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

Programme paper P4 of the CAOS_LDA_HSI series. 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. The present manuscript asks the orthogonal question: does the recipe winner depend on the topic-model backbone? We run the full V1-V20 sweep (nineteen recipes; V16 scaffolded only) under three additional backbones: Hierarchical Dirichlet Process (HDP, nonparametric K), Product LDA (ProdLDA, logistic-normal prior with amortised inference) and the Embedded Topic Model (ETM, joint word-topic embedding), 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, both with Dirichlet-like priors, agree that V12 wins; HDP with its stick-breaking truncation prior picks V7 (absorption-feature triplets); ProdLDA with its logistic-normal prior picks V3 (joint band-bin vocabulary). We give a per-recipe affinity score that quantifies how each recipe transfers across backbones, identify three robust backbone-recipe pairings, and recommend reporting the (backbone, wordification) pair as a single hyper-decision in any future LDA-on-HSI work. 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.