# Anchor-Free Correlated Topic Modeling: Identifiability and Algorithm

arXiv: https://arxiv.org/abs/1611.05010 · HTML: https://mlsanity.com/paper/1611.05010/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2016.

## Built on by (most cited first, 15 of 15)

- [Deep Learning From Crowdsourced Labels: Coupled Cross-entropy Minimization, Identifiability, and Regularization](https://mlsanity.com/paper/2306.03288/) (2023)
- [Unsupervised Learning under Latent Label Shift](https://mlsanity.com/paper/2207.13179/) (2022)
- [Memory-Efficient Convex Optimization for Self-Dictionary Separable Nonnegative Matrix Factorization: A Frank-Wolfe Approach](https://mlsanity.com/paper/2109.11135/) (2021)
- [Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approach](https://mlsanity.com/paper/2305.19391/) (2023)
- [Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software](https://mlsanity.com/paper/2402.06019/) (2024)
- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Learning Topic Models: Identifiability and Finite-Sample Analysis](https://mlsanity.com/paper/2110.04232/) (2021)
- [Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory](https://mlsanity.com/paper/2505.12713/) (2025)
- [Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation](https://mlsanity.com/paper/2606.18509/) (2026)
- [Author Clustering and Topic Estimation for Short Texts](https://mlsanity.com/paper/2106.09533/) (2021)
- [Probabilistic semi-nonnegative matrix factorization: a Skellam-based framework](https://mlsanity.com/paper/2107.03317/) (2021)
- [On-the-Fly Rectification for Robust Large-Vocabulary Topic Inference](https://mlsanity.com/paper/2111.06580/) (2021)
- [Semi-supervised Vertex Hunting, with Applications in Network and Text Analysis](https://mlsanity.com/paper/2510.22526/) (2025)
- [Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis](https://mlsanity.com/paper/2605.13312/) (2026)
- [Multiclass Classification without Labels via Posterior Simplex Geometry](https://mlsanity.com/paper/2607.24943/) (2026)

## Abstract (arXiv)

In topic modeling, many algorithms that guarantee identifiability of the topics have been developed under the premise that there exist anchor words -- i.e., words that only appear (with positive probability) in one topic. Follow-up work has resorted to three or higher-order statistics of the data corpus to relax the anchor word assumption. Reliable estimates of higher-order statistics are hard to obtain, however, and the identification of topics under those models hinges on uncorrelatedness of the topics, which can be unrealistic. This paper revisits topic modeling based on second-order moments, and proposes an anchor-free topic mining framework. The proposed approach guarantees the identification of the topics under a much milder condition compared to the anchor-word assumption, thereby exhibiting much better robustness in practice. The associated algorithm only involves one eigen-decomposition and a few small linear programs. This makes it easy to implement and scale up to very large problem instances. Experiments using the TDT2 and Reuters-21578 corpus demonstrate that the proposed anchor-free approach exhibits very favorable performance (measured using coherence, similarity count, and clustering accuracy metrics) compared to the prior art.