Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold. GAGA shows competitive performance in simulated and real world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

本研究针对传统方法在高维数据生成和流形学习中的不足，提出了一种几何感知生成自编码器GAGA，能够有效地处理数据生成、插值和人群迁移等问题。GAGA通过学习扭曲的黎曼度量，建立尊重内在几何的神经网络嵌入空间，表现出在单细胞轨迹推断中较现有方法提升30%的显著性能。

几何感知生成自编码器用于扭曲黎曼度量学习与数据流形的生成建模