Post-hoc Interpretability of LDA on Hyperspectral Imagery: SHAP Attributions, Counterfactual Topic Flips, and LLM-judge Alignment under Token-Mass-Dispersion Asymmetry
Felipe A. Santibáñez-Leal · Zenodo (CERN European Organization for Nuclear Research) · 2026
The interpretability claim of LDA-on-HSI rests on the assumption that topic-word distributions are human-readable. This study is restricted to the LDA backbone; the cross-backbone comparison (HDP, ProdLDA, ETM) is the subject of the companion paper P4. We test three orthogonal post-hoc interpretability axes on the V1-V15, V17-V20 wordification sweep (nineteen LDA-fitted recipes) from the companion paper P3: F-13 SHAP attribution of pixel-to-topic decisions via a closed-form posterior, F-22 counterfactual L1 perturbation required to flip a document's argmax topic, and F-15 LLM-as-judge alignment between a document's top tokens and its argmax topic's top tokens. We find three concrete results. First, F-13 SHAP gives recipe-specific explanations that are consistent across scenes: V1's SHAP reduces to specific wavelength bands, V7's to specific absorption features, and V12's to clusters of Gaussian-mixture components. Second, F-22 counterfactual L1 (sentinel-patched 19-recipe ranking) separates the recipes into an "ultra-robust" band (V20, V12, V3; sentinel-patched means 26.3 / 24.5 / 23.5), a "moderate" band (V1 = 6.1, V7 = 5.2) and a "fragile" band (V9 = 1.0, V10 = 1.2); within the ultra-robust band a large fraction of documents never flip within 50 steps, so the ordering is not strict (V12 is the most robust where flip-sampling is adequate). Third, F-15, computed with a deterministic stand-in for the LLM judge, is governed by how its top-10 overlap rule reads each recipe's documents rather than by agreement between documents and topics. It is 1.0 by construction for V2 and V8 (at most 12 word types, so a topic's top-10 covers the vocabulary) and for V9 (a one-token document can be judged aligned or ambiguous but never misaligned), and stays near 1.0 for recipes with three or four tokens per document. Where a document holds each of its tokens once, its top-10 is a tie, so we report the exact expectation of the rule under uniformly random tie-breaking rather than one sort order: V3 and V12 then score 0.17, against 0.03 to 0.18 across individual orders. V20 re-weights V3's identical (band, bin) alphabet and scores 0.65; its topics are also less dispersed (effective vocabulary N_eff = exp(H(phi_k)) of 309 against 431 for V3 and 400 for V12), but its per-band copies also make each document's top-10 its highest-copy bands, so the comparison cannot attribute the gap to topic dispersion. F-15 as defined therefore measures the documents' token structure more than topic interpretability, and an LLM oracle given the same token lists would face the same construction effects. We recommend reporting F-13 SHAP top-K attributions as the primary interpretability artefact, F-22 as the topic-stability artefact, and F-15 only with its construction effects reported beside it. Code and derived artefacts: https://github.com/fsantibanezleal/CAOS_LDA_HSI . Interactive web application: https://lda-hsi.fasl-work.com . Manuscript sources: https://github.com/fsantibanezleal/CAOS_LDA_HSI_Paper . Funding: The Advanced Mining Technology Center (AMTC) Basal project (ANID/PIA Project AFB220002) and ANID FONDECYT Postdoctorado 3220094.