("Parameter Data does not have exactly two feature columns. Returning.")
()
}
}
((XKernel)){
("Parameter XKernel is missing. Returning.")
()
}{
(!(XKernel)){
("Parameter XKernel is not of type vector. Returning.")
()
}
}
((YKernel)){
("Parameter YKernel is missing. Returning.")
()
}{
(!(YKernel)){
("Parameter YKernel is not of type vector. Returning.")
()
}
}
((XKernel) != (YKernel)){
("Parameter XKernel and YKernel must be vectors of same length. Returning.")
()
}
(((ContinuousDataPDE)[1] != (YKernel)) | ((ContinuousDataPDE)[2] != (YKernel))){
("Parameter ContinuousDataPDE must have dimensions the same size as the length of XKernel. Returning.")
()
}
(!(Means)){
(!(Means)){
("Parameter Means is not of type list. Returning.")
()
}{
(i 1:(Means)){
(!(Means[i]])){
("Parameter Means can only contain vectors. Returning.")
()
} ((Means[i]]) != 2){
("Parameter Means can only contain vectors of dimension 2. Returning.")
()
}
}
}
}
(!(Covariances)){
(!(Covariances)){
("Parameter Cov is not of type list. Returning.")
()
}{
(i 1:(Covariances)){
(!(Covariances[i]])){
("Parameter Cov can only contain matrices. Returning.")
()
} (((Covariances[i]])[1] != 2) | ((Covariances[i]])[2] != 2)){
("Parameter Cov can only contain matrices of dimension 2x2. Returning.")
()
}
}
}
}
(!(Weights)){
(!(Weights)){
("Parameter Weights is not of type vector. Returning.")
()
} (!(Weights[i])){
("Parameter Weights can only contain numerics. Returning.")
()
}
}
((Colors)){
("Parameter Colors is missing. Returning.")
()
}{
(!(Colors)){
("Parameter Colors is not of type vector. Returning.")
()
}
}
((Cls)){
("Parameter Cls is missing. Returning.")
()
}
((Colors) < ((Cls))){
("Length of parameter Colors must be greater than or equal to the number of unique entries in Cls. Returning.")
()
}
(!(Source)){
("Parameter Source is not a character type. Returning.")
()
}
(!(Debug)){
("Parameter Debug is not a logical type. Returning.")
()
}
(Debug){
( = (), "Plot 3D\n")
}
MinData = (Data)
MaxData = (Data)
#DomainGrid = as.matrix(expand.grid(XKernel, YKernel))
# Compute the density for a density dot plot
#GMMDensity = 0
#MaxDensityPerClass = c()
#for(i in 1:length(Means)){
# TmpDensity = mvtnorm::dmvnorm(y = DomainGrid, # Marginal density estimation
# mu = Means[[i]],
# sigma = Covariances[[i]])
# # Ensure probability density as part of mixture (respect weights of each component)
# TmpDensity = Weights[i] * TmpDensity/sum(TmpDensity)
# MaxDensityPerClass = c(MaxDensityPerClass, max(TmpDensity))
# GMMDensity = GMMDensity + TmpDensity
#}
#GMMDensity = GMMDensity/sum(GMMDensity)
#GMMDensity = t(matrix(data = GMMDensity, nrow = length(XKernel), ncol = length(YKernel)))
colfunc <- (("white","black"))
MyColorGradient = colfunc(10)
(("colorRamps"))
MyColorGradient = colorRamps::matlab.like(10)
MyColorGradient = colfunc(10)
#MyColorGradient = c(rep("#FFFFFF", 2), MyColorGradient)
plotOut = plotly::plot_ly(x = XKernel,
y = YKernel,
z = ContinuousDataPDE,
= "surface",
= MyColorGradient,
alpha = 1)
plotOut = plotly::add_surface(p = plotOut,
z = GridDensity,
colorscale = ((0,1), ("rgb(107,184,255)","rgb(0,90,124)")),
opacity = 0.6)
plotOut = plotly::hide_colorbar(p = plotOut)
plotOut = plotly::(p = plotOut,
= "Model (blue) vs. Emp. Grid Dens.",
showlegend = ,
scene = (
xaxis = ( = AxNames[1], = (MinData, MaxData)),
yaxis = ( = AxNames[2], = (MinData, MaxData)),
zaxis = ( = "Probability"),
#zaxis = list(range = c(0, max(EmpiricDataPDE))),
aspectratio = (x = 1, y = 1, z = 1),
#scene, Scene))
camera = Camera))
(plotOut)
}
