Rate-Distortion Optimization Guided Autoencoder for Isometric Embedding in Euclidean Latent Space
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Anomaly DetectionRelationUnsupervised Anomaly DetectionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Quantitative Understanding of VAE as a Non-linearly Scaled Isometric Embedding
Variational autoencoder (VAE) estimates the posterior parameters (mean and variance) of latent variables corresponding to each input data. While it is used for many tasks, the transparency of the model is still an underl…
Nearly Isometric Embedding by Relaxation
Many manifold learning algorithms aim to create embeddings with low or no distortion (i.e. isometric). If the data has intrinsic dimension d, it is often impossible to obtain an isometric embedding in d dimensions, but p…
Robust Nonrigid Registration by Convex Optimization
We present an approach to nonrigid registration of 3D surfaces. We cast isometric embedding as MRF optimization and apply efficient global optimization algorithms based on linear programming relaxations. The Markov rando…
global-optimizationRATE-DISTORTION OPTIMIZATION GUIDED AUTOENCODER FOR GENERATIVE APPROACH
In the generative model approach of machine learning, it is essential to acquire an accurate probabilistic model and compress the dimension of data for easy treatment. However, in the conventional deep-autoencoder based …
Anomaly DetectionUnsupervised Anomaly DetectionImproved Linear Embeddings via Lagrange Duality
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion fo…