# A Kernelized Manifold Mapping to Diminish the Effect of Adversarial Perturbations

arXiv: https://arxiv.org/abs/1903.01015 · HTML: https://mlsanity.com/paper/1903.01015/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2019.

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

- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [Survey on Adversarial Attack and Defense for Medical Image Analysis: Methods and Challenges](https://mlsanity.com/paper/2303.14133/) (2023)
- [Noise Optimization for Artificial Neural Networks](https://mlsanity.com/paper/2102.04450/) (2021)
- [The Security of Deep Learning Defences for Medical Imaging](https://mlsanity.com/paper/2201.08661/) (2022)
- [Adversarial Medical Image with Hierarchical Feature Hiding](https://mlsanity.com/paper/2312.01679/) (2023)
- [Saliency Guided Adversarial Training for Learning Generalizable Features with Applications to Medical Imaging Classification System](https://mlsanity.com/paper/2209.04326/) (2022)
- [Medical Aegis: Robust adversarial protectors for medical images](https://mlsanity.com/paper/2111.10969/) (2021)
- [Stationary Point Losses for Robust Model](https://mlsanity.com/paper/2302.09575/) (2023)
- [Robustness bounds on the successful adversarial examples in probabilistic models: Implications from Gaussian processes](https://mlsanity.com/paper/2403.01896/) (2024)
- [Harmonizing Feature Maps: A Graph Convolutional Approach for Enhancing Adversarial Robustness](https://mlsanity.com/paper/2406.11576/) (2024)
- [Improving Adversarial Robustness Through Adaptive Learning-Driven Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2507.20996/) (2025)

## Abstract (arXiv)

The linear and non-flexible nature of deep convolutional models makes them vulnerable to carefully crafted adversarial perturbations. To tackle this problem, we propose a non-linear radial basis convolutional feature mapping by learning a Mahalanobis-like distance function. Our method then maps the convolutional features onto a linearly well-separated manifold, which prevents small adversarial perturbations from forcing a sample to cross the decision boundary. We test the proposed method on three publicly available image classification and segmentation datasets namely, MNIST, ISBI ISIC 2017 skin lesion segmentation, and NIH Chest X-Ray-14. We evaluate the robustness of our method to different gradient (targeted and untargeted) and non-gradient based attacks and compare it to several non-gradient masking defense strategies. Our results demonstrate that the proposed method can increase the resilience of deep convolutional neural networks to adversarial perturbations without accuracy drop on clean data.