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t-SNE clearly explained

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t-SNE clearly explained

Author: Kemal Erdem
Source: https://medium.com/data-science/t-sne-clearly-explained-d84c537f53a

Summary

Intuitive explanation of t-SNE including comparison with PCA, the math of the probability distributions, and two optimization tricks (early compression, early exaggeration). Ends with a CNN feature map application (Andrej Karpathy’s ImageNet t-SNE).

PCA vs t-SNE at a Glance

PCA uses the global covariance matrix — you can compute it once and project new data onto the same matrix. This makes PCA reusable across datasets.

t-SNE is iterative and non-deterministic — no reusable matrix. Each run may produce different results. You cannot apply t-SNE learned on train data to test data. This is the critical practical limitation.

Algorithm Summary

  1. Compute conditional probabilities (Gaussian in high-D, perplexity sets σᵢ)
  2. Initialize random low-dim points
  3. Compute low-dim similarities using Student t-distribution (1 degree of freedom) — heavy tails prevent crowding
  4. Gradient descent minimizing KL divergence between high-D and low-D distributions

Optimization Tricks

Early Compression: L2 penalty added to cost function early in training → prevents premature local clustering → keeps points mobile.

Early Exaggeration: Multiply pᵢⱼ by a large constant early → clusters can move more freely, don’t block each other.

CNN Application

t-SNE excels at visualizing CNN feature maps. Andrej Karpathy ran t-SNE on 50K ImageNet images (4096-dim fc7 features from a deep CNN) to produce a 2D map where visually similar images cluster together — revealing what the network considers “similar.”

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