Multidimensional Scaling (MDS) | Dimensionality Reduction Techniques (3/5)

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▬▬ Papers / Resources ▬▬▬
Colab Notebook: https://colab.research.google.com/drive/1n_kdyXsA60djl-nTSUxLQTZuKcxkMA83?usp=sharing

Kruskal Paper 1964: http://cda.psych.uiuc.edu/psychometrika_highly_cited_articles/kruskal_1964a.pdf
Very old MDS Website: http://www.analytictech.com/borgatti/mds.htm
Rearrange Scalar Product:
- https://www.sjsu.edu/faculty/guangliang.chen/Math250/lec10mds.pdf
- https://github.com/drewwilimitis/Manifold-Learning/blob/master/Multidimensional_Scaling.ipynb
Metrics Blog Post: https://towardsdatascience.com/9-distance-measures-in-data-science-918109d069fa
Proof that MDS has no unique solution: https://github.com/drewwilimitis/Manifold-Learning/blob/master/Multidimensional_Scaling.ipynb

Best MDS Tutorials:
- https://www.jstatsoft.org/article/download/v073i08/1052
- https://rich-d-wilkinson.github.io/MATH3030/6-mds.html
- https://pages.mtu.edu/~shanem/psy5220/daily/Day16/MDS.html
- https://www.stat.pitt.edu/sungkyu/course/2221Fall13/lec8_mds_combined.pdf
- Past, Present & Future of MDS: https://repub.eur.nl/pub/39177/EI2013-07.pdf
- https://jessicastringham.net/2018/05/20/Multidimensional-Scaling/
- https://ccrma.stanford.edu/~unjung/mylec/mds.html
- https://github.com/drewwilimitis/Manifold-Learning/blob/master/Multidimensional_Scaling.ipynb
- http://cda.psych.uiuc.edu/mds_509_2013/borg_groenen/chapter_nine.pdf
- https://rstudio-pubs-static.s3.amazonaws.com/243040_fd2c3a25f33e48db994a01b517cbc341.html

Tübingen University Video:
https://www.youtube.com/watch?v=tJBVC2kzPCY&t=1340s&ab_channel=T%C3%BCbingenMachineLearning

Image Sources:
- https://www.researchgate.net/figure/36-sentiment-words-multidimensional-scaling-MDS-map-Reproduced-with-permission-from_fig2_333771792

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▬▬ Timestamps ▬▬▬▬▬▬▬▬▬▬▬
00:00 Introduction
00:36 Why learning old stuff?
01:19 Basics of MDS
02:26 Example from Psychometrics
03:50 Symmetry of Distance Matrix
04:17 Mathematical Framework
05:58 3 MDS Variants
07:20 Symbolic notations
07:45 Classical MDS (potentially boring)
12:31 Metric MDS
20:25 Brilliant.org Sponsoring
21:31 Code
25:20 Non-metric MDS
28:26 Summary Table

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