Statistics 744, McMaster University

packages

Some of these packages may be hard to install, i.e. depending on system resources (especially rggobi).

library(tourr)
library(rggobi)
library(factoextra)
library(tidyverse)
library(ggalt)
library(rgl)

(ggobi has been archived: use remotes::install_version("rggobi", "2.1.22") or remotes::install_github("ggobi/rggobi"); see the github repository https://github.com/ggobi/rggobi and the ggobi web site http://ggobi.org/)

Buja, Cook, and Swayne (1996)

• scatterplots (point locations)
• traces (functions: parallel coordinates, Andrews plots)
• glyphs (stars/radar charts/faces/etc.)

tasks

• finding gestalt: focusing views (projection)
• posing queries: brushing/linking
• making comparisons: arranging many views

focusing: animation/motion

• adds a dimension (2D to 3D)
• smoothness/object continuity
• real-time user control: allows user to search/tune

interactive example

ggobi(laser)

tours

three components:

• data matrix (n × p)
• tour path that produces a smooth sequence of projection matrices (p × d) (apropos("_tour$"))
• display method that renders the projected data (apropos("animate_"))

optional extras (for “guided tour”):

• search strategy (apropos("^search_"))
• index (objective) function (cmass, holes, lda_pp)

Goal: allow automated, systematic search through entire space of projections

f <- flea[, 1:6]
animate(f,
        ## tour_path = guided_tour(holes()),
        tour_path = grand_tour(),
        display = display_xy(col = flea$species))

available display methods

apropos("animate_")

##  [1] "animate_andrews"   "animate_density2d" "animate_depth"    
##  [4] "animate_dist"      "animate_faces"     "animate_groupxy"  
##  [7] "animate_image"     "animate_pca"       "animate_pcp"      
## [10] "animate_sage"      "animate_scatmat"   "animate_slice"    
## [13] "animate_stars"     "animate_stereo"    "animate_trails"   
## [16] "animate_xy"

apropos("_tour$")

##  [1] "dependence_tour"     "frozen_guided_tour"  "frozen_tour"        
##  [4] "grand_tour"          "guided_section_tour" "guided_tour"        
##  [7] "little_tour"         "local_tour"          "new_tour"           
## [10] "planned_tour"

PCA adjustment

Examples/data from Holmes and Huber (2019)

• prcomp (SVD): preferred (also princomp)
• same data; projects in a way that (hopefully) focuses on interesting angles in the data
• assumes linear features
• normality not necessary, but better-behaved with normal data

wine PCA example

load("../data/wine.RData")      ## numeric matrix (wine)
load("../data/wineClass.RData") ## metadata (wine.class)

winePCAd <- prcomp(wine, scale = TRUE) ## compute PCA
f0 <- fviz_pca_biplot(winePCAd, geom = "point", habillage = wine.class,
                      col.var = "violet", addEllipses = TRUE, ellipse.level = 0.69)
tmp_plot <- function(p) { ## tweaks
  p + ggtitle("") + coord_fixed() +
    scale_colour_brewer(palette="Dark2") +
    scale_fill_brewer(palette="Dark2")
}

plot

print(tmp_plot(f0))

get augmented data

aug_data <- (get_pca_ind(winePCAd)$coord
  %>% as_tibble()
  %>% mutate(class = wine.class, .before=1)
)

improved plot

f1 <- fviz_pca_biplot(winePCAd, geom = "point", habillage = wine.class,
   col.var = "violet")
f2 <- tmp_plot(f1) + ggalt::geom_encircle(data = aug_data,
                                aes(x=Dim.1,y=Dim.2,group=class,
                                    colour=class,
                                    fill=class),alpha=0.2,
                                show.legend=FALSE)

print(f2)

adjust_pcaplot <- function(p, pca, dims=1:2) {
  sdvec <- pca$sdev[dims]
  p + coord_fixed(ratio = sdvec[2]/sdvec[1])
}
f3 <- adjust_pcaplot(f2, winePCAd)

## Coordinate system already present. Adding new coordinate system, which will replace the existing one.

print(f3)

cvec <- RColorBrewer::brewer.pal("Dark2", n=3)
with(aug_data,
     plot3d(Dim.1, Dim.2, Dim.3, col=cvec[wine.class], size=4))
with(aug_data,
     plot3d(Dim.1, Dim.2, Dim.3, col=cvec[wine.class], size=2, type = "s"))

references

Buja, Andreas, Dianne Cook, and Deborah F. Swayne. 1996. “Interactive High-Dimensional Data Visualization.” Journal of Computational and Graphical Statistics 5 (1): 78–99. https://doi.org/10.2307/1390754.

Holmes, Susan, and Wolfgang Huber. 2019. Modern Statistics for Modern Biology. 1 edition. Cambridge: Cambridge University Press.