tsne.md

TSNE

Language: English Last updated: 2026-05-09 Path: statgpu.unsupervised.TSNE

Overview

TSNE embeds dense data by matching high-dimensional Gaussian affinities with low-dimensional Student-t affinities. Phase 3A implements exact dense Euclidean t-SNE.

Path

Import from statgpu.unsupervised:

from statgpu.unsupervised import TSNE

Objective Function / Loss Function

t-SNE minimizes KL divergence:

$$ \operatorname{KL}(P | Q) = \sum_{i \ne j} p_{ij}\log\frac{p_{ij}}{q_{ij}}. $$

Estimating Equation

The high-dimensional conditional probabilities are calibrated by binary search so each row matches the target perplexity. The low-dimensional affinities use:

$$ q_{ij} = \frac{(1+|y_i-y_j|_2^2)^{-1}} {\sum_{a \ne b}(1+|y_a-y_b|_2^2)^{-1}}. $$

The embedding is optimized with early exaggeration, momentum, and adaptive per-coordinate gains.

Parameters

n_components, perplexity, early_exaggeration, learning_rate, max_iter, init, random_state, metric, and device.

CPU+GPU Examples

from statgpu.unsupervised import TSNE

embedding = TSNE(perplexity=30, device="cpu").fit_transform(X)
embedding_gpu = TSNE(perplexity=30, device="torch").fit_transform(X_torch)

Strict/Approx Difference

This is exact dense t-SNE. Barnes-Hut, FFT/FIt-SNE, and openTSNE acceleration are external baselines only.

Outputs

embedding_, kl_divergence_, n_iter_, and n_features_in_.

FAQ

Sparse input, non-Euclidean metrics, Barnes-Hut, FFT/FIt-SNE, and new-data transform are not supported in Phase 3A.

External Validation

Tests: dev/tests/test_unsupervised_tsne.py. Benchmark: dev/benchmarks/benchmark_unsupervised_phase3.py. Baselines: sklearn exact TSNE, openTSNE, and cuML TSNE if available remotely.

References

• van der Maaten, L., & Hinton, G. (2008). Visualizing data using t-SNE. Journal of Machine Learning Research, 9, 2579-2605.
• Linderman, G. C., Rachh, M., Hoskins, J. G., Steinerberger, S., & Kluger, Y. (2019). Fast interpolation-based t-SNE for improved visualization of single-cell RNA-seq data. Nature Methods, 16, 243-245.