# Multi-Objective Matrix Normalization for Fine-grained Visual Recognition

arXiv: https://arxiv.org/abs/2003.13272 · HTML: https://mlsanity.com/paper/2003.13272/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2020.

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

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- [Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization](https://mlsanity.com/paper/2102.04523/) (2021)
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- [Improving Fine-Grained Visual Recognition in Low Data Regimes via Self-Boosting Attention Mechanism](https://mlsanity.com/paper/2208.00617/) (2022)
- [R2-Trans:Fine-Grained Visual Categorization with Redundancy Reduction](https://mlsanity.com/paper/2204.10095/) (2022)
- [Coping with Change: Learning Invariant and Minimum Sufficient Representations for Fine-Grained Visual Categorization](https://mlsanity.com/paper/2306.04893/) (2023)
- [Data-free Knowledge Distillation for Fine-grained Visual Categorization](https://mlsanity.com/paper/2404.12037/) (2024)
- [Mask or Non-Mask? Robust Face Mask Detector via Triplet-Consistency Representation Learning](https://mlsanity.com/paper/2110.00523/) (2021)
- [Concept Drift and Long-Tailed Distribution in Fine-Grained Visual Categorization: Benchmark and Method](https://mlsanity.com/paper/2306.02346/) (2023)
- [Adversarial Lagrangian Integrated Contrastive Embedding for Limited Size Datasets](https://mlsanity.com/paper/2210.03261/) (2022)
- [Orthogonal Polynomial Approximation for Matrix Log Normalization in Global Covariance Pooling](https://mlsanity.com/paper/2608.19021/) (2026)

## Abstract (arXiv)

Bilinear pooling achieves great success in fine-grained visual recognition (FGVC). Recent methods have shown that the matrix power normalization can stabilize the second-order information in bilinear features, but some problems, e.g., redundant information and over-fitting, remain to be resolved. In this paper, we propose an efficient Multi-Objective Matrix Normalization (MOMN) method that can simultaneously normalize a bilinear representation in terms of square-root, low-rank, and sparsity. These three regularizers can not only stabilize the second-order information, but also compact the bilinear features and promote model generalization. In MOMN, a core challenge is how to jointly optimize three non-smooth regularizers of different convex properties. To this end, MOMN first formulates them into an augmented Lagrange formula with approximated regularizer constraints. Then, auxiliary variables are introduced to relax different constraints, which allow each regularizer to be solved alternately. Finally, several updating strategies based on gradient descent are designed to obtain consistent convergence and efficient implementation. Consequently, MOMN is implemented with only matrix multiplication, which is well-compatible with GPU acceleration, and the normalized bilinear features are stabilized and discriminative. Experiments on five public benchmarks for FGVC demonstrate that the proposed MOMN is superior to existing normalization-based methods in terms of both accuracy and efficiency. The code is available: https://github.com/mboboGO/MOMN.