New displays and applications for tour methods

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<br>

## ** Tours for the dynamic visualization of high-dimensional data**

.my-gray[
.large[**Ursula Laa**]

.largeish[ Institute of Statistics <br>
University of Natural Resources and Life Sciences <br>
Vienna, Austria
]
]

JSM 2022, Washington DC

]]

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<img src="plots/Boku-wien.png" width="60%">
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---
# The grand tour and hypercubes

With the grand tour we are using linear projections to visualize data in more than 3D - a nice way of visualizing the tour is to show it for hypercubes (generated with `geozoo`)

<br>

.center[
<div >
    <div style="width: 33%; float: left">
        <b> 3D </b>
        <a href="">
<img src="plots/c3.gif" width = "90%"/>
        </a>
    </div>
        <div style="width: 33%; float: left">
       <b>4D</b>
        <a href="">
<img src="plots/c4.gif" width = "90%" />        </a>
    </div>
    <div style="width: 33%; float: left">
        <b>6D</b>
        <a href="">
<img src="plots/c6.gif" width = "90%"/>        </a>
    </div>
    </div>
]

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<br>

# Implementation in R

<br>

```r
library(tourr)
library(palmerpenguins)

penguins <- na.omit(penguins)
animate_xy(penguins[,3:6], 
           col=penguins$species, 
           axes="bottomleft", 
           fps=15)
```

]

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<img src="plots/penguins2d.gif" width = "90%"/>
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---
# Short overview

Short history:

- First proposed in [Asimov (1985)](https://doi.org/10.1137/0906011)
- Lot of new developments in the 1990's, e.g. the guided tour [Cook et al (1995)](https://www.jstor.org/stable/1390844))
- R implementation in 2011 in the `tourr` package [Wickham et al (2011)](https://www.jstatsoft.org/article/view/v040i02)

Common usage:

- explore the shape of a multivariate distribution
- understand class differences and which variables are important
- identify (multivariate) outliers
- visualize statistical models, as described in [Wickham et al (2015)](https://doi.org/10.1002/sam.11271)

These and more recent developments were summarized in a recent review: [Lee et al (2021)](https://doi.org/10.1002/wics.1573)

---
# What is new?

Recent work has focused on two questions:

### How can we use tours in the case of **large data**?

- Large number of **observations**: overplotting can hide features, especially in the case of concave distributions.
- Large number of **variables**: projected data points tend to fall close to the center (crowding problem)

### Can we make tour displays interactive to learn more?

- Having **manual controls** of the projection allows the viewer to understand which variables are important, e.g. for separating groups.
- Leverage javascript interfaces, shiny apps, etc. to build an **interactive display**, e.g. for replaying or exporting projections, or for linked brushing

---
# Sage tour

When we project linearly from a high-dimensional space points start to **pile up** near the center of the projection, obscuring features or separation between groups. We can understand this as a large part of the high-D volume being projected onto a small area.

The sage display transforms the **radius** (i.e. the distance from the center) of all projected data points such that equal volume in the high-dimensional space gets projected onto equal area in the two-dimensional plane.

<center>
.footnote[[Laa, Cook, Lee (2022) Burning sage: Reversing the curse of dimensionality](https://doi.org/10.1080/10618600.2021.1963264)]
</center>

---
# Clustering and sage display

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# Liminal

With high-dimensional data a common approach is to use non-linear dimension reduction like t-SNE, also here we can leverage the tour in a linked display:

.footnote[[Lee, Cook, Laa (2022) Casting Multiple Shadows JDSSV](https://doi.org/10.52933/jdssv.v2i3)]

---
# The slice tour display

Even when projecting from relatively low number of dimensions we can still have overplotting issues if there are a lot of observations. When we have a lot of data there might be features inside the distribution that are hidden in projections but visible when "slicing" through the distribution.

.center[<img src="plots/slice.png" width="60%">]

.footnote[[Laa, Cook, Valencia (2020) A slice tour for finding hollowness in high-dimensional data](https://doi.org/10.1080/10618600.2020.1777140)]

---
# Slice tour of geometric shapes

We can combine the slice display with a grand tour to gain intuition about a surface.

.center[
<div >
    <div style="width: 33%; float: left">
        <b> 3D sphere </b>
        <a href="">
<img src="plots/sphere-3-anchored.gif" width = "90%"/>
        </a>
    </div>
        <div style="width: 33%; float: left">
       <b>4D torus</b>
        <a href="">
<img src="plots/torus-4-centered.gif" width = "90%" />        </a>
    </div>
    <div style="width: 33%; float: left">
        <b>Roman surface</b>
        <a href="">
<img src="plots/roman-surface.gif" width = "90%"/>        </a>
    </div>
    </div>
]

The slice tour is especially useful when looking at classification models using tools from the `classifly` package, and it also inspired work on "section pursuit".

---
# Manual tour in mathematica

Ongoing work (with Alex Auman, Di Cook, German Valencia): interactive manual slice tour implemented in mathematica, with manual controls for the projection and the slicing.

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# Interactivity

Hart and Wang (2022) [detourr:](https://cran.biotools.fr/web/packages/detourr/index.html) Animations for {tourr} using htmlwidgets for performance and portability. <br>

Harrison (2022) [Langevin dynamics based tours](https://logarithmic.net/langevitour/) of data, in Javascript with R wrapper. <br>

---
# Summary
.largeish[

- Tour methods can visualize high-dimensional data and reveal multivariate structure and outliers, and help us understand grouping
- The `tourr` package includes different methods for basis selection, an algorithm for geodesic interpolation and many display functions
- Visualization of modern (big) data is a challenge and recent work is already providing interesting solutions
- Tours can be used as a complementary method together with non-linear dimension reduction
- Interactive interfaces help with exploration and especially with interpretation, this was challenging within R but interfaces (in particular with Javascript) help - more to come soon!
]