  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
constantlyscaled 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.
