Package: othdrplot
otHDRPlotWhat is it?This project implements the functional highest density region boxplot technique (Hyndman and Shang, 2009).When you have functional data (i.e. a set of curves), you will want to answer
some questions such as:What is the mode curve?Can I draw a confidence interval?Or, is there any outlier curves?This module allows you to do this:import othdrplot
algo = othdrplot.ProcessHighDensityRegionAlgorithm(
    processSample, reducedComponents, reducedDistribution, [0.8, 0.5]
)
algo.run()
algo.drawOutlierTrajectories()
algo.draw()The output is the following figure:In the situation where a multivariate sample is given, the
HighDensityRegionAlgorithm allows to plot the
regions where the density is associated with a
given fraction of the population.import openturns
# Estimate the distribution
myks = ot.KernelSmoothing()
distribution = myks.build(sample)
# Create the HDR algorithm
algo = othdrplot.HighDensityRegionAlgorithm(sample, distribution)
algo.run()
algo.draw()The output is the following figure:How to install?RequirementsThe dependencies are:Python >= 2.7 or >= 3.3numpy>= 0.10matplotlib>= 1.5.3OpenTURNS>= 1.16InstallationUsing the latest python version is prefered!To install from pip:pip install othdrplotTo install from github:git clone git@github.com:mbaudin47/othdrplot.git
cd othdrplot
python setup.py installDocumentationA short introduction to the algorithm is provided in theIntroduction to high density region plots.ExamplesSeveral examples are available in thedocdirectory.aMatrixPlot exampleaHDRAlgorithm 2D exampleaHDRAlgorithm 3D exampleaProcessHDR in 2Don the El-Nino dataaProcessHDR in 3Don the El-Nino dataaProcessHDR on logistic caseaProcessHDR on free fall caseReferencesRob J Hyndman and Han Lin Shang. Rainbow plots , bagplots and boxplots for functional data. Journal of Computational and Graphical Statistics, 19:29-45, 2009AlgorithmsThree classes are provided:HighDensityRegionAlgorithm: An algorithm to draw the density of a multivariate sample.ProcessHighDensityRegionAlgorithm: An algorithm to compute and draw the density of a multivariate process sample.KarhunenLoeveDimensionReductionAlgorithm: Simplifies the dimension reduction
with Karhunen-Loève decomposition.TheHighDensityRegionAlgorithmclassThis is an algorithm to draw the density of a multivariate sample.Compute the minimum levelset associated with the sample.Plots the required minimum level sets and the outliers.Compute and draw the inliers and the outliers, based on theMatrixPlot.The main ingredient is distribution of the sample, which is required.The basic method to estimate this distribution is kernel smoothing,
but any other method can be used, such as a gaussian mixture for example.TheProcessHighDensityRegionAlgorithmclassThis is an algorithm to draw the density of a process sample.Plots the trajectories in the physical space.Plots the projection of the trajectories in the reduced space, based on theHighDensityRegionAlgorithm.The main ingredients are the dimension reduction method and the method to estimate the density in the reduced space.In the current implementation, the dimension reduction can be provided
on the Karhunen-Loeve decomposition (but other methods can be used).
The method to estimate the density in the reduced space can be
the kernel smoothing estimator or any other density estimation
method (e.g. a Gaussian mixture).