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

To analyze high-dimensional and complex data in the real world, deep\ngenerative models, such as variational autoencoder (VAE) embed data in a\nlow-dimensional space (latent space) and learn a probabilistic model in the\nlatent space. However, they struggle to accurately reproduce the probability\ndistribution function (PDF) in the input space from that in the latent space.\nIf the embedding were isometric, this issue can be solved, because the relation\nof PDFs can become tractable. To achieve isometric property, we propose Rate-\nDistortion Optimization guided autoencoder inspired by orthonormal transform\ncoding. We show our method has the following properties: (i) the Jacobian\nmatrix between the input space and a Euclidean latent space forms a\nconstantlyscaled orthonormal system and enables isometric data embedding; (ii)\nthe relation of PDFs in both spaces can become tractable one such as\nproportional relation. Furthermore, our method outperforms state-of-the-art\nmethods in unsupervised anomaly detection with four public datasets.\n