In fanne-stat/radviz3d: A package for 3D radial visualization

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Introduction

This package is developed for 3D radial visualization of high-dimensional datasets. Our display engine is called RadViz3D and extends the classic 2D radial visualization and displays multivariate data on the 3D space by mapping every record to a point inside the unit sphere. RadViz3D obtains equi-spaced anchor points exactly for the five Platonic solids and approximately for the other cases via a Fibonacci grid. We also propose a Max-Ratio Projection (MRP) method that utilizes the group information in high dimensions to provide distinctive lower-dimensional projections that are then displayed using Radviz3D. Our methodology is extended to datasets with discrete and mixed features where a generalized distributional transform (GDT) is used in conjuction with copula models before applying MRP and RadViz3D visualization. This document gives a brief introduction to the functions included in radviz3d with several application examples.

Instructions for interactive views

The 3D interative plots are implemented with the \texttt{rgl} functions and here are instructions for manipulation: - Rotation: Click and hold with the left mouse button, then drag the plot to rotate it and gain different perspectives. - Resize: Zoom in and out with the scroll wheel, or the right mouse button.

Functions

radviz3d contains 3 functions:

• Gtrans: Transform discrete or mixture of discrete and continuous datasets to continuous datasets with marginal normal(0,1).
• mrp: Project high-dimensional datasets to lower dimention with max-ratio projection.
• radialvis3d: Visualize appropriately tranformed datasets in the unit sphere.

The main function radialvis3d is able to displays and classifies data points from the pre-known groups and provide visual clues to how the grouped data are separately from each other.

Examples

We illustrate the usage of radialvis3d on datasets with small (< 10) and large dimensions and with continuous or discrete features. The interactive 3D plot are produced from rgl and can be rotated manually to get better perspectives on rgl-supported devices.

Displaying original datasets

For small datasets with continuous values, function radialvis3d can be applied directly with options domrp = F and doGtrans = F. The 3D plot below are displayed for the (Fisher's or Anderson's) iris data. The dataset contains 50 flowers measurements for 4 variables, sepal length, sepal width, petal length and petal width which are represented by the 4 anchor points in the plot. Flowers come from each of 3 species, Iris setosa, Iris versicolor, and Iris virginica. Speicies groups are shown in different colors and tagged with name labels.

library(radviz3d)
data("iris")
radialvis3d(data = iris[, -5], cl = factor(iris$Species), domrp = F, doGtrans = F, 
            lwd = 2, alpha = 0.05, pradius = 0.025, class.labels = levels(iris$Species))

# rgl::rgl.viewpoint(zoom = 0.85)
# rgl::rglwidget()

Display reduced datasets

For large datasets with continuous values, we use function radialvis3d with options doGtrans = F and domrp = T along with the number of principal components $k$ specified by npc = k. The plot for a wine dataset are shown below. The dataset (reference link: \url{https://rdrr.io/cran/rattle.data/man/wine.html}) contains 178 samples of three types of wines grown in a specific area of Italy. 13 chemical analyses were recorded for each sample.

wine = read.table(file = "~/Desktop/wine.dat", sep=",",
                  header=F, col.names = c("cultivar","Ahl","Malic","Ash", "Alk","Mgm",
                                          "pnls","Flvds","Nonfp","Pthyns",
                                          "Color","Hue","ODdil","Prol")) 
wine$cultivar = as.factor(wine$cultivar)
class = wine$cultivar
class <- as.factor(class)
sn <- as.matrix(wine[,-1])
wine <- data.frame(sn,class)

radialvis3d(data = wine[, -14], cl = factor(wine[,14]), domrp = T, npc = 4, doGtrans = F, 
            lwd = 2, alpha = 0.05, pradius = 0.025, class.labels = levels(wine[,14]))

# rgl::rgl.viewpoint(zoom = 0.6)
# rgl::rglwidget()

Display transformed datasets

Datasets with discrete values can be transformed using options doGtrans = T. (Currently, GDT is not applicable to categorical variables). Here we present an example for an Indic scripts dataset (reference link: \url{https://sites.google.com/site/skmdobaidullah/dataset-code}) which is on 116 different features from handwritten scripts of 11 Indic languages. A subset of 5 languages is chosen from 4 regions, namely Bangla (from the east), Gurmukhi (north), Gujarati (west), and Kannada and Malayalam (languages from the neighboring southern states of Karnataka and Kerala) and a sixth language (Urdu, with a distinct Persian script). Some of the features contains discrete values so the dataset is essentially of mixed attributes. We apply radialvis3d with GDT and MRP (npc = 6) to display for distinctiveness of samples from each languages.

load("~/Desktop/indic.rda") 

radialvis3d(data = script[,-117], cl = class, domrp = T, npc = 6, doGtrans = T, 
            lwd = 2, alpha = 0.05, pradius = 0.025, class.labels = levels(class))

# rgl::rgl.viewpoint(zoom = 0.4)
# rgl::rglwidget()

fanne-stat/radviz3d documentation built on Aug. 24, 2022, 9:50 p.m.