VAE with Hyperspherical Coordinates: Improving Anomaly Detection from Hypervolume-Compressed Latent Space

TL;DR

This paper introduces a hyperspherical coordinate approach for VAEs to enhance anomaly detection, addressing high-dimensional latent space challenges and outperforming existing methods on real-world and benchmark datasets.

Contribution

The paper proposes a novel hyperspherical coordinate formulation for VAE latent variables, improving anomaly detection performance in high-dimensional settings.

Findings

Improved unconditional-OOD and conditional-OOD detection accuracy.

Outperforms existing methods on complex real-world datasets.

Effective in high-dimensional latent space scenarios.

Abstract

Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, one can hope to detect out-of-distribution (abnormal) latent vectors, but several issues arise when the latent space is high dimensional. This includes an exponential growth of the hypervolume with the dimension, which severely affects the generative capacity of the VAE. In this paper, we draw insights from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are distributed on the `equators' of a hypersphere, challenging the detection of anomalies. We propose to formulate the latent variables of a VAE using hyperspherical coordinates, which allows compressing the latent vectors towards a given direction on the hypersphere, thereby allowing for a more expressive approximate posterior. We show that this improves both the fully unconditional-OOD and conditional-OOD anomaly detection ability of the VAE, achieving the best performance on the datasets we considered, outperforming existing methods. For the unconditional-OOD and conditional-OOD modalities, respectively, these are: i) detecting unusual landscape from the Mars Rover camera and unusual Galaxies from ground based imagery (complex, real world datasets); ii) standard benchmarks like Cifar10 and subsets of ImageNet as the in-distribution (ID) class.