Touring multivariate data

class: center, middle, inverse, title-slide

.title[
# Touring multivariate data
]
.subtitle[
## SISBID 2024 <a href="https://github.com/dicook/SISBID" class="uri">https://github.com/dicook/SISBID</a>
]
.author[
### Di Cook (<a href="mailto:dicook@monash.edu" class="email">dicook@monash.edu</a>) Heike Hofmann (<a href="mailto:hhofmann4@unl.edu" class="email">hhofmann4@unl.edu</a>) Susan Vanderplas (<a href="mailto:susan.vanderplas@unl.edu" class="email">susan.vanderplas@unl.edu</a>)
]
.date[
### 08/14-16/2024
]

---

# Pairwise plots

.pull-left[

]

.pull-right[

What don't you see? Unless you have tours, you'll never know 🫣

]

---
class: inverse middle center

# Our first tour

What patterns do you see?

---

.pull-left[

``` r
# Run the tour
animate_xy(penguins[,2:5], 
           col=penguins$species, 
           axes="off", 
           fps=15)
```
]

.pull-right[
<img src="penguins2d.gif" width="100%"> 
]

---
class: inverse middle
# What did you see?

- clusters ✅
--

- outliers ✅
--

- linear dependence ✅
--

- elliptical clusters with slightly different shapes ✅
--

- separated elliptical clusters with slightly different shapes ✅
--

---
# Which shows better separation?

.pull-left[
<img src="penguins2d.gif" width="80%"> 
]

.pull-right[
<img src="index_files/figure-html/unnamed-chunk-5-1.png" width="100%" style="display: block; margin: auto;" />
]

---
# What is a tour?

.pull-left[

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.

<img src="images/hands.png" width="80%"> 
]

.pull-right[
`${\mathbf x}_i \in \mathcal{R}^p$`, `$i^{th}$` data vector

`$F$` is a `$p\times d$` orthonormal basis, `$F'F=I_d$`, where `$d$` is the projection dimension.

The projection of `${\mathbf x_i}$` onto `$F$` is `${\mathbf y}_i=F'{\mathbf x}_i$`.

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 `${\mathbf y}_i(t)=F'(t){\mathbf x}_i$`.

]

---

# Geodesic interpolation between planes

.pull-left[
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 `${\mathbf y}_i(t)=F'(t){\mathbf x}_i$`.

]
.pull-right[

]

---
class: inverse middle center

# Reading axes - interpretation

Length and direction of axes relative to the  pattern of interest

---

---

---
# Reading axes - interpretation

---

.pull-left[

``` r
ggplot(penguins, 
   aes(x=fl, 
       y=bd,
       colour=species,
       shape=species)) +
  geom_point(alpha=0.7, 
             size=2) +
    scale_colour_discrete_divergingx(palette = "Zissou 1") + 
  theme(aspect.ratio=1,
  legend.position="bottom")
```

Gentoo from others in contrast of fl, bd
]
.pull-right[

``` r
ggplot(penguins, 
   aes(x=bl, 
       y=bm,
       colour=species,
       shape=species)) +
  geom_point(alpha=0.7, 
             size=2) +
    scale_colour_discrete_divergingx(palette = "Zissou 1") + 
  theme(aspect.ratio=1,
  legend.position="bottom")
```

Chinstrap from others in contrast of bl, bm

]

---
class: inverse middle left

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

The tour can help to discover these, too. 😂

---
# Other tour types

- .orange[guided]: follows the optimisation path for a projection pursuit index.
- .orange[little]: interpolates between all variables. 
- .orange[local]: rocks back and forth from a given projection, so shows all possible projections within a radius.
- .orange[dependence]: two independent 1D tours
- .orange[frozen]: fixes some variable coefficients, others vary freely. 
- .orange[manual]: control coefficient of one variable, to examine the sensitivity of structure this variable. 
- .orange[slice]: use a section instead of a projection.
- .orange[sage]: transform a 2D projection, to avoid data  piling.

---
class: inverse middle center

# guided tour

new target bases are chosen using a projection pursuit index function

---
`$$\mathop{\text{maximize}}_{F} g(F'x) ~~~\text{ subject to }
F \text{ being orthonormal}$$`

.font_small[
- `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.
]

---

.pull-left[
Grand

.small[
Might accidentally see best separation
]
]

.pull-right[

Guided, using LDA index

.small[
Moves to the best separation
]
]

---
class: inverse middle center

# manual tour

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

---
# Manual tour

.pull-left[

- 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

]

.pull-right[

]

---
# Manual tour

.pull-left[

- 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

]

.pull-right[

]
---
# Local tour

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

]

.pull-right[
<img src="penguins2d_local.gif" width="90%">

]

---
class: inverse middle
# Your turn

Using the sample code from the tour package, check how many clusters in the example data.

``` r
library(tourr)
data(flea)
?animate_xy
animate_xy(flea[, 1:6])
```

---
# Saving and sharing: Animated gif

.pull-left[

``` r
render_gif(    
  penguins[,2:5], 
  grand_tour(), 
  display_xy(col=penguins$species, 
             axes="bottomleft"), 
  file="penguins2d.gif", 
  frames=100, 
  width=300, 
  height=300)
```
]

.pull-right[
<img src="penguins2d.gif" width="80%">
]

---
# Saving and sharing: Single frame

.pull-left[

``` r
load(here::here("data/p_tour_path.rda"))
penguins_pcti <- interpolate(penguins_pct, 0.2)
f27 <- matrix(penguins_pcti[,,27], ncol=2)
p27 <- render_proj(penguins[,2:5],
 f27,
 obs_labels=penguins$species)
```

Draw it with ggplot, and possibly pass to plotly.

]

.pull-right[

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---
# Resources

- [Cook and Laa (2024)](https://dicook.github.io/mulgar_book/)
- Emerson et al (2013) The Generalized Pairs Plot, Journal of Computational and Graphical Statistics, 22:1, 79-91
- [Natalia da Silva](http://natydasilva.com/) [PPForest](https://cran.r-project.org/web/packages/PPforest/index.html) and [shiny app](https://natydasilva.shinyapps.io/shinyV03/).
- Wickham et al (2011) [tourr: An R Package for Exploring Multivariate Data with Projections](https://www.jstatsoft.org/article/view/v040i02/v40i02.pdf) and the R package [tourr](https://cran.r-project.org/web/packages/tourr/index.html)
- Schloerke et al (2016) [Escape from Boxland](https://journal.r-project.org/archive/2016/RJ-2016-044/index.html), [the web site zoo](http://schloerke.com/geozoo/) and the R package [geozoo](https://cran.r-project.org/web/packages/geozoo/index.html)
- Spyrison and  Cook (2020). spinifex: Manual Tours, Manual
  Control of Dynamic Projections of Numeric Multivariate Data. https://CRAN.R-project.org/package=spinifex
- Stuart Lee [liminal](https://github.com/sa-lee/liminal) New tools to do linked brushing between tours and PCA/tSNE/PDS views

---
# Share and share alike

<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a> This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.