# Trajectory-aware Principal Manifold Framework for Data Augmentation and Image Generation

arXiv: https://arxiv.org/abs/2310.07801 · HTML: https://mlsanity.com/paper/2310.07801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 30 Jul 2023.

## Builds on (most cited first, 17 of 17)

- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [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)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Generalizing from a Few Examples: A Survey on Few-Shot Learning](https://mlsanity.com/paper/1904.05046/) (2019)
- [Few-shot Image Generation via Cross-domain Correspondence](https://mlsanity.com/paper/2104.06820/) (2021)
- [Free Lunch for Few-shot Learning: Distribution Calibration](https://mlsanity.com/paper/2101.06395/) (2021)
- [Few-shot Image Generation with Elastic Weight Consolidation](https://mlsanity.com/paper/2012.02780/) (2020)
- [Delta-encoder: an effective sample synthesis method for few-shot object recognition](https://mlsanity.com/paper/1806.04734/) (2018)
- [Understanding and Improving Interpolation in Autoencoders via an Adversarial Regularizer](https://mlsanity.com/paper/1807.07543/) (2018)
- [Low-shot Learning via Covariance-Preserving Adversarial Augmentation Networks](https://mlsanity.com/paper/1810.11730/) (2018)
- [Transductive Few-Shot Classification on the Oblique Manifold](https://mlsanity.com/paper/2108.04009/) (2021)
- [Gaussian Prototypical Networks for Few-Shot Learning on Omniglot](https://mlsanity.com/paper/1708.02735/) (2017)
- [Asymmetric Distribution Measure for Few-shot Learning](https://mlsanity.com/paper/2002.00153/) (2020)
- [Augmentation-Interpolative AutoEncoders for Unsupervised Few-Shot Image Generation](https://mlsanity.com/paper/2011.13026/) (2020)

## Built on by (most cited first, 1 of 1)

- [Curvature Enhanced Data Augmentation for Regression](https://mlsanity.com/paper/2506.06853/) (2025)

## Abstract (arXiv)

Data augmentation for deep learning benefits model training, image transformation, medical imaging analysis and many other fields. Many existing methods generate new samples from a parametric distribution, like the Gaussian, with little attention to generate samples along the data manifold in either the input or feature space. In this paper, we verify that there are theoretical and practical advantages of using the principal manifold hidden in the feature space than the Gaussian distribution. We then propose a novel trajectory-aware principal manifold framework to restore the manifold backbone and generate samples along a specific trajectory. On top of the autoencoder architecture, we further introduce an intrinsic dimension regularization term to make the manifold more compact and enable few-shot image generation. Experimental results show that the novel framework is able to extract more compact manifold representation, improve classification accuracy and generate smooth transformation among few samples.