基于超球面坐标的变分自编码器：改善超体积压缩潜在空间中的异常检测

Variational autoencoders (VAEs) encode data into lower-dimensional latent vectors before decoding them back to data. Once trained, detecting out-of-distribution (anomalous) latent vectors is a common objective. However, several issues arise when the latent space is high-dimensional, notably the exponential growth of hypervolume with dimension, which severely impacts the VAE's generative capacity. Drawing insights from high-dimensional geometry, this paper introduces a novel VAE architecture that maps the latent space onto a hypersphere. By modeling latent variables in a hyperspherical coordinate system, the proposed method effectively addresses the hypervolume expansion problem in high-dimensional latent spaces. Specifically, this approach leverages the properties of spherical coordinates to decouple the norm and direction of latent vectors, enabling better control over the latent space distribution. This design helps mitigate the degradation of generative capacity in traditional VAEs caused by data sparsity in high-dimensional latent spaces. Furthermore, constraining the latent space to a hypersphere encourages more compact representations for normal samples, making anomalous samples more likely to deviate from this compact region. This structural advantage significantly enhances anomaly detection performance. Experimental results demonstrate that the VAE with hyperspherical coordinates achieves substantial improvements in anomaly detection tasks across multiple public datasets compared to standard VAEs with Euclidean latent spaces, particularly in high-dimensional data scenarios. This method offers a novel and effective avenue for generative models and anomaly detection in high-dimensional data settings.