# Nuclear Norm based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes

arXiv: https://arxiv.org/abs/1405.1207 · HTML: https://mlsanity.com/paper/1405.1207/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2014.

## Built on by (most cited first, 19 of 19)

- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Self-restrained Triplet Loss for Accurate Masked Face Recognition](https://mlsanity.com/paper/2103.01716/) (2021)
- [End2End Occluded Face Recognition by Masking Corrupted Features](https://mlsanity.com/paper/2108.09468/) (2021)
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- [Spectrum-to-Kernel Translation for Accurate Blind Image Super-Resolution](https://mlsanity.com/paper/2110.12151/) (2021)
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- [Genetic Programming-Based Evolutionary Deep Learning for Data-Efficient Image Classification](https://mlsanity.com/paper/2209.13233/) (2022)
- [OTFace: Hard Samples Guided Optimal Transport Loss for Deep Face Representation](https://mlsanity.com/paper/2203.14461/) (2022)
- [Face recognition via compact second order image gradient orientations](https://mlsanity.com/paper/2201.09246/) (2022)
- [Representer Point Selection for Explaining Regularized High-dimensional Models](https://mlsanity.com/paper/2305.20002/) (2023)
- [Robust Learning under Hybrid Noise](https://mlsanity.com/paper/2407.04029/) (2024)
- [Efficient Differentiable Approximation of Generalized Low-rank Regularization](https://mlsanity.com/paper/2505.15407/) (2025)
- [WDR FACE: The First Database for Studying Face Detection in Wide Dynamic Range](https://mlsanity.com/paper/2101.03826/) (2021)
- [Region attention and graph embedding network for occlusion objective class-based micro-expression recognition](https://mlsanity.com/paper/2107.05904/) (2021)
- [Semantic Encoder Guided Generative Adversarial Face Ultra-Resolution Network](https://mlsanity.com/paper/2211.10532/) (2022)
- [A Unified Framework to Super-Resolve Face Images of Varied Low Resolutions](https://mlsanity.com/paper/2306.03380/) (2023)
- [Hybrid second-order gradient histogram based global low-rank sparse regression for robust face recognition](https://mlsanity.com/paper/2511.05893/) (2025)
- [Conditional Random Ordered Transport Spaces](https://mlsanity.com/paper/2606.08113/) (2026)

## Abstract (arXiv)

Recently regression analysis becomes a popular tool for face recognition. The existing regression methods all use the one-dimensional pixel-based error model, which characterizes the representation error pixel by pixel individually and thus neglects the whole structure of the error image. We observe that occlusion and illumination changes generally lead to a low-rank error image. To make use of this low-rank structural information, this paper presents a two-dimensional image matrix based error model, i.e. matrix regression, for face representation and classification. Our model uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers method to calculate the regression coefficients. Compared with the current regression methods, the proposed Nuclear Norm based Matrix Regression (NMR) model is more robust for alleviating the effect of illumination, and more intuitive and powerful for removing the structural noise caused by occlusion. We experiment using four popular face image databases, the Extended Yale B database, the AR database, the Multi-PIE and the FRGC database. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression based face recognition methods.