# Class Prior-Free Positive-Unlabeled Learning with Taylor Variational Loss for Hyperspectral Remote Sensing Imagery

arXiv: https://arxiv.org/abs/2308.15081 · HTML: https://mlsanity.com/paper/2308.15081/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 19 of 19)

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Does label smoothing mitigate label noise?](https://mlsanity.com/paper/2003.02819/) (2020)
- [A Survey of Label-noise Representation Learning: Past, Present and Future](https://mlsanity.com/paper/2011.04406/) (2020)
- [Perturbed and Strict Mean Teachers for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2111.12903/) (2021)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective](https://mlsanity.com/paper/2212.02801/) (2022)
- [Cascaded Recurrent Neural Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/1902.10858/) (2019)
- [PU Learning for Matrix Completion](https://mlsanity.com/paper/1411.6081/) (2014)
- [FPGA: Fast Patch-Free Global Learning Framework for Fully End-to-End Hyperspectral Image Classification](https://mlsanity.com/paper/2011.05670/) (2020)
- [Positive-Unlabeled Learning using Random Forests via Recursive Greedy Risk Minimization](https://mlsanity.com/paper/2210.08461/) (2022)
- [One-Class Risk Estimation for One-Class Hyperspectral Image Classification](https://mlsanity.com/paper/2210.15457/) (2022)

## Built on by (most cited first, 8 of 8)

- [HyperFree: A Channel-adaptive and Tuning-free Foundation Model for Hyperspectral Remote Sensing Imagery](https://mlsanity.com/paper/2503.21841/) (2025)
- [C3DG: Conditional Domain Generalization for Hyperspectral Imagery Classification with Convergence and Constrained-risk Theories](https://mlsanity.com/paper/2407.04100/) (2024)
- [Noisy-Pair Robust Representation Alignment for Positive-Unlabeled Learning](https://mlsanity.com/paper/2510.01278/) (2025)
- [AbLWR:A Context-Aware Listwise Ranking Framework for Antibody-Antigen Binding Affinity Prediction via Positive-Unlabeled Learning](https://mlsanity.com/paper/2604.11272/) (2026)
- [HOpenCls: Training Hyperspectral Image Open-Set Classifiers in Their Living Environments](https://mlsanity.com/paper/2502.15163/) (2025)
- [From Image- to Pixel-level: Label-efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2503.06852/) (2025)
- [Needles in the Landscape: Semi-Supervised Pseudolabeling for Archaeological Site Discovery under Label Scarcity](https://mlsanity.com/paper/2510.16814/) (2025)
- [Mapping melliferous tree species in Kenya via one-class classification with hyperspectral unsupervised domain adaptation](https://mlsanity.com/paper/2608.02045/) (2026)

## Abstract (arXiv)

Positive-unlabeled learning (PU learning) in hyperspectral remote sensing imagery (HSI) is aimed at learning a binary classifier from positive and unlabeled data, which has broad prospects in various earth vision applications. However, when PU learning meets limited labeled HSI, the unlabeled data may dominate the optimization process, which makes the neural networks overfit the unlabeled data. In this paper, a Taylor variational loss is proposed for HSI PU learning, which reduces the weight of the gradient of the unlabeled data by Taylor series expansion to enable the network to find a balance between overfitting and underfitting. In addition, the self-calibrated optimization strategy is designed to stabilize the training process. Experiments on 7 benchmark datasets (21 tasks in total) validate the effectiveness of the proposed method. Code is at: https://github.com/Hengwei-Zhao96/T-HOneCls.