A Manifold-Aware Topic Modeling Approach via Rank-Based Prototypes

Thiago César Castilho Almeida; Daniel Carlos Guimarães Pedronette

cs.LGAug 29, 2026

A Manifold-Aware Topic Modeling Approach via Rank-Based Prototypes

Authors: Thiago César Castilho Almeida, Daniel Carlos Guimarães Pedronette

Organizations: Department of Statistics, Applied Mathematics and Computing State University of São Paulo (UNESP), Rio Claro, Brazil

Abstract

Recent topic models leverage pretrained embeddings, but neural architectures produce latent representations without grounding in specific texts, and clustering-based pipelines assign representative documents only post hoc, relying on absolute distances distorted by hubness and anisotropy in high-dimensional spaces. We introduce MARETopic, a training-free framework that casts topic discovery as rank-based prototype selection. After projecting embeddings onto a low-dimensional manifold, MARETopic builds ranked lists encoding ordinal neighborhood structure. A greedy algorithm selects exactly K exemplar documents, real corpus texts, whose neighborhoods cover the corpus. Two variants share this criterion. MARETopic $_\text{Corr}$ scores candidates with a query performance predictor and a rank correlation measure, leading Purity and NMI on the two benchmarks with the most categories, ahead of both neural and clustering-based topic models. MARETopic $_\text{Diff}$ scores them with a rank-based diffusion matrix, needs neither measure, and runs 1.7 to 1.9 times faster. Without a single gradient update, MARETopic leads topic coherence on two of three datasets. A novel inter-topic Maximal Marginal Relevance step raises vocabulary diversity at little cost in coherence. Our code is available at https://github.com/thcastilho/maretopic.

Figures & tables

Figure 1: Spatial illustration of a ranked list for a query document

d_{i}

in an embedding space. Rank-based methods operate on this relative ordering rather than on absolute distances, providing robustness to the geometric distortions of high-dimensional spaces.

Figure 2: Overview of the MARETopic framework.

20 Newsgroups
	Generative					Clustering-based
								Ours
Metric	LDA	NMF	ETM	ECRTM	FASTopic	BERTopic	Top2Vec	MARETopic	MARETopic
	( Blei et al., 2003 )	( Lee and Seung, 1999 )	( Dieng et al., 2020 )	( Wu et al., 2023 )	( Wu et al., 2024a )	( Grootendorst, 2022 )	( Angelov, 2020 )	Diffusion	Correlation
C v	0.5352 $\pm$ .007	0.5573 $\pm$ .016	0.4522 $\pm$ .004	0.6116 $\pm$ .013	0.5993 $\pm$ .019	0.5942 $\pm$ .007	0.6649 $\pm$ .011	0.6708 $\pm$ .015	0.6818 $\pm$ .003
NPMI	0.0472 $\pm$ .003	0.0613 $\pm$ .007	-0.0171 $\pm$ .003	-0.0372 $\pm$ .021	-0.0689 $\pm$ .002	0.0842 $\pm$ .003	0.1032 $\pm$ .003	0.0958 $\pm$ .005	0.1027 $\pm$ .002

Table 1: Topic modeling evaluation across three datasets (mean

\pm

std of 3 runs,

K=50

). Columns are grouped by paradigm. Best value per metric per dataset in bold ; runner-up underlined . Time is end-to-end wall clock in seconds on an Apple M4 with 16 GB of memory, averaged over three runs, and lower is better.

MARETopic ${}_{\text{Corr}}$
	20NG	NYT	WoS
C v	0.6817 $-$ 0.026	0.6449 $-$ 0.053	0.7189 $-$ 0.028
TD	0.8854 +0.025	0.8764 +0.016	0.8542 $-$ 0.014
Purity	0.6161 +0.017	0.7102 +0.061	0.8094 $-$ 0.002
NMI	0.5398 +0.031	0.3982 +0.041	0.4697 +0.002
MARETopic ${}_{\text{Diff}}$

Table 2: Effect of UMAP pre-processing. Each cell shows the UMAP-enabled value with the delta from raw SBERT ( green : improvement; red : degradation).

Figure 3: Sensitivity to neighborhood size

k

across all four metrics. Solid lines: MARETopic

{}_{\text{Corr}}

; dashed lines: MARETopic

{}_{\text{Diff}}

. Vertical dotted line marks the recommended

k=100

		20 Newsgroups		New York Times		Web of Science
Method	$\lambda$	C v	TD	C v	TD	C v	TD
	0.0	0.6777	0.6627	0.6398	0.6845	0.7299	0.6938
	0.3	0.6674 $-$ 0.010	0.8813 +0.219	0.6384 $-$ 0.001	0.8729 +0.188	0.7206 $-$ 0.009	0.8600 +0.166
	0.5	0.6539 $-$ 0.014	0.9538 +0.073	0.6349 $-$ 0.004	0.9582 +0.085	0.6850 $-$ 0.036	0.9533 +0.093
MARETopic Correlation	0.7	0.6257 $-$ 0.028	0.9925 +0.039	0.6043 $-$ 0.031	0.9893 +0.031	0.6689 $-$ 0.016	0.9902 +0.037
	0.0	0.6854	0.6502	0.6516	0.7080	0.7287	0.6906

Table 3: Sensitivity to the MMR diversity parameter

\lambda

. Only C v and TD are reported, as MMR acts on word extraction and does not affect cluster assignments. Colored deltas show change relative to the previous

\lambda

( green : improvement; red : degradation). Recommended

\lambda=0.3

highlighted (gray).

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

	20 Newsgroups				New York Times				Web of Science
Configuration	C v	TD	Purity	NMI	C v	TD	Purity	NMI	C v	TD	Purity	NMI
BERTopic, native words	0.6120	0.7666	0.4261	0.3770	0.6341	0.8067	0.6187	0.3155	0.6903	0.7707	0.7909	0.4488
+ inter-topic MMR, $\lambda=0.3$	0.5991 $-$ 0.013	0.9382 +0.172	0.4261	0.3770	0.6445 +0.010	0.9382 +0.132	0.6187	0.3155	0.6531 $-$ 0.037	0.9195 +0.149	0.7909	0.4488

Appendix

Table 4: The proposed diversification applied to BERTopic’s own c-TF-IDF (mean of 3 runs,

K=50

). Deltas are against BERTopic’s native word lists ( green : increase; red : decrease). At

\lambda=0

the step reduces to selecting the highest-scoring words, which is what BERTopic does natively, and reproduces its word lists exactly on every run. Purity and NMI are unchanged by construction, since the diversification acts on word lists after

\Theta

is fixed. This is an independent run, so BERTopic’s native values differ slightly from those in Table 1 .

20 Newsgroups
	Generative					Clustering-based
								Ours
Metric	LDA	NMF	ETM	ECRTM	FASTopic	BERTopic	Top2Vec	MARETopic	MARETopic
								Diffusion	Correlation
C v	0.4817 $-$ 0.053	0.5444 $-$ 0.013	0.4508 $-$ 0.001	0.5751 $-$ 0.037	0.5584 $-$ 0.041	0.5874 $-$ 0.007	0.5995 $-$ 0.065	0.6020 $-$ 0.069	0.6123 $-$ 0.070
TD	0.5678 +0.048	0.4129 $-$ 0.096	0.8111 $-$ 0.036	0.8098 $-$ 0.059	0.9160 $-$ 0.069	0.7218 $-$ 0.051	0.8548 $-$ 0.011	0.8413 $-$ 0.020	0.8138 $-$ 0.065

Appendix

Table 5: The evaluation repeated at

K=100

topics (mean of 3 runs). Each cell carries the value at

K=100

and, in small type, its change from

K=50

( green : increase; red : decrease). Best value per metric per dataset in bold ; runner-up underlined .

		20 Newsgroups				New York Times				Web of Science
Method	Encoder	C v	TD	Purity	NMI	C v	TD	Purity	NMI	C v	TD	Purity	NMI
MARETopic Correlation	MiniLM	0.6818	0.8787	0.6227	0.5419	0.6496	0.8702	0.7084	0.3975	0.7150	0.8547	0.8106	0.4664
	MPNet	0.6875	0.8653	0.6141	0.5405	0.6633	0.8840	0.7062	0.3950	0.7033	0.8715	0.8019	0.4647
	DistilRoBERTa	0.6686	0.8609	0.6170	0.5326	0.6310	0.8658	0.6997	0.3874	0.7097	0.8591	0.8158	0.4753
MARETopic Diffusion	MiniLM	0.6708	0.8613	0.4144	0.4011	0.6570	0.8831	0.6046	0.3305	0.7198	0.8569	0.6082	0.3660
	MPNet	0.6754	0.8707	0.4040	0.3932	0.6684	0.8649	0.6078	0.3341	0.6995	0.8800	0.5894	0.3687

Appendix

Table 6: Robustness to SBERT backbone (all-MiniLM-L6-v2, all-mpnet-base-v2, all-distilroberta-v1), with all other parameters fixed at default (

k=100

d_{\text{UMAP}}=5

\lambda=0.3

K=50

, mean of 3 runs). Best value per method per dataset per metric in bold .

Figure 4: Ten representative topics from MARETopic

{}_{\text{Corr}}

on 20NG. Each panel is a leader document; bars show its top-5 c-TF-IDF terms. Topic indices follow the ordering from the greedy selection.

Figure 5: Document–topic affinity matrix $\Theta$ for MARETopic ${}_{\text{Corr}}$ on the 20NG test set ( $N{=}7{,}532$ , $K{=}50$ ). Rows: topic leaders sorted by dominant class, labelled by top-3 words. Columns: test documents sorted by ground-truth class; red lines mark class boundaries. Color: $\theta_{ij}$ (JaccardMax affinity).

Topic Modeling

Topic modeling discovers recurring themes and document-topic structure in text, helping organize, compare, and track large collections.

See all 57 papers

TriTopic: Tri-Modal Graph-Based Topic Modeling with Iterative Refinement and Archetypes
Feb 22, 2026Roman EggerTopic Modeling
Smartvisions.at & Modul University Vienna
Model Directions, Not Words: Mechanistic Topic Models Using Sparse Autoencoders
Jul 31, 2025Carolina Zheng, Nicolas Beltran-Velez, Sweta Karlekar +5Topic Modeling
Columbia University · Independent · Google Research
Human-Centric Topic Modeling with Goal-Prompted Contrastive Learning and Optimal Transport
Apr 14, 2026Rui Wang, Yi Zheng, Dongxin Wang +5Topic Modeling
School of Computer Science, Nanjing University of Posts and Telecommunications · School of Computer Science and Information Engineering, Hefei University of Technology · School of Electronic Engineering and Computer Science, Queen Mary University of London +1

Feb 22, 2026J/K move · Enter open · S save

TriTopic: Tri-Modal Graph-Based Topic Modeling with Iterative Refinement and Archetypes

Roman Egger

Smartvisions.at & Modul University Vienna

Topic Modeling

Open paper AskPDF arXiv

Topic modeling extracts latent themes from large text collections, but leading approaches like BERTopic face critical limitations: stochastic instability, loss of lexical precision ("Embedding Blur"), and reliance on a single data perspective. We present TriTopic, a framework that addresses these weaknesses through a tri-modal graph fusing semantic embeddings, TF-IDF, and metadata. Three core innovations drive its performance: hybrid graph construction via Mutual kNN and Shared Nearest Neighbors to eliminate noise and combat the curse of dimensionality; Consensus Leiden Clustering for reproducible, stable partitions; and Iterative Refinement that sharpens embeddings through dynamic centroid-pulling. TriTopic also replaces the "average document" concept with archetype-based topic representations defined by boundary cases rather than centers alone. In benchmarks across 20 Newsgroups, BBC News, AG News, and Arxiv, TriTopic achieves the highest NMI on every dataset (mean NMI 0.575 vs. 0.513 for BERTopic, 0.416 for NMF, 0.299 for LDA), guarantees 100% corpus coverage with 0% outliers, and is available as an open-source PyPI library.

Abstract

Topic Modeling

Explore similar work

TriTopic: Tri-Modal Graph-Based Topic Modeling with Iterative Refinement and Archetypes

Model Directions, Not Words: Mechanistic Topic Models Using Sparse Autoencoders

Human-Centric Topic Modeling with Goal-Prompted Contrastive Learning and Optimal Transport