In this document we describe the main features of the HistDAWass package. The name is the acronym for Histogram-valued 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 Histogram-valued 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) Qf and Qg. 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 DescriptiondistributionH
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 Histgram-valued time series
library(HistDAWass)
mydist=distributionH(x=c(0,1,2),p=c(0,0.3,1))
data2hist functions
The average hisogram of a column
The standard deviation of a variable
The covarince matrix of a MatH
The correlation matrix of a MatH
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
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