Dimensionality Reduction Techniques | Introduction and Manifold Learning (1/5)

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▬▬ Papers / Resources ▬▬▬
Intro to Dim. Reduction Paper:
https://drops.dagstuhl.de/opus/volltexte/2012/3747/pdf/12.pdf

T-SNE Visualization Video:
https://www.youtube.com/watch?v=wvsE8jm1GzE&ab_channel=GoogleforDevelopers

On the Surprising Behavior of Distance Metrics in High Dimensional Space: https://link.springer.com/chapter/10.1007/3-540-44503-X_27

On the Intrinsic Dimensionality of Image Representations
https://arxiv.org/abs/1803.09672

Manifold Learning Intro:
https://nbviewer.org/github/drewwilimitis/Manifold-Learning/blob/master/Manifold_Learning_Intro.ipynb

Cornell Lecture Dim.Red:
https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/lecturenote02_kNN.html

Curse of Dimensionality:
https://www.visiondummy.com/2014/04/curse-dimensionality-affect-classification/

Manifold visualization:
https://minimal.sitehost.iu.edu/archive/NonOrientable/NonOrientable/Bryant-anim/web/index.html

Dimensionality reduction by UMAP to visualize physical and genetic interactions:
https://pubmed.ncbi.nlm.nih.gov/32210240/

Dimensionality reduction and clustering of time series for anomaly detection in a supermarket heating system
https://iopscience.iop.org/article/10.1088/1742-6596/2042/1/012027/pdf

Dynamical Analysis of the Dow Jones Index Using Dimensionality Reduction and Visualization
https://www.mdpi.com/1099-4300/23/5/600

Image Sources:
MNIST Cloud: https://colah.github.io/posts/2014-10-Visualizing-MNIST/
Word Embeddings Cloud: https://www.ruder.io/word-embeddings-1/
Molecules Cloud: https://www.nature.com/articles/s41524-023-01099-0
Manifold Visualization: https://minimal.sitehost.iu.edu/archive/NonOrientable/NonOrientable/Bryant-anim/web/index.html
Swiss Roll: https://freepik.com/free-photos-vectors/swiss-roll
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▬▬ Timestamps ▬▬▬▬▬▬▬▬▬▬▬
00:00 Introduction
00:35 Basics
01:35 Taxonomy and Overview
02:54 Dim. red. Math Definition
04:01 Curse of Dimensionality
05:55 Brilliant.org Sponsor
07:08 Blessing of Non-Uniformity
08:37 Manifolds
10:00 Manifold Learning / Manifold Hypothesis
11:17 Real-world examples
12:22 Take Aways

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