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Non-negative matrix factorization algorithms generally improve topic model fits.

Peter Carbonetto¹, Abhishek Sarkar^1,2, Zihao Wang³

¹Department of Human Genetics, University of Chicago, Chicago, IL USA.

Statistics and Computing

|May 8, 2026

Summary

This summary is machine-generated.

This study introduces efficient topic modeling by leveraging non-negative matrix factorization (NMF) optimization. These new methods significantly improve fitting speed and accuracy for large datasets.

Keywords:

Expectation maximization Maximum-likelihood estimation Non-negative matrix factorization Nonconvex optimization Topic models

Related Experiment Videos

Area of Science:

Computational statistics
Machine learning
Natural language processing

Background:

Topic models are essential for analyzing large text datasets.
Maximum-likelihood estimation (MLE) is a standard approach for fitting topic models.
Existing MLE methods can be computationally intensive for large datasets.

Purpose of the Study:

To develop faster and more accurate topic modeling methods for large datasets.
To formally connect topic modeling MLE with non-negative matrix factorization (NMF).
To leverage advances in NMF optimization for topic model fitting.

Main Methods:

Revisiting maximum-likelihood estimation in topic models.
Establishing a formal connection between topic model MLE and non-negative matrix factorization (NMF).
Applying recent NMF optimization techniques to fit topic models.

Main Results:

Demonstrated that advances in NMF optimization can efficiently fit topic models.
Achieved significantly better fits in less time compared to existing topic modeling algorithms.
Showed that the Expectation-Maximization (EM) algorithm for topic models is equivalent to classic NMF multiplicative updates.

Conclusions:

Novel methods based on NMF provide a highly efficient approach for topic modeling.
The "fastTopics" R package implements these advanced NMF-based topic modeling techniques.
This work bridges the gap between NMF and topic modeling, offering practical benefits for large-scale text analysis.