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

Jul 12, 2020

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To analyze high-dimensional and complex data in the real world, generative model approach of machine learning aims to reduce the dimension and acquire a probabilistic model of the data. For this purpose, deep-autoencoder based generative models such as variational autoencoder (VAE) have been proposed. However, in previous works, the scale of metrics between the real and the reduced-dimensional space (latent space) is not well-controlled. Therefore, the quantitative impact of the latent variable on real data is unclear. In the end, the probability distribution function (PDF) in the real space cannot be estimated from that of the latent space accurately. To overcome this problem, we propose Rate-Distortion Optimization guided autoencoder. We show our method has the following properties theoretically and experimentally: (i) the columns of Jacobian matrix between two spaces is constantly-scaled orthonormal system and data can be embedded in a Euclidean space isometrically; (ii) the PDF of the latent space is proportional to that of the real space. Furthermore, to verify the usefulness in the practical application, we evaluate its performance in unsupervised anomaly detection and it outperforms current state-of-the-art methods.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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