Rate-Distortion Optimization Guided Autoencoder for Isometric Embedding in Euclidean Latent Space

Abstract

To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However, they struggle to accurately reproduce the probability distribution function (PDF) in the input space from that in the latent space. If the embedding were isometric, this issue can be solved, because the relation of PDFs can become tractable. To achieve isometric property, we propose Rate-Distortion Optimization guided autoencoder inspired by orthonormal transform coding. We show our method has the following properties: (i) the Jacobian matrix between the input space and a Euclidean latent space forms a constantly-scaled orthonormal system and enables isometric data embedding; (ii) the relation of PDFs in both spaces can become tractable one such as proportional relation. Furthermore, our method outperforms state-of-the-art methods in unsupervised anomaly detection with four public datasets.