Multivariate Data Visualization and Thinking

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# .monash-blue[Multivariate Data Visualization and Thinking]
 
<h2 style="font-weight:900!important;">IFFRUG</h2>
.bottom_abs.width100[
 
*Nicholas Spyrison* 
[nspyrison.netlify.app](https://nspyrison.netlify.app/) Nicholas.Syrison@iff.com 
IFF, Madison 
April 2023 
Slides -- [nspyrison.github.io/pred_ebs](https://nspyrison.github.io/pred_ebs/#1)
]
---

# Terminology & bias

- Stats background, your preferred terms may vary
- __Variable__ - _p_, attribute, measure, column
- __Observation__ - _n_, item, instance, sample, repetition, row
- __Projection__ - an embedded space, of _d < p_ dimension
- __Dimension__ - Overloaded, but __p__ data or approximated space, __d__ projection
- R, Grammar of Graphics, & __ggplot2__

# Etiquette

- Please interrupt for clarifications & elaboration
- Tangential or extension questions at the end, time permitting

---

# Contents

- Context and data
- Traditional techniques
- Dimension reduction
- Tours
- Cheem

---

# Context: data types

<img src="./figures/munzner_datatypes.PNG" width="70%" style="display: block; margin: auto;" />
*Munzner, 2014*

- Complete numerical matrix
- Alternatively, feature decomposition of other formats

---

# Example data -- Palmer penguins

- Penguins near Palmer Station, Antarctica
- 330 observations
- X variables: 4 physical measurements
- Species of penguin mapped to color & shape

<table>
 <thead>
 <tr>
 <th style="text-align:right;"> bill_length_mm </th>
 <th style="text-align:right;"> bill_depth_mm </th>
 <th style="text-align:right;"> flipper_length_mm </th>
 <th style="text-align:right;"> body_mass_g </th>
 <th style="text-align:left;"> species </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:right;"> 39.1 </td>
 <td style="text-align:right;"> 18.7 </td>
 <td style="text-align:right;"> 181 </td>
 <td style="text-align:right;"> 3750 </td>
 <td style="text-align:left;"> Adelie </td>
 </tr>
 <tr>
 <td style="text-align:right;"> 39.5 </td>
 <td style="text-align:right;"> 17.4 </td>
 <td style="text-align:right;"> 186 </td>
 <td style="text-align:right;"> 3800 </td>
 <td style="text-align:left;"> Adelie </td>
 </tr>
 <tr>
 <td style="text-align:right;"> 40.3 </td>
 <td style="text-align:right;"> 18.0 </td>
 <td style="text-align:right;"> 195 </td>
 <td style="text-align:right;"> 3250 </td>
 <td style="text-align:left;"> Adelie </td>
 </tr>
 <tr>
 <td style="text-align:right;"> 36.7 </td>
 <td style="text-align:right;"> 19.3 </td>
 <td style="text-align:right;"> 193 </td>
 <td style="text-align:right;"> 3450 </td>
 <td style="text-align:left;"> Adelie </td>
 </tr>
 <tr>
 <td style="text-align:right;"> 39.3 </td>
 <td style="text-align:right;"> 20.6 </td>
 <td style="text-align:right;"> 190 </td>
 <td style="text-align:right;"> 3650 </td>
 <td style="text-align:left;"> Adelie </td>
 </tr>
 <tr>
 <td style="text-align:right;"> 38.9 </td>
 <td style="text-align:right;"> 17.8 </td>
 <td style="text-align:right;"> 181 </td>
 <td style="text-align:right;"> 3625 </td>
 <td style="text-align:left;"> Adelie </td>
 </tr>
</tbody>
</table>

---

# Scatterplot matrix (SPLOM, small multiples)

<img src="images/index.rmd/unnamed-chunk-4-1.png" width="50%" style="display: block; margin: auto;" />
_Chambers, 1983_

```
GGally::ggpairs(...)
```

- Scalability?
- Structure in 3+ variables?

---

# Parallel coordinate plot

<img src="images/index.rmd/unnamed-chunk-5-1.png" width="50%" style="display: block; margin: auto;" />
_Ocagne, 1885_
```
GGally::ggparcoord(...)
```

- Scalability?
- Poor comparison across non-adjacent variables; asymmetric across variable order
- Correlation is harder to extract

---

# Bonus: observation-based (observation-mapped axes)

- Scalability? Interpretability? Correlation?
- Asymmetric across variable order

---

# Bonus: Chernoff faces

- Scalability? Interpretability? Correlation?

```
tourr::animate_faces() ## Only for fun?
```

---

# Dimension reduction

**Linear**

- *Affine* transformations: "parrellel lines stay parrellel"
- Examples:
    - Principal Component Analysis (PCA), oriented by variance
    - Linear Discriminant Analysis (LDA), oriented by the separation of the supervised class
    - Visualization _tours_ (next section)

**Nonlinear**

- Other transformations: variable interactions, exponents, _etc._
- Examples:
    - Sammon mapping
    - Self Organizing Maps (SOM)
    - t-distributed Stochastic Neighbor Embedding (tSNE)
    - Uniform Manifold Approximation and Projection (UMAP)

---

# Nonlinear projections

Good news; you are already familiar with `$(p=3, d=2)$` non-linear projections!

<img src="./figures/intuition_nonlinear_proj.PNG" width="60%" style="display: block; margin: auto;" />
[wikipedia - Map projections](https://en.wikipedia.org/wiki/Map_projection)

- Inconsistent space; hard to explain & interpret
- Many methods, many hyperparmeters; how _faithful_ is the representation?

“All non-linear projections are wrong, but some are useful.”
 --- Anatasios Panagiotelis (play on George Box’s quote about models)

---
class: transition

## Linear projections & _tours_

---

# Linear projections -- intuition

Good news; you are already familiar with ($p=3, d=2$) linear projections!

- Not all orientations hold interesting structure
- But structural information could be gleaned from rotation

---

# Linear projections  -- rotation

<img src="./figures/linear_proj_wide.png" width="100%" style="display: block; margin: auto;" />
LDA: _Fischer, 1936_, supervised cluster separation

Given the distributions and orientations of different clusters, find a basis (rotation) that separate clusters the most

- Often times our output space is of the same dimensionality as our input space
    - eg. PCA returns a `$pxp$` basis
    - The reduction happens when the space is approximated with fewer components, often involving guided, but _subjective_ selection. eg. Finding an "elbow" in screeplot
    - Or worse -- only showing PC1:2, with no recognition or discussion of the others

---

# Linear projections -- traditional process

1) Scale each variable to [0, 1] or by standard deviations away from the mean (z-score) 
2) Some people 'whiten' or 'sphere' transform the covariance matrix to an identity matrix; should be justified 
3) If `$p$` is sizable, say more than 10 or, may first approximate the data in fewer components to get to a realistic dimensionality to view
- Typically with PCA by eyeballing an elbow in the screeplot
- "We approximate 90% of the variation of our 20 variable in the first 5 principal components"
- Alternative mathematical approximations: "intrinsic dimensionality estimation"

4) Visualize data- or component- space

--
 
Visualize _one rotation (or more if lucky);_ **static, not interactive**

---

# Tours

- Instead of viewing only static views, *animate* small changes in the basis over time
    - Object permanence between frames; can see observations and cluster moving together

<img src="./figures/tour_frames.PNG" width="50%" style="display: block; margin: auto;" />
*Buja et al., 2005*

---

# Grand tour
*Asimov, 1984*

.left-two-thirds[
<img src="./figures/grand_tour.gif" width="100%" style="display: block; margin: auto;" />
]

.right-third[
```
library(spinifex)
grand_tour() %>%
  ggtour() +
  proto_point() +
  proto_basis() +
  proto_origin() %>%
  animate_gganimate()
```
]

---

# Tour taxonomy

Distinguished by how the basis path is produced

<table>
 <thead>
 <tr>
 <th style="text-align:left;"> Tour type </th>
 <th style="text-align:left;"> Target bases </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:left;"> grand </td>
 <td style="text-align:left;"> random bases </td>
 </tr>
 <tr>
 <td style="text-align:left;"> guided </td>
 <td style="text-align:left;"> objective function (simulated annealing) </td>
 </tr>
 <tr>
 <td style="text-align:left;"> manual </td>
 <td style="text-align:left;"> change the contribution of selected variable </td>
 </tr>
 <tr>
 <td style="text-align:left;"> local </td>
 <td style="text-align:left;"> random bases within a local vacinity </td>
 </tr>
 <tr>
 <td style="text-align:left;"> _et al._ </td>
 <td style="text-align:left;"> slicing, lensing </td>
 </tr>
</tbody>
</table>

- The grand tour is good for EDA, but selects target frames randomly, no objective function
- Hypothesis; Bill length is important for distinguishing the orange cluster
- Issue; Component spaces and grand tour have no user interaction to "steer" the basis
- Response; Control its contribution with a _manual tour_

---

# Manual tour
*Cook & Buja, 1997. Spyrison & Cook, 2020*

.left-two-thirds[
<img src="./figures/manual_tour.gif" width="100%" style="display: block; margin: auto;" />
]

.right-third[
```
manual_tour() %>%
  ggtour() +
  proto_point() +
  proto_basis() +
  proto_origin() %>%
  animate_gganimate()
```
]

---

# Tours in R

<table>
 <thead>
 <tr>
 <th style="text-align:left;"> Package </th>
 <th style="text-align:left;"> Description </th>
 <th style="text-align:left;"> Authors </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:left;"> {tourr} </td>
 <td style="text-align:left;"> Tour paths, geodesic interpolation, display in *interactive* base R </td>
 <td style="text-align:left;"> Wickham et al., 2011 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> _{spinifex}_ </td>
 <td style="text-align:left;"> Manual tours, compose animations exportable to plotly/gganimate </td>
 <td style="text-align:left;"> Spyrison &amp; Cook, 2020 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> {ferrn} </td>
 <td style="text-align:left;"> Diagnostic plots for projection pursuit (guided tour), tracing basis-paths </td>
 <td style="text-align:left;"> Zhang et al., 2021 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> {liminal} </td>
 <td style="text-align:left;"> Ensemble graphics with tSNE and tours side-by-side </td>
 <td style="text-align:left;"> Lee, 2021 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> {loon.tour} </td>
 <td style="text-align:left;"> Graphics display system 'loon' for tours </td>
 <td style="text-align:left;"> Xu &amp; Oldford, 2021 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> _{cheem}_ </td>
 <td style="text-align:left;"> Explore local explanations of non-linear models with the radial tour </td>
 <td style="text-align:left;"> Spyrison, 2022 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> {detour} </td>
 <td style="text-align:left;"> Alternative HTML with brushing and 3D proj, but no basis </td>
 <td style="text-align:left;"> Hart &amp; Wang, 2022 </td>
 </tr>
</tbody>
</table>

- Reminder: other geometric display can be used when `$d!=2$`
    - 1D density curves
    - 3D scatterplot
    - `$d$`-dim scatterplot matrix, parallel coordinate plots

---

# Overview tours

Also see: [A review of State-of-the-Art on Tours, arxiv.org/pdf/2104.08016.pdf](https://arxiv.org/pdf/2104.08016.pdf), preprint of accept WIREs article

- User interaction
- Basis paths, as inscribed on `$p-$`spheres/torii
- Slicing to explore hollowness and structure
- Scalar Vector Machine boundaries
- Guided tours on classification Random Forests
- Visualizing neural networks

---
class: transition

## Local explanation of a black-box models & application of radial tours, _cheem_

---

# Local explanation

- Given a non-linear ("blackbox") model, how can we maintain interpretability
- Approximation of the linear variable importance to the model in the vicinity of _one_ observation of a model

<img src="./figures/lime_nonlinear.png" width="60%" style="display: block; margin: auto;" />
_Ribeiro, et al. (2017). Why Should I Trust You?_

---

.pull-left[
# SHAP values

- SHapley Additive exPlanation
- FIFA 2020 data, 5000 observations, ~35 skill measurements aggregated to 9 variables, Y: wages [2020 Euros]
- Model: Random forest regressing wages from 9 skill measurements
- SHAP is a model-agnostic local explanation
- Approximate linear variable importance at one observation; the median importance, permuting over combinations of the explanatory variables

**The model has very different variable importance across the player position**
]

.pull-right[
<img src="./figures/cheem_fifa_messi_dijk.png" width="100%" style="display: block; margin: auto;" />
]

---

# Cheem, concept

- Create a non-linear model
- Extract explanations for every observation (computationally expensive)
- __Global view__: approximate data- and attribution-space side-by-side
    - Explore with liked brushing, tooltips, interactive tabular display
    - Select a primary and comparison point to explore their explanation
- __Cheem radial tour__:
    - Primary point attribution of the becomes the initial basis
    - Evaluate/explore the explanation by testing the support of variable contributions

--
 
__New__, at a github server near you,

- model- and local explanation-agnostic (BYO)
- Illustrationed with random forests and a tree SHAP (reduced computational complexity)

---

# Global View

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- Select a primary and comparison point, typically misclassified and neighboring correctly classified
- Use the SHAP values of the primary point as the basis, perform a 1D radial (manual) tour to interrogate the models explanation

???

- PC1:2 of data (left) and SHAP (right)
- Points color and shape are mapped to *predicted* cluster
- Misclassified have red circle

---

.left-third[
# Cheem radial tour

- Primary & comparison observation: dashed & dotted lines
- SHAP values displayed as parallel coordinate lines on basis

- **The misclassified point downplays the weight on V2; this discrepancy is a measure of how differently this misclassified point is, compared with its peers**
]

.right-two-thirds[
<img src="./figures/cheem_tour.gif" width="100%" height="600px" style="display: block; margin: auto;" />
]

---

# Demo the app

Explore interactively with an R shiny application

Local resources:

```r
cheem::run_app()
```

- Externally hosted shiny app (outdated): [ebsmonash.shinyapps.io/cheem_initial/](https://ebsmonash.shinyapps.io/cheem_initial/)
- __cheem__ (back) on CRAN soon, available on GitHub: [github.com/nspyrison/cheem](https://github.com/nspyrison/cheem)

---

# Cheem -- getting started

```
## Install cheem development version & its CRAN dependancies.
remotes::install_github("nspyrison/cheem", dependencies = TRUE)
## Run the {cheem} app
cheem::run_app()
## BYO data, model, local explanation:
?cheem::cheem_ls
```

---

# Namesake

- __Cheem__ are a fictional race of bipedal trees from the Dr. Who universe
- (Original implementation) on tree based models, __DALEX__ ecosystem

---

# Acknowledgments

Thanks to Professor Przemyslaw Biecek for his guidance and input, in addition to the __DALEX__ package ecosystem and _Exploratory Model Analysis_ book

Thanks to Di Cook and Kim Marriott for their supervision

This research was supported by an Australian government Research Training Program (RTP) scholarship. These slides created in __R__ using __rmarkdown__ and __xaringan__ *(R Core Team, 2021; Xie et al. 2018; Xie, 2018)*

_Tentatively,_ IFF may support continued development of related content; broader preprocessing functions, more/better geom-like displays

---
background-size: cover
class: title-slide
count: false

# Thank you for attending
<hr> 
<h2 class="monash-blue" style="font-size: 20pt!important;">Multivariate Data Visualization and Thinking</h1>
 
<h3 style="font-weight:900!important;">IFFRUG</h2>
.bottom_abs.width100[
 
*Nicholas Spyrison* 
[nspyrison.netlify.app](https://nspyrison.netlify.app/) Nicholas.Syrison@iff.com 
IFF, Madison 
April 2023 
Slides -- [nspyrison.github.io/pred_ebs](https://nspyrison.github.io/pred_ebs/#1)
]