Which Backbone Picks Which Wordification? A Factorial Study of Topic-Model Families on Hyperspectral Imagery

The companion paper (P3) showed that nineteen wordification recipes (V1-V15, V17-V20) produce measurably different topic bases under a fixed LDA backbone, with no universal winner: V12 (Gaussian-mixture tokens) has the highest mean coherence and topic-label coupling (winning two of six scenes on each), V20 (mutual-information-weighted bands) has the highest counterfactual robustness F-22, and V1 (band-frequency tokens, the canonical) is the most reliable of the per-band recipes under reseeding, while F-1 macro-F1 separates the recipes by less than 0.01. This paper asks the orthogonal question: does the recipe winner depend on the topic-model backbone? We run the full V1-V20 sweep (nineteen recipes; V16 is scaffolded only) under three additional backbones, namely the Hierarchical Dirichlet Process (HDP, nonparametric K), the amortised neural topic model labelled ProdLDA (run in its mixture-decoder form, with a standard logistic-normal prior) and the Embedded Topic Model (ETM, the same prior and encoder with a word-topic embedding decoder), producing a 4 x 19 factorial on six labelled-scene benchmarks (456 cells in the headline F-2 coherence axis). The headline finding is that the wordification ranking inverts across backbones. LDA and ETM agree that V12 wins, HDP picks V7 (absorption-feature triplets) and ProdLDA picks V3 (joint (band, bin) vocabulary). ETM and ProdLDA differ only in the decoder parameterisation, so their different winners come from the decoder or from optimisation; the runs do not separate the two. We give a per-recipe affinity score that quantifies how each recipe transfers across backbones, identify three empirical backbone-recipe pairings, and recommend reporting the (backbone, wordification) pair as a single hyper-decision in any future LDA-on-HSI work. LDVAE-T, a Dirichlet-prior unmixing VAE, is a candidate fifth backbone; it is not evaluated because no public implementation is available. 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.