# Truncated Cauchy Non-negative Matrix Factorization

arXiv: https://arxiv.org/abs/1906.00495 · HTML: https://mlsanity.com/paper/1906.00495/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2019.

## Built on by (most cited first, 11 of 11)

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Regularly Truncated M-estimators for Learning with Noisy Labels](https://mlsanity.com/paper/2309.00894/) (2023)
- [Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption](https://mlsanity.com/paper/2201.03182/) (2022)
- [Entropy Minimizing Matrix Factorization](https://mlsanity.com/paper/2103.13487/) (2021)
- [An Entropy Weighted Nonnegative Matrix Factorization Algorithm for Feature Representation](https://mlsanity.com/paper/2111.14007/) (2021)
- [Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation](https://mlsanity.com/paper/2211.03934/) (2022)
- [Contaminated Images Recovery by Implementing Non-negative Matrix Factorisation](https://mlsanity.com/paper/2211.04247/) (2022)
- [An ADMM-Incorporated Latent Factorization of Tensors Method for QoS Prediction](https://mlsanity.com/paper/2212.01606/) (2022)
- [Symmetry Nonnegative Matrix Factorization Algorithm Based on Self-paced Learning](https://mlsanity.com/paper/2410.15306/) (2024)
- [Robust Orthogonal NMF with Label Propagation for Image Clustering](https://mlsanity.com/paper/2504.21472/) (2025)
- [A Generalized Deep Non-negative Matrix Factorization Approach for SAR Automatic Target Recognition](https://mlsanity.com/paper/2607.09779/) (2026)

## Abstract (arXiv)

Non-negative matrix factorization (NMF) minimizes the Euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper, we propose a Truncated CauchyNMF loss that handle outliers by truncating large errors, and develop a Truncated CauchyNMF to robustly learn the subspace on noisy datasets contaminated by outliers. We theoretically analyze the robustness of Truncated CauchyNMF comparing with the competing models and theoretically prove that Truncated CauchyNMF has a generalization bound which converges at a rate of order O(√ln n/n), where n is the sample size. We evaluate Truncated CauchyNMF by image clustering on both simulated and real datasets. The experimental results on the datasets containing gross corruptions validate the effectiveness and robustness of Truncated CauchyNMF for learning robust subspaces.