class: center, middle, inverse, title-slide # <i class="fas fa-cubes "></i> Visualisation of high-dimensional particle physics data ### <br><br> Di Cook, Ursula Laa <br><br> Monash University ### <a href="bit.ly/ISCB-Cook" class="uri">bit.ly/ISCB-Cook</a> <br><br> <br><br>Aug 28, 2018 --- background-image: url(img/You_can't_see_beyond_3D.png) background-size: contain .left-column[ # High-dimensions ### You can't see beyond 3D ] .right-column[  ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ] .right-column[  Source: https://ultraculture.org/blog/2014/12/16/heres-visual-guide-10-dimensions-reality/ ] --- class: inverse middle center [Its not like that at all!](https://media1.tenor.com/images/d4c398703092842d4d17020b5414b0ee/tenor.gif?itemid=4995777) --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ### Its more like... [Flatland: A Romance of Many Dimensions (1884) Edwin Abbott Abbott](https://en.wikipedia.org/wiki/Flatland) ] .pull-right[ <p> <img src="img/Houghton_EC85_Ab264_884f_-_Flatland,_cover.jpg" width="80%"> The story describes a two-dimensional world occupied by geometric figures, where women are simple line-segments, and men are polygons with various numbers of sides. ] --- # How we see high-dimensions in statistics.. <img src="img/cubes.png" width="100%"> Increasing dimension adds an additional orthogonal axis. <p>If you want more high-dimensional shapes there is an R package, [geozoo](http://schloerke.com/geozoo/all/), which will generate cubes, spheres, simplices, mobius strips, torii, boy surface, enneper surface, dini surface, klein bottles, cones, various polytopes, ... --- .left-column[ # High-dimensions ### You can't see beyond 3D ### A universe of 10 dimensions ### Its more like... ### And in statistics it is everywhere ] .right-column[ - Principal component analysis - Multidimensional scaling - Projection pursuit - Regression - Linear discriminant analysis - Multivariate distributions - Posterior distributions ] --- class: center <iframe src="s5.html" width="800" height="500" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe> Can you tell the difference between these 5D objects? -- <p> .red[ Yep? You can see beyond 3D!] --- class: center <iframe src="multiDA.html" width="700" height="400" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe> Can you tell the difference between these 10D objects? -- <p> .red[ Yep? You really can see beyond 3D!] -- <p> Set A are genes identified by Sarah Romanes [multiDA](https://github.com/sarahromanes/multiDA) procedure; set B are a random sample of genes. Sarah's selection are much more distinctly different than the random sample. --- .left-column[ # Packages <img src="img/tour_path.png" width="300px"> ] .right-column[ - Visualisation of high-dimensions using tours: the [tourr](https://cran.r-project.org/web/packages/tourr/index.html) package - *Grand:* Randomly choose target - *Little:* Basis of *d* of the *p* variables - *Local:* Randomly within a small radius - *Guided:* Define structure of interest in projection, and optimise function - *Manual:* Control the contribution of a single variable, and move along this axis (coming soon in the R package `spinifex`) - A library of high-dimensional shapes: the [geozoo](https://cran.r-project.org/web/packages/geozoo/index.html) package, and paper [Escape from Boxland](https://journal.r-project.org/archive/2016/RJ-2016-044/index.html) ] --- # Philosophy - It is common to show the data in the model space, for example, predicted vs observed plots for regression, linear discriminant plots, and principal components. - By displaying the model in the high-d data space, rather than low-d summaries of the data produced by the model, we expect to better understand the fit. .footnote[Wickham et al (2015) Visualizing statistical models: Removing the blindfold, SAM] --- # Hierarchical clustering Dendrogram: .red[data] in the .red[model space] .pull-left[ <img src="figure/unnamed-chunk-3-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ <img src="figure/unnamed-chunk-4-1.svg" style="display: block; margin: auto;" /> ] --- Tour: .red[Model] in the .red[data space] .pull-left[ <iframe src="single.html" width="400" height="500" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe> ] .pull-right[ <iframe src="ward.html" width="400" height="500" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe> ] --- # Summary - The tourr package is available for you to look beyond 2D - High-dimensional shapes, how they are defined, what they look like, how they differ is interesting - Think about ways to look at the model in the data space --- # Multidimensional physics You can read what we are doing with physics data here: [Dynamical projections for the visualization of PDFSense data](https://arxiv.org/abs/1806.09742) Dianne Cook, Ursula Laa, German Valencia --- class: inverse # Joint work! - *Tours:* Andreas Buja, Debby Swayne, Heike Hofmann, Hadley Wickham, Ursula Laa and Nick Spyrison - *Library of high-d shapes:* Barret Schloerke - *Physics application:* Ursula Laa, German Valencia - Animations made with [plotly](https://plotly-book.cpsievert.me) Contact: [<i class="fas fa-envelope "></i>](http://www.dicook.org) dicook@monash.edu, [<i class="fab fa-twitter "></i>](https://twitter.com/visnut) visnut, [<i class="fab fa-github "></i>](https://github.com/dicook) dicook <img src="img/lorikeets.png" width="200px"> .footnote[Slides made with Rmarkdown, xaringan package by Yihui Xie, and lorikeet theme using the [ochRe package](https://github.com/ropenscilabs/ochRe). Available at [https://github.com/dicook/ISCBASC2018](https://github.com/dicook/ISCBASC2018].) --- # Further reading - Buja et al (2004) [Computational Methods for High-Dimensional Rotations in Data Visualization](http://stat.wharton.upenn.edu/~buja/PAPERS/paper-dyn-proj-algs.pdf) - Cook, D., and Swayne, D. [Interactive and Dynamic Graphics for Data Analysis with examples using R and GGobi](http://www.ggobi.org) - Wickham et al (2011) [tourr: An R Package for Exploring Multivariate Data with Projections](http://www.jstatsoft.org/v40) - Wickham et al (2015) Visualising Statistical Models: Removing the Blindfold (with Discussion), Statistical Analysis and Data Mining. - Schloerke, et al (2016) [Escape from Boxland](https://journal.r-project.org/archive/2016/RJ-2016-044/ index.html) --- class: middle center <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png" /></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a>.