Going beyond 2D and 3D to visualise higher dimensions, for ordination, clustering and other models

Di Cook
Monash University

vISEC
June 22, 2020

https://dicook.org/files/vISEC2020/slides_tourr.html

Image credit: Gentoo Penguins, Wikimedia Commons

1 / 46

OutlineGetting started: tourr, spinifex, geozoo
What is a tour?
Different types of tours
Interpreting what you see
Saving your tour plot
2 / 46

Getting set up3 / 46

`tourr`

install.packages("tourr")
help(package="tourr")

library("tourr")

Implements geodesic interpolation and basis generation functions that allow you to create new tour methods from R.

4 / 46

`spinifex`

install.packages("spinifex")
help(package="spinifex")

library("spinifex")

Implements manual control, where the contribution of a selected variable can be adjusted between -1 to 1, to examine the sensitivity of structure in the data to that variable. The result is an animation where the variable is toured into and out of the projection completely.

5 / 46

`geozoo`

install.packages("geozoo")
help(package="geozoo")

library("geozoo")

Geometric objects defined in 'geozoo' can be simulated or displayed in the R package 'tourr'.

6 / 46

## R version 4.0.1 (2020-06-06)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Mojave 10.14.6
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_AU.UTF-8/en_AU.UTF-8/en_AU.UTF-8/C/en_AU.UTF-8/en_AU.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] geozoo_0.5.1         spinifex_0.2.0       tourr_0.5.6         
## [4] xaringanthemer_0.3.0
## 
## loaded via a namespace (and not attached):
##  [1] sysfonts_0.8.1  digest_0.6.25   showtextdb_3.0  bitops_1.0-6   
##  [5] magrittr_1.5    evaluate_0.14   xaringan_0.16   rlang_0.4.6    
##  [9] stringi_1.4.6   rmarkdown_2.3   tools_4.0.1     stringr_1.4.0  
## [13] showtext_0.8-1  xfun_0.14       yaml_2.2.1      compiler_4.0.1 
## [17] htmltools_0.5.0 knitr_1.28
7 / 46

Grab the runthis.R file from https://github.com/dicook/vISEC2020

in the skills_showcase folder. (Or the slides_tour.Rmd for everything!)

8 / 46

Get some new data9 / 46

remotes::install_github("allisonhorst/palmerpenguins")

library(tidyverse)
library(palmerpenguins)
penguins <- penguins %>% filter(!is.na(bill_length_mm))

Show entries

Search:

	species	island	bill_length_mm	bill_depth_mm	flipper_length_mm	body_mass_g	sex
1	Adelie	Torgersen	39.1	18.7	181	3750	male
2	Adelie	Torgersen	39.5	17.4	186	3800	female
3	Adelie	Torgersen	40.3	18	195	3250	female
4	Adelie	Torgersen	36.7	19.3	193	3450	female
5	Adelie	Torgersen	39.3	20.6	190	3650	male

Showing 1 to 5 of 342 entries

Previous1 2 3 4 5…69Next

See https://allisonhorst.github.io/palmerpenguins/ for more details.

10 / 46


Adélie Wikimedia Commons	Gentoo Wikimedia Commons	Chinstrap Wikimedia Commons

11 / 46

library(ochRe)
ggplot(penguins, 
   aes(x=flipper_length_mm, 
       y=body_mass_g,
       colour=species,
       shape=species)) +
  geom_point(alpha=0.7, 
             size=2) +
  scale_colour_ochre(
    palette="nolan_ned") + 
  theme(aspect.ratio=1,
  legend.position="bottom")

12 / 46

Our first tour13 / 46

clrs <- ochre_pal(
  palette="nolan_ned")(3)
col <- clrs[
  as.numeric(
    penguins$species)]
animate_xy(penguins[,3:6], 
           col=col, 
           axes="off", 
           fps=15)

14 / 46

What did you see?
00:30
15 / 46

clusters ✅
16 / 46

clusters ✅
outliers ✅
16 / 46

clusters ✅
outliers ✅
linear dependence ✅
16 / 46

clusters ✅
outliers ✅
linear dependence ✅
elliptical clusters with slightly different shapes ✅
16 / 46

clusters ✅
outliers ✅
linear dependence ✅
elliptical clusters with slightly different shapes ✅
separated elliptical clusters with slightly different shapes ✅
16 / 46

clusters ✅
outliers ✅
linear dependence ✅
elliptical clusters with slightly different shapes ✅
separated elliptical clusters with slightly different shapes ✅
16 / 46

What is a tour?

A grand tour is by definition a movie of low-dimensional projections constructed in such a way that it comes arbitrarily close to showing all possible low-dimensional projections; in other words, a grand tour is a space-filling curve in the manifold of low-dimensional projections of high-dimensional data spaces.

$x_{i} \in R^{p}$ , $i^{t h}$ data vector

$F$ is a $p \times d$ orthonormal basis, $F^{'} F = I_{d}$ , where $d$ is the projection dimension.

The projection of $x_{i}$ onto $F$ is $y_{i} = F^{'} x_{i}$ .

Tour is indexed by time, $F (t)$ , where $t \in [a, z]$ . Starting and target frame denoted as $F_{a} = F (a), F_{z} = F (t)$ .

The animation of the projected data is given by a path $y_{i} (t) = F^{'} (t) x_{i}$ .

17 / 46

Geodesic interpolation between planes

Tour is indexed by time, $F (t)$ , where $t \in [a, z]$ . Starting and target frame denoted as $F_{a} = F (a), F_{z} = F (t)$ .

The animation of the projected data is given by a path $y_{i} (t) = F^{'} (t) x_{i}$ .

18 / 46

A grand tour is like a random walk (with interpolation) through the space of all possible planes.

19 / 46

Let's take a look at some common high-d shapes with a grand tour20 / 46

4D spheres

Hollow

Solid

21 / 46

4D cubes

Hollow

Solid

22 / 46

Others

Torus

Mobius

23 / 46

Reading axes - interpretation

Length and direction of axes relative to the pattern of interest

24 / 46

25 / 46

26 / 46

Reading axes - interpretation 27 / 46

Gentoo from others in contrast of fl, bd

Chinstrap from others in contrast of bl, bm

28 / 46

There may be multiple and different combinations of variables that reveal similar structure. ☹️

The tour can help to discover these, too. 😂

29 / 46

Other tour typesguided: follows the optimisation path for a projection pursuit index.
little: interpolates between all variables. 
local: rocks back and forth from a given projection, so shows all possible projections within a radius.
dependence: two independent 1D tours
frozen: fixes some variable coefficients, others vary freely. 
manual: control coefficient of one variable, to examine the sensitivity of structure this variable. (In the spinifex package)
slice: use a section instead of a projection.
30 / 46

guided tour

new target bases are chosen using a projection pursuit index function

31 / 46

$\underset{F}{maximize} g (F^{'} x) subject to F being orthonormal$

holes: This is an inverse Gaussian filter, which is optimised when there is not much data in the center of the projection, i.e. a "hole" or donut shape in 2D.
central mass: The opposite of holes, high density in the centre of the projection, and often "outliers" on the edges.
LDA/PDA: An index based on the linear discriminant dimension reduction (and penalised), optimised by projections where the named classes are most separated.

32 / 46

Grand

Might accidentally see best separation

Guided, using LDA index

Moves to the best separation

33 / 46

manual tour

control the coefficient of one variable, reduce it to zero, increase it to 1, maintaining orthonormality

34 / 46

Manual tour

start from best projection, given by projection pursuit
bl contribution controlled
if bl is removed form projection, Adelie and chinstrap are mixed
bl is important for Adelie

35 / 46

Manual tour

start from best projection, given by projection pursuit
fl contribution controlled
cluster less separated when fl is fully contributing
fl is important, in small amounts, for Gentoo

36 / 46

Local tour

Rocks from and to a given projection, in order to observe the neighbourhood

37 / 46

Projection dimension and displays

38 / 46

How do I use tours39 / 46

Classification: to check assumptions of models
to examine separations between groups
determine variable importance
examine boundaries 
random forest diagnostics vote matrix

Dimension reductiongo beyond 2 PCs
work with much higher dimensional data
check for not linear dependencies

40 / 46

Clusteringexamine shape of clusters
separation between clusters
compare cluster solution
view the dendrogram in data space

Compositional datashapes and clusters in a simplex

41 / 46

Saving for publication

Method 1, using plotly (see reading axes code chunk):

Generate each frame, index each frame, a big array
Make one big ggplot, with all frames overplotted, and a non-used argument frame pointing to your index
Pass to ggplotly
Save to html using htmltools::save_html()

or try using

spinifex::play_tour_path()

42 / 46

Saving for publication

Method 1, using gifski and tourr::render_gif(). See lots of code chunks!

43 / 46

Summary

We can learn a little more about the data if have a tour in the toolbox. It can help us to understand

dependencies between multiple variables
examine shapes, of clusters
detect outliers

44 / 46

If you want to read more

45 / 46

Thanks

Slides created via the R package xaringan, with iris theme created from xaringanthemer.

The chakra comes from remark.js, knitr, and R Markdown.

Slides are available at https://dicook.org/files/vISEC20/slides_tourr.html and supporting files at https://github.com/dicook/vISEC2020.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

↑, ←, Pg Up, k	Go to previous slide
↓, →, Pg Dn, Space, j	Go to next slide
Home	Go to first slide
End	Go to last slide
Number + Return	Go to specific slide
b / m / f	Toggle blackout / mirrored / fullscreen mode
c	Clone slideshow
p	Toggle presenter mode
t	Restart the presentation timer
?, h	Toggle this help

Going beyond 2D and 3D to visualise higher dimensions, for ordination, clustering and other models

Di Cook Monash University

vISEC June 22, 2020

Outline

Getting set up

tourr

spinifex

geozoo

Get some new data

Our first tour

What did you see?

What is a tour?

Geodesic interpolation between planes

Let's take a look at some common high-d shapes with a grand tour

4D spheres

4D cubes

Others

Reading axes - interpretation

Reading axes - interpretation

Other tour types

guided tour

manual tour

Manual tour

Manual tour

Local tour

Projection dimension and displays

How do I use tours

Saving for publication

Saving for publication

Summary

If you want to read more

Thanks

Outline

Help

Di Cook
Monash University

vISEC
June 22, 2020

`tourr`

`spinifex`

`geozoo`