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

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/DeepFindr . The first 200 of you will get 20% off Brilliant’s annual premium subscription ▬▬ 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 ▬▬ Support me if you like 🌟 ►Link to this channel: https://bit.ly/3zEqL1W ►Support me on Patreon: https://bit.ly/2Wed242 ►Buy me a coffee on Ko-Fi: https://bit.ly/3kJYEdl ►E-Mail: [email protected] ▬▬ Used Music ▬▬▬▬▬▬▬▬▬▬▬ Music from #Uppbeat (free for Creators!): https://uppbeat.io/t/sulyya/weather-compass License code: ZRGIWRHMLMZMAHQI ▬▬ Used Icons ▬▬▬▬▬▬▬▬▬▬ All Icons are from flaticon: https://www.flaticon.com/authors/freepik ▬▬ 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 ▬▬ My equipment 💻 - Microphone: https://amzn.to/3DVqB8H - Microphone mount: https://amzn.to/3BWUcOJ - Monitors: https://amzn.to/3G2Jjgr - Monitor mount: https://amzn.to/3AWGIAY - Height-adjustable table: https://amzn.to/3aUysXC - Ergonomic chair: https://amzn.to/3phQg7r - PC case: https://amzn.to/3jdlI2Y - GPU: https://amzn.to/3AWyzwy - Keyboard: https://amzn.to/2XskWHP - Bluelight filter glasses: https://amzn.to/3pj0fK2