In pca3d: Three Dimensional PCA Plots

library(knitr)
library(rgl)
opts_chunk$set(cache=FALSE, autodep=FALSE, tidy=FALSE)
opts_knit$set(width=75)
knit_hooks$set(webgl = hook_webgl)

Introduction

This package is actually a bunch of shortcuts to the RGL graphics library, which does the actual job. The idea is to have a few functions that can be quickly and reliably used to visualize and explore multivariate models, and then create a publication-ready figure. By default, pca3d can handle prcomp, princomp and matrix objects.

The provided data set, metabo, includes metabolic profiles for over 400 metabolites sampled from 136 tuberculosis (TB) patients and healthy volunteers, and has been described previously [@weiner2012biomarkers]. The samples fall into one of three groups: healthy, non-infected ("NEG"), healthy infected ("POS") and individuals with active tuberculosis (TB).

First, we prepare the principal component analysis (PCA) object to work with. The data is contained in the data frame "metabo"; first column of the data set contains group assignments, and we need to remove it to work with the rest of the data set:

library(pca3d)
data(metabo)
pca <- prcomp(metabo[,-1], scale.=TRUE)
gr  <- factor(metabo[,1])
summary(gr)

When pca3d is called, the opened window is interactive and can be used to explore differences. Here, we call pca3d() and then save a screenshot (snapshot) to a file.

pca3d(pca, group=gr)
snapshotPCA3d(file="first_plot.png")

There is a two-dimensional version of pca3d, called (of course) pca2d. Essentially, you can run exactly the same command, and you should see a very similar output -- just 2D, and not 3D. The idea is that you can fiddle around with the 3D version to explore your graphics and / or choose the components, and then use pca2d to create a figure for a publication.

pca2d(pca, group=gr, legend="topleft")

Both functions have several options for tweaking the visuals and adding bells and whistles.

Plotting options

Shapes, colors and palettes

The functions pca3d and pca2d try hard to guess the right values and there are many ways to specify the colors and shapes. Colors and shapes can be specified as follows:

• a single value; in that case, all drawn data points will have this associated value (e.g. the same color)
• a vector equal to the number of samples, specifying color / shape for each data point separately
• a named vector equal in length to the number of levels of the group option, that is, equal to the number of groups present in the data. In this case, the names of the vector must correspond to the levels of group.
• If color or shape are not specified, but group is not NULL, then shapes and colors will be attributed automatically to groups

Shapes / pch

Currently, there are four possible 3D shapes to choose from: tetrahedrons, cubes, spheres and octahedrons. The corresponding 2D pch values are 17, 15, 16 and 18, respectively. You can get the list of permissible shapes and their pch counterparts using the listShapes function.

listShapes()

The shapes for 3D plots should be specified using these character values, or with an abbreviation (e.g. t for tetrahedrons).

For 2D plots, shapes can be specified using any valid numeric values of the pch parameter. However, shapes defined by their 3D names (tetrahedrons etc.) are also permissible.

Shape sizes

The parameter "radius" scales the symbols (much like cex for regular plots, or rather, exactly like cex for pca2d).

Colors and palettes

For 3D plots, colors and palette should not contain an alpha channel; that is, #FF0000 is permisible, but #FF000033 not.

Palette is a character vector with color names. A default, colorblind-friendly palette is predefined in the package (see the defaultPalettePCA3D function).

Ellipses / ellipsoids (option show.ellipses)

These option show a confidence interval (CI) ellipse (2D) or ellipsoid (3D). The option ellipse.ci corresponds to the level for which the CI is supposed to be drawn (default 0.95). A less conservative level (e.g. 0.75) will result in a morre narrow ellipse. For the 3D representation, it is worthwile to remove the grey plane at z=0 with the show.plane=FALSE option.

pca3d(pca, group=gr, show.ellipses=TRUE,
  ellipse.ci=0.75, show.plane=FALSE)
snapshotPCA3d(file="ellipses.png")

Biplots

A biplot shows information on variable loadings, which helps to interpret a PCA. To see a biplot, use the biplot parameter. If TRUE, then variable loadings will be extracted from the princomp or prcomp object. If biplot is a matrix, then it is assumed to be a matrix of variable loadings.

The second option is biplot.vars, which describes how many variables are shown on the plot. The top N variables are selected based on their absolute loadings.

pca2d(pca, group=gr, biplot=TRUE, biplot.vars=3)

Shadows (lollipops), centroids, labels, group labels

The options show.shadows, show.centroids, show.labels and show.group.labels determine about adding additional graphical information. You can set them all to "TRUE" with the fancy=TRUE option -- mostly for demonstration purposes, because the plot is then hardly readable.

• show.shadows Draw a thin grey line from the point to the xy plane
• show.centroids Show a large symbol of the group at the average coordinates of samples in that group (centroids)
• show.labels Show text labels at each point
• show.group.labels Show group labels at the centroids

pca3d(pca, group=gr, fancy=TRUE)
snapshotPCA3d(file="fancy.png")

Legends

Both pca3d and pca2d will produce a legend if the option legend is not NULL. The argument to this option is anything acceptable by xy.coords. Typically, you will want something like "topleft" or "bottomright".

pca2d(pca, group=gr, legend="bottomleft")

Return value

Both pca2d and pca3d return a data frame containing the assignments between groups, colors and shapes that can be used to plot a legend. Since shapes are character vectors, additionally a mapping to the 2D plotting "pch" parameter is provided. This can be used to draw a legend (however, it is more convenient to specify the legend option).

l <- pca2d(pca, group=gr)
l
legend("topleft", l$groups, col=l$colors, pch=l$pch, box.lty=0)

References

pca3d documentation built on Oct. 23, 2020, 8:26 p.m.