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Experimental protocol

1. Primary Graph-RMS procedure

For a hyperspectral cube with (N) pixels and (B) bands, Graph-RMS applies:

  1. per-band full-scene z-score standardization;
  2. PCA-20 only for ranking local neighbours;
  3. reciprocal local graph construction inside a radius-7 spatial window, retaining at most 20 candidates and repairing degree below four;
  4. Gaussian spectral-spatial edge affinities using median edge-distance bandwidths;
  5. row-normalized damped diffusion (Y^{(t+1)}=0.5Y^{(t)}+0.5WY^{(t)});
  6. PCA to at most ten components in the checkpoint representation followed by population-standardization of each retained component;
  7. capped 50-neighbour radius connectivity to obtain fine modes;
  8. radius-3 spatial majority cleanup, retaining the centre label on ties;
  9. reciprocal prototype consolidation over at most 30 candidate neighbours;
  10. reference-free endpoint guards for stability, largest-region fraction, normalized entropy, and compression.

The mode dispersion is

[ s_a^{\rm raw}=\sqrt{\frac{1}{n_a}\sum_{i\in a}\lVert z_i-\mu_a\rVert_2^2}. ]

This is an RMS Euclidean radius in standardized diffusion-PCA space. It is not the expansion of the method acronym. The method acronym denotes Robust Mean Shift.

The floor is calculated once from initial fine modes whose raw dispersion is above (10^{-6}) and size is at least five. It is the 25th percentile of that set, or (10^{-3}) if the set is empty. Subsequent pooled updates use the already floored stored dispersions, matching the frozen implementation.

All exact shared and scene-specific values are in configs/primary.yaml.

2. Endpoint selection

The primary candidate sequence includes the frozen threshold grid from zero through 3.0 and both size exponents 0 and 0.5. A candidate endpoint is admissible when the stored partition satisfies:

  • adjacent-threshold ARI at least 0.95;
  • largest-region fraction at most 0.40;
  • normalized partition entropy at least 0.35; and
  • compression of the cleaned fine partition at least 0.20.

The primary procedure selects an admissible size-aware endpoint when supported; otherwise it uses the conservative beta-zero branch. LongKou is the only primary scene using that conservative fallback. The selected partition is frozen before loading its reference map.

3. Automatic operating-point experiment

Automatic-v2 separates global calibration from deployment:

  • Global rule calibration used reference-based NMI and ARI on eight development scenes to choose one rule from a predeclared rule grid.
  • Per-scene deployment of the locked rule uses the cube and reference-free partition statistics only. It receives neither target labels nor target (K).
  • The local scale is the median positive finite tenth non-self-neighbour distance in standardized diffusion-PCA space.
  • The full candidate grid and deterministic hierarchy are frozen in configs/automatic_selector.yaml and preserved in the development lock.
  • scripts/run_automatic_selector.py executes the recovered automatic-v2 component selector; _run_automatic_selection.py is retained only as the automatic-scale-v1 endpoint-surface generator.
  • Seven development scenes selected the conservative branch; KSC selected the size-aware branch. No development scene abstained.
  • Trento was already known when automatic-v2 was designed. Its automatic result is retrospective and must not be presented as a second independent holdout.

Eight-scene means changed from primary OA/BA/NMI/ARI 0.6086/0.5137/0.7089/0.5666 to automatic 0.5744/0.5384/0.7239/0.5813. The retrospective Trento automatic result used (T=100), gamma 1.25, realized radius 0.1360, tau 0.75, and beta 0.5, returning 67 regions and OA/BA/NMI/ARI 0.6148/0.5122/0.7656/0.7164.

4. Comparison groups and fairness

True-class-count classical group

PCA-KMeans, MiniBatch-KMeans, fuzzy c-means, and SLIC-KMeans receive the reference class count as the requested number of clusters. They use full-scene band standardization and PCA-20 and are summarized using five fixed seeds. These methods form the predefined five-method Friedman/Holm family together with Graph-RMS.

Class-count-free group

  • HDBSCAN uses the declared scikit-learn defaults on standardized PCA-20. Noise remains label -1 during evaluation.
  • Leiden operates on the exact frozen weighted Graph-RMS graph. Its resolution is chosen from a fixed grid using cross-seed and adjacent-resolution agreement plus largest-community and entropy guards. It uses five evaluation seeds.

HDBSCAN and Leiden receive neither true (K) nor labels for fitting or selection. Their paired tests are reported separately from the true-K family. Leiden is a strong same-graph control and is not uniformly inferior to Graph-RMS.

Excluded modern adaptation diagnostics

Stored DLSS and S2DL adaptation outputs are preserved in supporting evidence for transparency but were excluded from superiority claims and inferential tests because an author-native sanity anchor was not established. A fair modern self-supervised comparison would require a separately standardized training, patch, augmentation, and output-count protocol.

5. Evaluation

All methods partition every scene pixel. Metrics use only nonzero reference pixels. OA and BA use one-to-one Hungarian assignment; unmatched predicted regions count as errors. NMI and ARI are permutation-invariant and are the principal structural-partition measures. Supplementary AMI, homogeneity, completeness, V-measure, purity, and fragmentation diagnostics are also stored.

The full-scene region count and the count intersecting the labelled support are kept separate. This distinction is essential for KSC and Botswana, whose reference maps cover only 1.66% and 0.86% of their scenes.

6. Diagnostic studies

  • Ablation: eight Pavia University configurations covering graph gate, spatial affinity, diffusion, cleanup, fine-mode grouping, consolidation, and size weighting.
  • Sensitivity: 51 one-factor runs on Salinas-A, Indian Pines, and Pavia University over window radius, search PCA dimension, checkpoint, and fine radius.
  • Selector audit: oracle gaps and removal of persistence, largest-region, entropy, and compression guards.
  • Perturbation: two seeds each for 1% additive noise and 5% pixel replacement on three representative scenes; Pavia reselects its endpoint.
  • Cross-device: frozen CPU versus new GPU partitions for KSC, HanChuan, and Botswana.
  • Uncertainty: 300 spatial block-bootstrap replicates per scene and metric.
  • Granularity controls: post hoc Trento consolidation to six groups and count-matched MiniBatch-KMeans using full-scene and labelled-support budgets.
  • Profiling: three end-to-end A100 runs for each scene, recording runtime, process RSS, peak allocated GPU memory, and peak reserved GPU memory.

7. Compute expectations

Curated analysis products are immediately inspectable on CPU. Full scene reruns require much more compute. The recorded A100 mean runtime ranges from 1.21 s to 42.34 s, but preparation, downloads, environment setup, and repeated diagnostic grids add substantial wall time. Peak allocated GPU memory reaches 14.9 GB on HongHu. CPU-only execution is supported but was not the hardware profile reported in the main runtime table.