t-SNE
- t-Distributed Stochastic Neighbor Embedding
Best for: 2D/3D visualization Aliases: t-Distributed Stochastic Neighbor Embedding
How it works
$$C=\mathrm{KL}(P\|Q)=\sum_{i\ne j}p_{ij}\log\frac{p_{ij}}{q_{ij}}$$Defines high-dimensional affinities $p_{j|i}=\frac{\exp(-\|x_i-x_j\|^2/2\sigma_i^2)}{\sum_{k\ne i}\exp(-\|x_i-x_k\|^2/2\sigma_i^2)}$, symmetrised to $p_{ij}=\tfrac{1}{2n}(p_{j|i}+p_{i|j})$, with bandwidth $\sigma_i$ chosen so each conditional hits a target perplexity. Low-dimensional affinities use a heavy-tailed Student-t kernel, $q_{ij}=\frac{(1+\|y_i-y_j\|^2)^{-1}}{\sum_{k\ne l}(1+\|y_k-y_l\|^2)^{-1}}$, which relieves the crowding problem. The embedding $\{y_i\}$ is fit by gradient descent to minimise $C=\mathrm{KL}(P\|Q)=\sum_{i\ne j}p_{ij}\log\frac{p_{ij}}{q_{ij}}$, preserving local neighbourhoods rather than global geometry.
When to use
Visualizing high-dimensional data in 2D/3D where preserving local neighborhood structure matters.
Watch out
For visualization only — not for downstream modeling; costly on large n; distorts global structure; tune perplexity.
Common fields
NLP embeddings · genomics · exploratory analysis