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.

本研究通过验证在特征空间中使用主要流形分布相对于高斯分布的理论和实际优势，提出了一种新颖的轨迹感知主要流形框架，用于恢复流形骨干并沿特定轨迹生成样本。此外，通过引入一个内在维度正则化项，该框架能够使流形更紧凑，并实现少样本图像生成。实验结果表明，该框架能够提取更紧凑的流形表示，提高分类准确性，并在少样本之间生成平滑的变换。