In FJValverde/entropies: Plotting ternary entropy diagrams for joint distributions, contingency matrices, etc

This almost-vignette tries to demonstrate the differences in source entropy calculation by using several distinct methods of discretization of any of a number of databases.

Eventually, what we prove is that "equalfreq" discretization is not appropriate at all for entropy calculations, as expected.

Environment construction

Knitting options

#knitr::opts_chunk$set(dev = 'pdf') # plots in pdf, better for publication
knitr::opts_chunk$set(comment=NA, fig.width=6, fig.height=4)
knitr::opts_chunk$set(warning=FALSE)# Should not appear in the knitted document

Library loading

library(tidyverse)  # Acceding to that infamous Mr. Wickham's requests!
library(infotheo)  # The functionality provided by this has to be rerouted through entropies
library(entropies) # This package. Needs "entropy" and "caret" too.
library(ggtern)    # Ternary diagrams on ggplot
library(vcd)       # Categorical benchmarks
library(mlbench)   # ml benchmarkss
library(candisc)   # Wine dataset
fancy <- TRUE  # set this for nicer on-screen visualization
#fancy <- FALSE # Set this for either printing matter

Dataset metainformation loading and preparing

datasets <- getDatasets() #%>% filter(name=="iris")

#Types of discretizations explored: look up meaning in infotheo::discretize
discs <- c("equalwidth", "equalfreq","globalequalwidth")

Obtaining the entropies

Obtain the entropies and some other data for plotting from discretizations.

edf <- data.frame()
for(i in 1:nrow(datasets)) {
    dsRecord <-  datasets[i,] #filter(datasets, name == dsName)
    dsName <- dsRecord$name
    ds <- evalDataset(dsName)
    for (discType in discs) {
        disc.ds <- infotheo::discretize(ds, disc=discType)
        edf <- rbind(
            edf,
            cbind( disc = discType,
                   getDatasetSourceEntropies(disc.ds,
                                             dsName,
                                             disc=discType,
                                             className = dsRecord$className,
                                             idNumber = dsRecord$idNumber,
                                             withClass = TRUE,
                                             type = "total",
                                             method = "emp" #Method to work out entropies, from infotheo::entropy
                   )
            )
        )
    }
}
str(edf)

Plotting the multisplit data

Now let's plot on a per-database basis the results of the three discretizations.

We choose some of the interesting datasets from the diagram above to investigate:

#TODO: make a grid of these plots to be able to see anything different. 
# thisDsName <- "Ionosphere" # CAVEAT! Not enough different glyphs!!!
thisDsName <- "iris" # first run this value, then say, "Glass"
# thisDsName <- "Glass"# Try this for setting a gradient for features
# thisDsName <- "Arthritis"
# thisDsName <- "BreastCancer"
# thisDsName <- "Sonar"
# thisDsName <- "Wine"
# negatively subsetting recipe from Stack Overflow
thisEdf <- edf %>% 
    filter(dsName == thisDsName & name != "ALL") %>% 
    select(-starts_with("isClass"))
# Create different geometries for different feature set cardinalities:
# First consider the features in the dataset without the class variable
thisEt <-  ggmetern(filter(thisEdf, withClass == TRUE),  fancy) 
if ((nrow(thisEdf) - 1)/2 > 14){#too many points to be represented with glpsh
    thisEt <- thisEt + #geom_density_tern(aes(fill=..level..)) +
        stat_density_tern(geom='polygon',
                        aes(fill=..level..),
                        colour='grey50') + 
        scale_fill_gradient(low='green',high='red')  +
        geom_point(aes(shape=disc), size=2) +
        scale_shape_manual(values=c(21, 22, 24))  + 
        labs(fill="Feature", shape="Discretizations")
}else {
    thisEt <- thisEt + 
        geom_point(aes(shape=name,color=disc), size=3) +
        scale_shape_manual(values=1:14) + 
        labs(shape="Feature",color="Discretization type") #+
}
thisEt + 
    ggtitle("Source Multivariate Entropies per Feature and discretization")
ggsave(filename=sprintf("%s_discretizationss_W_class.jpeg", thisDsName))

We may conclude, as expected, that, for our purposes, equal frequency binning is not adequate, since it loses information of the uncertainty in the distribution domain.

For estimating entropies and plotting them in the SMET, equal width binning should be preferred, pending a more thorough evaluation of "globalequalwidth" discretization.

Postscriptum

sessionInfo()

FJValverde/entropies documentation built on Oct. 12, 2023, 10:17 p.m.