t-distributed Stochastic Neighbor Embedding (t-SNE) | Dimensionality Reduction Techniques (4/5)

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

Entropy: https://gregorygundersen.com/blog/2020/09/01/gaussian-entropy/
Attractive / Repulsive Forces Gradient: https://jmlr.org/papers/volume23/21-0055/21-0055.pdf
t-SNE Parameters distill: https://distill.pub/2016/misread-tsne/

Other great resources:
- By the t-SNE author: https://lvdmaaten.github.io/tsne/
- A good view on probability: https://siegel.work/blog/tSNE/
- CalTech tutorial: http://bebi103.caltech.edu.s3-website-us-east-1.amazonaws.com/2016/tutorials/aux8_tsne.html
- Great visuals: https://newsletter.theaiedge.io/p/formulating-and-implementing-the
- SNE vs T-SNE: https://www.linkedin.com/pulse/visualization-method-sne-vs-t-sne-implementation-using-tandia/
- t-SNE in raw numpy: https://nlml.github.io/in-raw-numpy/in-raw-numpy-t-sne
- t-SNE in raw javascript: https://observablehq.com/@nstrayer/t-sne-explained-in-plain-javascript
- Video by the t-SNE author: https://www.youtube.com/watch?v=MgawSHnYQGw&t=2604s&ab_channel=ComputerVisionFoundationVideos
Image Sources:
- Perplexity image: https://stats.stackexchange.com/questions/399868/why-does-larger-perplexity-tend-to-produce-clearer-clusters-in-t-sne
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▬▬ Timestamps ▬▬▬▬▬▬▬▬▬▬▬
00:00 Intro
00:30 Manifold learning
02:40 Relevant Papers & Agenda
03:25 Stochastic Neighbor Embedding (SNE)
03:56 Pairwise distances
04:35 Distance to Probability
06:06 Conditional Probability Math
07:05 Adjustment of Variance
08:20 Perplexity
09:55 How to find the variance
11:15 KL-divergence
12:55 Shepard Diagram
13:15 Gradient and it's interpretation
14:15 N-body simulation
14:35 Full SNE Algorithm
15:15 t-distributed Stochastic Neighbor Embedding (t-SNE)
15:28 Crowding Problem and how to solve it
17:58 Gaussian vs. Student's t Distribution
19:21 Symmetric Probabilities
20:35 Early Exaggeration
22:50 SNE vs. t-SNE
23:08 Brilliant.org Sponsoring
24:14 Code
27:15 Distill.pub Blogpost
27:49 Barnes-Hut t-SNE
29:54 Comparison
31:06 Outro

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