In this document we describe the main features of the HistDAWass package. The name is the acronym for Histogramvalued Data analysis using Wasserstein metric. The implemented classes and functions are related to the anlysis of data tables containing histograms in each cell instead of the classical numeric values.
In this document we describe the main features of the HistDAWass package. The name is the acronym for Histogramvalued Data analysis using Wasserstein metric. The implemented classes and functions are related to the anlysis of data tables containing histograms in each cell instead of the classical numeric values.
What is the L2 Wasserstein metric?
given two probability density functions f and g, each one has a cumulative distribution function F and G and thei respectively quantile functions (the inverse of a cumulative distribution function) Q_{f} and Q_{g}. The L2 Wasserstein distance is
\[d\_W(f,g)=\\sqrt{\\int\\limits\_0^1{(Q\_f(p)  Q\_g(p))^2 dp}}\]
The implemented classes are those described in the following table
Class  wrapper function for initializing  Description 

distributionH

distributionH(x,p)

A class describing a histogram distibution 
MatH

MatH(x, nrows, ncols,rownames,varnames, by.row )

A class describing a matrix of distributions 
TdistributionH

TdistributionH()

A class derived from distributionH equipped with a timestamp or a time window 
HTS

HTS()

A class describing a Histgramvalued time series 
data2hist functions
plot of a distributionH
plot of a MatH
plot of a HTS
Clustering
Kmeans
Adaptive distance based Kmeans
Fuzzy cmeans
Fuzzy cmeans based on adaptive Wasserstein distances
Kohonen batch self organizing maps
Kohonen batch self organizing maps with Wasserstein adaptive distances
Hierarchical clustering
Dimension reduction techniques
Principal components analysis of a single histogram variable
Principal components analysis of a set of histogram variables (using Multiple Factor Analysis)
Smoothing
Moving averages
Exponential smoothing
Predicting
A two component model for a linear regression using Least Square method