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<!DOCTYPE html>
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<head>
<title>Geometric Morphometrics (GMM) and Archaeological Science</title>
<meta charset="utf-8" />
<meta name="author" content="Dr. Christian Hoggard" />
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class: center, middle, inverse, title-slide
# Geometric Morphometrics (GMM) <br/> and Archaeological Science
### Dr. Christian Hoggard
### July 2020
---
class: center, middle
# Welcome to these workshops!
---
class: left
# Instructor
**Dr. Christian Steven Hoggard** (Visiting Fellow, University of Southampton)
[<svg style="height:0.8em;top:.04em;position:relative;" viewBox="0 0 512 512"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg> @cshoggard](http://twitter.com/cshoggard) / [<svg style="height:0.8em;top:.04em;position:relative;" viewBox="0 0 496 512"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> @cshoggard](http://github.com/cshoggard) / [<svg style="height:0.8em;top:.04em;position:relative;" viewBox="0 0 640 512"><path d="M592 0H48C21.5 0 0 21.5 0 48v320c0 26.5 21.5 48 48 48h245.1v32h-160c-17.7 0-32 14.3-32 32s14.3 32 32 32h384c17.7 0 32-14.3 32-32s-14.3-32-32-32h-160v-32H592c26.5 0 48-21.5 48-48V48c0-26.5-21.5-48-48-48zm-16 352H64V64h512v288z"/></svg> www.sites.google.com/site/christianhoggard](https://www.sites.google.com/site/christianhoggard/home)
[<svg style="height:0.8em;top:.04em;position:relative;" viewBox="0 0 512 512"><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> C.S.Hoggard@soton.ac.uk](mailto:C.S.Hoggard@soton.ac.uk)
Research Interests:
1. Quantitative Archaeology in the R Environment
2. The European Lower and Middle Palaeolithic
3. Cultural Evolution and Taxonomies
4. Open Science Approaches to Archaeology
Previous Workshops:
* September 2019: [Sendai (Japan)](https://github.com/CSHoggard/-Morph2019)
* December 2019: [Cologne (Germany)](https://github.com/CSHoggard/-cologne_workshop)
* May 2020: [#StayHomeButStudy (Online)](https://github.com/CSHoggard/-workshopjapan2020)
Publications:
[Click here](https://www.sites.google.com/site/christianhoggard/home/publications)
---
# Workshop Structure
There are **three workshops** in total...
--
- **Workshop One** (now): Introduction to GMM and Archaeology
--
- **Workshop Two** (20th July): Landmark-based approaches to GMM (R practical: Geomorph/Tidyverse)
--
- **Workshop Three** (27th July): Outline-based approaches to GMM (R practical: Momocs/Tidyverse)
--
About these workshops...
- No prior experience in R is necessary 😄
- All data and R Markdowns (documents and presentations) are on [GitHub](https://www.github.com/CSHoggard/-gmm_liverpool_2020)
- Additional software demonstrations: IDAV Landmark Editor (Checkpoint) and TPSdig2/TpsUtil
- Breaks throughout the workshops will facilitate additional questions and guidance! ✔️
---
class: inverse, left
# What are we going to do today?
I will introduce the subject of geometric morphometrics (GMM), specifically:
1. Shape and shape theory
2. Advantages (and disadvantages) of using GMM
3. History of GMM
4. How we 'do' GMM (data creation, transformation, analysis and visualisation)
---
background-image: url(figures/math.jpg)
background-size: contain
---
class: inverse, middle, center
# GMM & Archaeological Science ✨
---
background-image: url("figures/selden_et_al_2018.PNG")
background-size: 75%
background-position: 50% 30%
.footnote[Selden, R.Z. et al. (2018). Lithic morphological organisation: Gahagan bifaces from the Southern Caddo Area. *Digitial Applications in Archaeology and Cultural Heritage* 10: e00080.]
---
background-image: url("figures/mounier_et_al_2018.jpg")
background-position: center
background-size: 35%
background-position: 50% 30%
.footnote[Mounier, A. et al. (2018). Who were the Nataruk people? Mandibular morphology among late Pleistocene and early Holocene fisher-forager populations of West Turkana (Kenya). *Journal of Human Evolution* 121: 235-253.]
---
class: left, bottom, inverse
# But what is shape?
---
class: left
background-image: url("figures/circles.jpg")
background-position: center
background-size: 45%
background-position: 50% 60%
# Shape as...
“In general terms, the shape of an object, dataset or image that can be defined as the total of all information that is invariant under **translation**, **rotation**, and **isotropic rescalings**” (Small, 1996: 6)
.footnote[Small, C. (1996). *The statistical theory of shape*. New York: Springer.]
---
class: center
background-image: url("figures/hippo.jpg")
background-position: center
background-size: 35%
background-position: 50% 70%
# But what about size?
Do we use the length? the volume of the object? the mass of an object?
---
class: center, bottom
background-image: url("figures/mitteroecker_et_al_2013.jpg")
background-position: center
background-size: 35%
background-position: 50% 30%
**Centroid size:** square root of the summed squared lengths of the dashed lines
.footnote[Mitteroecker et al. (2013). A brief review of shape, form, and allometry in geometric morphometrics, with applications to human facial morphology. *Hysterix, the Italian Journal of Mammalogy*: 59-66.
]
---
class: center, middle
background-image: url("figures/ssf.jpg")
background-position: center
background-size: 60%
background-position: 50% 50%
---
class: inverse, left
# Morphometrics 101
* Term: Professor of Zoology Robert Blackith (1957)
* Quantitative study of shape, shape variation and shape covariation
* Two types of morphometric studies:
- Traditional morphometrics (length measurements, angles, ratios…)
- Geometric morphometrics or GMM (landmarks, outlines, curves, surfaces…)
---
class: left
# Benefits and Drawbacks
.pull-left[###👍 Benefits 👍
- Degree of **shape resolution**
- **Information loss** (vs. linear measurements)
- **Data can easily be collected** from methods including photographs, drawings and scans
- Abstraction and registration procedure allow an analysis of **shape *sensu stricto***
- Useful **visualisation** tool]
.pull-right[### 👎 Drawbacks 👎
- Required **skill level** (software, statistics...)
- **Proceduralisation** (R is helping!)
- **Landmark subjectivity**]
---
class: inverse, center
# We can use GMM to determine whether…
#### two or more assemblages are different in shape?
#### shape is related to: size? sex? raw material? hominin?
#### shape differences correspond to a hypothesis or a model?
#### mean or median shapes are representative of a site?
#### there are biologically inherent relationships?
#### networks of specific shapes can be identified? (over several sites)
---
class: bottom
background-image: url("figures/time.jpg")
background-size: contain
background-size: 40%
background-position: 95% 20%
#A short history of Geometric Morphometrics...
---
class: left
background-image: url("figures/metmuseum.jpg")
background-size: 50%
background-position: 50% 75%
# Albrecht Dürer (1471-1528)
* Renaissance Paint, printer, theorist and **founder of descriptive geometry**
* Worked on helices, conchoids, epicycloids and the Delian Problem (doubling the cube)
* **Grid transformations** to catalogue and investigate morphological variation
.footnote[*Draughtsman Making a Perspective Drawing of a Reclining Woman* c. 1525 Albrecht Dürer (The Met Museum: Public Domain).]
---
class: left
background-image: url("figures/dwt.jpg")
background-size: 30%
background-position: 95% 50%
### Sir D’Arcy Wentworth Thompson (1860-1948)
* Biologist, mathematician and classics scholar
* Famous for his quotes on the mathematical beauty of nature <br> (inspiring Huxley, Turing, Lévi Strauss and van der Rohe) <br/> <br> <br/>
### On Growth and Form (1916)
* **Fundamental book on morphological variation in nature**
* Emphasis on **mathemtical structures** accounting for diversity
* Counter-argument to **vitalism** (while challenging **natural selection**)
.footnote[Professor Sir D'Arcy Wentworth Thompson (after a 1938 original). <br> *David Shanks Ewart (1901-1965). University of Dundee Fine Art Collections.* CC BY-NC-ND. <br/>]
---
class: bottom, center
background-image: url("figures/thompson.jpg")
background-size: 30%
background-position: 50% 25%
Thompson, D.W. (1917). *On Growth and Form*. Cambridge University.
---
class: left
# Transition to Multivariate Morphometrics
* **Fred Bookstein**: Cartesian transformations, Bookstein transformations, etc.
* **David George Kendall (1918-2007)**: Objects of the same shape as seperate points in a geometric space
* **Miriam Zelditch**: Complex shapes, morphological evolution and ecology
* **Ian Dryden and Kanti Mardia**: Development of Fourier-based outline analysis
* **Norman MacLeod**: Eigenshape analysis and palaeontological applications
* **James Rohlf**: Statistical developments, biological applications and software
---
class: left
# Another Ten Minute Break! ⏰
<br> <br/>
## Any Questions?
### Slack Workspace ("workshop_1") and Zoom!
<div class="countdown" id="timer_5f0732bc" style="top:0;right:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">10</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
---
class: center, middle
background-image: url("figures/coffee.jpg")
background-size: contain
---
class: left
background-image: url("figures/computer.jpg")
background-size: 25%
background-position: 90% 50%
# Stage 1: Collecting Input Data
### Methods include:
- **CT Scanning**
- **Photogrammetry** and **Structure-from-Motion**
- **Structured-light** Scanning
- **Mono IR** (e.g. Kinect) and **Stereo IR** (Intel RealSense) Scanning
- **MicroScribe** digitisers
- **3D scanners** e.g. NextEngine Desktop
- **Photographs**
- **Professional Illustrations**
---
class: left, inverse
background-image: url("figures/claude_2008_1.jpg")
background-size: 35%
background-position: 100% 50%
# Stage 2: Landmark Choice
* Landmarks are central to GMM
* Definition: a coordinate point used to represent a shape <br> and/or a homologous point on a structure <br/>
* Quantifiable as Cartesian coordinates (x, y / z coordinates)
* Flexibility in what types of landmark are required
* Can be treated as individual points [workshop two] <br> or converted into curves and outlines [workshop three] <br/>
.footnote[Claude, J. (2008). *Morphometrics with R*. Springer Publishing.]
---
class: left, inverse
background-image: url("figures/combo.jpg")
background-size: 35%
background-position: 100% 50%
# Stage 2: Landmark Choice
#### Various types of landmarks
* Type I: Homologous biological structures
* Type II: Geometric definition e.g. greatest curvature
* Type III: Point with reference to another point
#### A special case: semi-landmarks
* Placed using an algorithm
* Can cover the whole or part of a shape
* Equidistant and placed between one or two end points
* A special Type III landmark (*sensu* Bookstein)
.footnote[Ros et al. (2013). Geometric morphometric analysis of grain shape and <br> the identification of two-rowed barley (Hordeum vulgare subsp. distichum L.) <br> in southern France. *Journal of Archaeological Science*. 41.]
---
class: left, inverse
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# Stage 2: Landmark Choice
#### Landmarks should...
* sample aspects which are of archaeological interest
* be repeatable and identifiable on all examples (if possible)
* cover as much of the shape as possible
* be sufficient as to not increase the ‘weighting of areas’
* always be plotted in the same order!
.footnote[Ros et al. (2013). Geometric morphometric analysis of grain shape and <br> the identification of two-rowed barley (Hordeum vulgare subsp. distichum L.) <br> in southern France. *Journal of Archaeological Science*. 41.]
---
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# Some observations...
<br>
<br>
<br>
**For archaeological material...** | **For bioarchaeological material...**
--------------------------------------- | ------------------------
Poor morphological correspondence | Greater morphological correspondence
Less intuitive to examine in 3D | More intuitive to examine in 3D...
Fewer number of examples to compare with | Greater number of examples to compare with
Fragmentation: major issue | Fragmentation: major issue
Higher sample size | Lower sample size is necessary (esp. prehistory)
Often outline-centric | Often landmark-centric
<br/> <br/> <br/>
---
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# Stage 3: Landmark digitisation
### A variety of software is available, including:
* TPS Suite (**TpsUtil** and **TpsDig2**)
* CRAN-certified R Packages e.g. **geomorph**, **Momocs**, **StereoMorph** and **shape**
* GitHub-based R Packages e.g. **GUIMorph**
* **SlicerMorph** and **3DSlicer**
* **PhyloNimbus**
* **Stratovan Checkpoint** (£)
* **EVAN Toolkit** (£)
* and many, many more...
Note: IDAV Landmark Editor (no longer available)
Output: various file types including **.tps**, **.nts**, **.csv** and **.txt** formats
---
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# GMM (and Archaeology) in the R Environment
* **Increasing number of packages** for shape (and archaeological) data
* **Powerful** and **fairly straight-forward** to use
* Last decade: **Archaeology as a more code-literate discipline**
* **Advantages in data visualisation**
* Product: **reproducible** and **replicable** **Open Science** approach
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.footnote[https://media.giphy.com/media/l0K4hqqqwgFijgVLa/giphy.gif]
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background-size: 55%
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.footnote[https://xkcd.com/1945/]
---
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# Stage 4: Data screening
* Do all my specimens have the **correct number of points**?
* Are all my landmarks in the **correct order**?
* Are the **ID labels correct**?
* Are they to **scale**? (for size-integrated analyses)
* Are **sliders** defined? (if using sliding semi-landmarks)
### Importance of a code-book
* Necessary to **'know'** your meta-data (e.g. #ID, technology, sex or raw material)
* Ensure all your meta-data is **clear**, **easy to understand** and **formatted appropriately**
---
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# Know your research question!
---
# Ten Minute Break! ⏰
<br> <br/>
## Any Questions?
### Slack Workspace ("workshop_1") and Zoom!
<div class="countdown" id="timer_5f073474" style="top:0;right:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">10</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
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background-size: contain
---
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#Stage 5: Data Registration (isolating shape)
A variety of analyses are available in GMM:
1. **Landmark Analysis** (using landmarks)
2. **Outline Analysis** (using semi-landmarks)
* **Elliptic Fourier Analysis** (semi-landmarks of a closed outline)
* **Radii Fourier Analysis** (semi-landmarks of a closed outline)
* **Discrete Cosine Transform** (semi-landmarks of an open outline)
3. **Miscellaneous**
* **Eigenshape Analysis** (semi-landmarks of a closed outline)
<br>
<center> The registration method changes depending on if you're analysing landmarks or outlines! <center/>
Landmarks: **Generalised Procrustes Analysis** | Outlines: **Fourier-based transformation**
---
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#Generalised Procrustes Analysis (GPA)
#### (Procrustes Superimposition / Procrustes Fitting / Generalised Least Squares)
<br>
### **A procedure to isolate shape from a number of variables: <br> rotation, size and translation.**
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.footnote[https://media.giphy.com/media/11DFuwckOK9mdG/giphy.gif]
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### Generalised Procrustes Analysis
<br>
The raw coordinates (for all shapes) are…
* Translated to a **common centroid** (A-B)
* Scaled to a **common centroid size** (B-C)
* Rotated to **minimise the sum of <br> squared-distances between landmarks** (C-D) <br/>
* Outcome: **Procrustes coordinates** (shape)
<br/>
.footnote[Mitteroecker et al. (2013). A brief review of shape, form, and allometry in geometric morphometrics, <br> with applications to human facial morphology. *Hysterix, the Italian Journal of Mammalogy*. pp. 59-66.] <br/>
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.pull-left[## Why Procrustes?
* Damastes was a son of Poseidon <br> who lived on a sacred way (Attica)
* There he had a bed, in which he invited every passer-by to spend the night. He would set to work on them with his blacksmith's hammer, to stretch them to "fit" the bed
* Nickname: Procrustes ("The Stretcher")
* If the guest proved too tall, Procrustes would amputate the excess length - nobody ever fitted the bed exactly! (**Procrustes Fitting**)
* Procrustes continued his reign of terror until he was "fitted" to his own bed by Theseus!
* Link to source: [click here](https://medium.com/@bradyholmer/the-procrustean-bed-of-science-b499d79b81de)]
---
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# Fourier-based transformation
In these methods, the **semi-landmarks are converted into curves**, <br> and the **coefficients which quantify these curves** are what we examine. <br> For example, in **Elliptic Fourier Analysis (EFA)** *sensu* Kuhl and Giardina (1982)... <br/>
.footnote[ k = the **total number of steps around the outline** <br> n = the **harmonic number** <br> ∆x = the **displacement** between point p and p+1 <br> ∆t = the **length of the step** between point p and p+1 <br> tp = **accumulated length** of step segments at point <br> pT = **sum of lengths** of all steps around outline <br><br>]
---
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## Stage 6: Some Exploratory & Analytical Procedures
Method | Data Input
-------|-----------
**Visualise Shape Change** | Procrustes coord. / Fourier coeff.
**Principal Component Analysis (PCA)**| Procrustes coord. / Fourier coeff.
**Discriminant Analysis (DA/DFA/LDA/CVA)** | Procrustes coord. / Fourier coeff. / PC Scores (+ Factor)
**Procrustes ANOVA / MANOVA** | Procrustes coord. / Fourier coeff. / PC Scores (+ factor)
**Correlation & Regression** | Procrustes coord. / Fourier coeff. / PC Scores (+ quant. variables)
**Tree-building / Cluster Exercises** | Procrustes coord. / Fourier coeff. / PC Scores (+ optional factor)
---
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# Visualising Shape Change
* Useful for comparing **individual** and **mean** shapes
* Shape change can be represented as:
* Deformation grids
* Contours
* Outlines
* Lollipop sticks
* Vectors
.footnote[Claude, J. (2008). *Morphometrics with R*. Springer Publishing.]
---
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background-image: url("figures/scholtz_et_al_2020.PNG")
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.footnote[Scholtz et al. (2020). D'Arcy W. Thompson's Cartesian transformations: a critical evaluation. *Zoomorphology*. (https://doi.org/10.1007/s00435-020-00494-1)]
---
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# Principal Component Analysis (PCA)
* Often the **first exploratory procedure**
* **Ordination (multi-dimensional)** method
* Each coordinate configuration = a shape
* **Principal components = sources of shape variation**
* Axis origin (0,0) = **mean shape**
* Scree plots (for examining PC contributions)
* **Important: total within-group variance is examined <br> and not between-group variance! (factors overlay the plot!)**
.footnote[Hoggard et al. (2019). The Potential of Geometric Morphometrics for Danish Archaeology: Two Case Studies. <br> *Arkæologisk Forum*, 40: 30-42. (http://www.archaeology.dk/16738/Nr.%2040%20-%202019). OSF: https://osf.io/en5d2/ ] <br/>
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---
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background-image: url("figures/vestergaard_and_hoggard_2019_2.jpg")
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## Discriminant Analysis (DA)
* Otherwise known as **Discriminant Function Analysis (DFA)** or...
* **Linear Discriminant Analysis** (LDA)
* **Canonical Variate Analysis** (CVA)
* Investigates *a priori* classification through <br> **maximum between-group classification** <br/>
* Percentage = success of classifier (as based on group data)
* **Jacknifed percentage** 👈👈👈
* **Leave-one-out cross-validation**
* **Success with which a random shape can be correctly classified**
<br><br>
Vestergaard, C. and Hoggard, C.S. (2019). A Novel Geometric Morphometric (GMM) <br>
Application to the Study of Bronze Age Tutuli. *Danish Journal of Archaeology*, 8: 5-28. <br/>
---
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# Procrustes ANOVA / MANOVA
* PCA and DA act as **exploratory devices** for looking at shape difference
* MANOVA and Procrustes ANOVA provide a **statistical framework** for examining shape
* Procrustes ANOVA: performed in `R::Geomorph`
* MANOVA: performed in `R::Momocs`
* **Null Hypothesis: same populations / same shape**
---
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background-image: url("figures/hoggard_et_al_2019b.jpg")
background-position: 95% 50%
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# Correlation and Regression
* Useful for shape vs. quantitative data.
* **Measure of association (impact of unit change)**
* Possible variables:
* **Centroid size**
* **Symmetry**
* **Latitude**
* **Shape score**
* Example methods: `base:: lm ()` or `tidyverse`
.footnote[Hoggard et al. (2019). The application of elliptic Fourier analysis in understanding biface shape <br> and symmetry through the British Acheulean. *Journal of Paleolithic Archaeology*, 2 (2): 115-133.] <br/>
---
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background-image: url("figures/ivanovaite_et_al_2020.jpg")
background-position: 105% 45%
background-size: 50%
# Cluster & Tree Exercises
* Useful for examining *a posteriori* classifications
* A variety of cluster analyses are available:
* `Momocs::CLUST` (Hierarchical Clustering)
* `Rphylip::contml` (Maximum Likelihood)
.footnote[Ivanovaite et al. (2020). All these fantastic cultures? Research history <br> and regionalisation in the Late Palaeolithic tanged point cultures <br> of Eastern Europe. *European Journal of Archaeology*, 23 (2): 162-185.] <br/>
---
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## <center> Technical Notes and Suggestions <center/>
Principal Component Analysis: consider **between-groups PCA (bgPCA)**
Discriminant Analysis: consider **Kovarovic et al. 2011** (notes on sample size!)
Other cool methods:
1) **Machine Learning** (Unsupervised vs. Supervised classificatory methods)
2) **Bayesian Approaches** to GMM
3) **Partial Least Squares (PLS) and Modularity Studies**
.footnote[Kovarovic et al. (2011). Discriminant function analyses in archaeology: are classification rates too good to be true? <br> *Journal of Archaeological Science*, 38: 3008-3018. doi: 10.1016/j.jas.2011.06.028]
---
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# Concluding Remarks
## Geometric Morphometrics = 😍😍😍
<br>
### In the future we will see...
#### a wider application of GMM in Archaeological Science!
#### a more powerful GMM analyses in Archaeological Science!
#### a more open, replicable and reproducible Archaeological Science!
<br/>
---
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# Thank you for listening!
Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan).
The chakra comes from [remark.js](https://remarkjs.com), [**knitr**](http://yihui.name/knitr), and [R Markdown](https://rmarkdown.rstudio.com).
Licensing: Presentation: [CC-BY-3.0](http://creativecommons.org/licenses/by/3.0/us/)
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