# Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder

arXiv: https://arxiv.org/abs/2105.00026 · HTML: https://mlsanity.com/paper/2105.00026/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 141 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 30 of 58)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [3D MRI brain tumor segmentation using autoencoder regularization](https://mlsanity.com/paper/1810.11654/) (2018)
- [Data Augmentation Generative Adversarial Networks](https://mlsanity.com/paper/1711.04340/) (2017)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Generative Adversarial Network in Medical Imaging: A Review](https://mlsanity.com/paper/1809.07294/) (2018)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [GAN-based Synthetic Medical Image Augmentation for increased CNN Performance in Liver Lesion Classification](https://mlsanity.com/paper/1803.01229/) (2018)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Medical Image Synthesis for Data Augmentation and Anonymization using Generative Adversarial Networks](https://mlsanity.com/paper/1807.10225/) (2018)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Convolutional Neural Networks for Classification of Alzheimer's Disease: Overview and Reproducible Evaluation](https://mlsanity.com/paper/1904.07773/) (2019)

## Built on by (most cited first, 27 of 27)

- [Deep Learning Approaches for Data Augmentation in Medical Imaging: A Review](https://mlsanity.com/paper/2307.13125/) (2023)
- [Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Case](https://mlsanity.com/paper/2206.08309/) (2022)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [A Probabilistic Fluctuation based Membership Inference Attack for Diffusion Models](https://mlsanity.com/paper/2308.12143/) (2023)
- [Auditing and Generating Synthetic Data with Controllable Trust Trade-offs](https://mlsanity.com/paper/2304.10819/) (2023)
- [VTAE: Variational Transformer Autoencoder with Manifolds Learning](https://mlsanity.com/paper/2304.00948/) (2023)
- [Exploring Privacy and Fairness Risks in Sharing Diffusion Models: An Adversarial Perspective](https://mlsanity.com/paper/2402.18607/) (2024)
- [A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data](https://mlsanity.com/paper/2408.02688/) (2024)
- [Improving Joint Speech-Text Representations Without Alignment](https://mlsanity.com/paper/2308.06125/) (2023)
- [MGAug: Multimodal Geometric Augmentation in Latent Spaces of Image Deformations](https://mlsanity.com/paper/2312.13440/) (2023)
- [Discriminative Hamiltonian Variational Autoencoder for Accurate Tumor Segmentation in Data-Scarce Regimes](https://mlsanity.com/paper/2406.11659/) (2024)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Hyperbolic Dual Feature Augmentation for Open-Environment](https://mlsanity.com/paper/2506.08906/) (2025)
- [XADLiME: eXplainable Alzheimer's Disease Likelihood Map Estimation via Clinically-guided Prototype Learning](https://mlsanity.com/paper/2207.13223/) (2022)
- [Improving Multimodal Joint Variational Autoencoders through Normalizing Flows and Correlation Analysis](https://mlsanity.com/paper/2305.11832/) (2023)
- [Unified High-binding Watermark for Unconditional Image Generation Models](https://mlsanity.com/paper/2310.09479/) (2023)
- [On Probabilistic Pullback Metrics for Latent Hyperbolic Manifolds](https://mlsanity.com/paper/2410.20850/) (2024)
- [Swift Hydra: Self-Reinforcing Generative Framework for Anomaly Detection with Multiple Mamba Models](https://mlsanity.com/paper/2503.06413/) (2025)
- [Heavy-Tailed Class-Conditional Priors for Long-Tailed Generative Modeling](https://mlsanity.com/paper/2509.02154/) (2025)
- [PiCSRL: Physics-Informed Contextual Spectral Reinforcement Learning](https://mlsanity.com/paper/2603.26816/) (2026)
- [Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering](https://mlsanity.com/paper/2605.24942/) (2026)
- [Variational Inference for Longitudinal Data Using Normalizing Flows](https://mlsanity.com/paper/2303.14220/) (2023)
- [Use the Detection Transformer as a Data Augmenter](https://mlsanity.com/paper/2304.04554/) (2023)
- [Sampling From Autoencoders' Latent Space via Quantization And Probability Mass Function Concepts](https://mlsanity.com/paper/2308.10704/) (2023)
- [Pseudo-Nonlinear Data Augmentation: A Constrained Energy Minimization Viewpoint](https://mlsanity.com/paper/2410.00718/) (2024)
- [An Elastic Shape Variational Autoencoder for Skeleton Pose Trajectories](https://mlsanity.com/paper/2605.09231/) (2026)
- [Task-Induced Riemannian Metrics for Vision Transformer Feature Spaces](https://mlsanity.com/paper/2609.27988/) (2026)

## Abstract (arXiv)

In this paper, we propose a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder. Our approach combines a proper latent space modeling of the VAE seen as a Riemannian manifold with a new generation scheme which produces more meaningful samples especially in the context of small data sets. The proposed method is tested through a wide experimental study where its robustness to data sets, classifiers and training samples size is stressed. It is also validated on a medical imaging classification task on the challenging ADNI database where a small number of 3D brain MRIs are considered and augmented using the proposed VAE framework. In each case, the proposed method allows for a significant and reliable gain in the classification metrics. For instance, balanced accuracy jumps from 66.3% to 74.3% for a state-of-the-art CNN classifier trained with 50 MRIs of cognitively normal (CN) and 50 Alzheimer disease (AD) patients and from 77.7% to 86.3% when trained with 243 CN and 210 AD while improving greatly sensitivity and specificity metrics.