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t-SNE & Stability Analysis

Dataset

PHY-3500 · G1 · 43,019 spectra — t-SNE and Procrustes results: run phy3500_umap_tsne_run_20260405T214233Z. Nothing on this page comes from the G2 runs.

t-SNE projection​

t-SNE is applied to the same 91 PCA components with perplexity=30, init='pca', 1,000 iterations (t = 80.2 s — approximately 2× UMAP). The projection produces an "archipelago" of compact, separated masses, as opposed to UMAP's continuous continent.

Structural differences:

  • Hot stars (A-F, T_eff > 7,000 K) form a distinct isolated cluster
  • The central mass groups G-K main-sequence stars
  • Log g colouring reveals partially isolated subgiant clusters

Complementarity with UMAP:

  • t-SNE excels at sharp separation of discrete sub-populations
  • UMAP better preserves continuous gradients (T_eff, [Fe/H])
t-SNE grid
t-SNE projection coloured by spectral type, T_eff, log g, [Fe/H]

Procrustes stability analysis​

Counter-intuitive result: t-SNE is 60× more stable than UMAP​

Both methods use stochastic gradient descent (SGD), making this result surprising.

MethodInitialisationMean Procrustes distance dPRelative stability
UMAPSpectral (Laplacian)3.0 × 10⁻²Baseline
t-SNEinit='pca'5.0 × 10⁻⁴60× more stable

Why UMAP is less stable:

  • Spectral initialisation varies between seeds
  • SGD with negative sampling introduces strong stochasticity in repulsive forces

Why t-SNE is more stable:

  • init='pca' fixes an identical starting position across seeds
  • KL penalty only penalises close neighbours — less sensitive to distant structure
UMAP stability (4 seeds)t-SNE stability (4 seeds)
UMAP: dP ~ 0.030 — significant run-to-run variabilityt-SNE: dP ~ 5×10⁻⁴ — 60× more stable

Perplexity sensitivity​

The t-SNE projection is robust to perplexity in the range [15, 50]. Below perplexity = 15, cluster separation becomes artifactual. Above perplexity = 50, local structure blurs toward a UMAP-like gradient.

Recommended setting: perplexity=30 — optimal for N ≈ 43,000 spectra.

Perplexity sensitivity

t-SNE robustness across perplexity ∈ [15, 50]

HR diagram coloured by t-SNE axis 1​

ρ(t-SNE axis 1, T_eff) = +0.623 — intermediate between PCA (0.831) and UMAP (0.464). The thermal gradient is visible on the HR diagram but with more local structure than PCA.

HR diagram t-SNE axis 1

HR diagram coloured by t-SNE axis 1 — thermal correlation in t-SNE space

UMAP vs t-SNE side-by-side​

UMAP vs t-SNE
Continuous continent (UMAP) vs compact archipelago (t-SNE)

See also​