Visualising physics

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# High-dimensional data visualisation with tours

# Ursula Laa

### School of Physics and Astronomy
### &
### Department of Econometrics and Business Statistics

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# A bit about me

<br>

<img src="figure/map1-1.png" style="display: block; margin: auto;" />
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<img src="plots/IMG_5105.jpg" width="55%">

<br>

<img src="plots/T1tttt_ICHEP2014_All.pdf" width="75%">
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# A bit about me

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<img src="figure/map2-1.png" style="display: block; margin: auto;" />
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<img src="plots/l_snu.png" width="75%">

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<img src="plots/Rmax_allowed_glu_N1_BinoLSP.png" width="95%">
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# A bit about me

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<img src="figure/map3-1.png" style="display: block; margin: auto;" />
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<img src="plots/tourr.png" width="40%">
<img src="plots/plotly.png" width="40%">

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<img src="plots/flyingBirds.gif" width="60%" height="60%" style="display: block; margin: auto;" />
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# Projections

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## Projections are everywhere

<br>

.large[The most common projections are from our **3 dimensional** world onto a **2 dimensional** plane]

<br>

.large[Examples:
* Photographs
* 3D objects on 2D screens
* Shadows
]

<br>

.large[We can fully understand the 3D object if we look at it from different angles, for example when we rotate the viewing angle of a 3D plot!]

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# We can understand the 3D shape from 2D  projections

.center[
<video width="450" loop autoplay>
        <source src="plots/media.io_cube-3.mp4" type="video/mp4">
      </video>
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Example video taken from [here](http://schloerke.com/geozoo/)
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# Looking at 3D plots

<br>

<div id="htmlwidget-70f22dfffd048e9459b0" style="width:60%;height:60%;" class="plotly html-widget"></div>
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.largeish[This is an example from [plotly](https://plot.ly/r/3d-scatter-plots/)]

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# Beyond 3 dimensions
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# Going to 4 dimensions

<br>

.center[<img src="plots/Dimension_levels.svg" width="55%"> <br> from [here](https://en.wikipedia.org/wiki/File:Dimension_levels.svg)]

<br>

.large[We can imagine a 4D cube by extending a 3D cube into a 4th dimension. That is also how we think about high dimensions in data, each dimension adds an orthogonal axis.]

.large[And we can look at different 2D views with a grand tour. Each plane corresponds to a **projection** from the original space down to two dimensions, and we project each data point onto the same plane.]

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# Grand tour showing a 4D cube

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<video width="450" loop autoplay>
        <source src="plots/media.io_cube-4.mp4" type="video/mp4">
      </video>
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<br>

Example videos taken from [here](http://schloerke.com/geozoo/)

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# Grand tour showing a 5D cube

.center[
<video width="450" loop autoplay>
        <source src="plots/cube-5.mov" type="video/mp4">
      </video>
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.large[This works for any number of dimensions and we can learn about the shape in the high dimensional space.]

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# Shapes in 5D

.largeish[Comparing samples on the surface of a sphere vs the faces of a cube in 5D. We can understand differences between the shapes through the interpolated 2D projections!]

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<iframe src="s5.html" width="800" height="500" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe>
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# Grand tour data displays

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# 2D scatter plot display

.large[
* All data points are projected onto 2D plane
* Draw scatter plot of the data points
* Represent the current projection as "axes"
]

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<img src="tour2d.gif" width="40%" height="40%" style="display: block; margin: auto;" />
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# Many other dispay types are possible

.large[Example displays for 1 or 3 dimensional projections]

<img src="tour1d.gif" width="70%" height="70%" style="display: block; margin: auto;" />
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# Using tours in (physics) research

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# Exploring structure in high dimensions

<br>

.large[Tour visualisations are a great way to explore structure beyond 2 or 3 dimensions. Typical applications include:

* Identifying and comparing clusters
* Find multivariate outliers
* Identifying complex relations between parameters (beyond simple linear correlations)
]

<br>

.largeish[Simple example: flea dataset, comparing 3 species on 6 measures]

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# A less simple example

.largeish[Comparing particle physics measurements based on what they tell us about the structure of the proton, in a 6 dimensional parameter space. We can group them into three different types of experiments, but the visualisation reveals much more structure than that!]

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# Going into details

<br>

.large[Focusing on one group, we can for example compare in detail the distributions obtained for different experiments, visually identify outlying points]
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# Summary

.large[&#9655; Projections and the grand tour allow to examine high dimensional data distributions in detail]

.large[&#9655; We can learn about shapes in high dimensional space, compare groups or identify outlying points]

.large[&#9655; This can provide valuable insights and intuition for researchers]

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#Thanks!

.large[These slides are made with R markdown using xaringan and the Kunoichi theme.]

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# References

.large[See https://uschilaa.github.io for references and additional resources!]