Deep Recursive Embedding for High-Dimensional Data

Zixia Zhou, Xinrui Zu, Yuanyuan Wang, Boudewijn P.F. Lelieveldt, Qian Tao

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Abstract

Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this article, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data embedding. We introduce a generic deep embedding network (DEN) framework, which is able to learn a parametric mapping from high-dimensional space to low-dimensional space, guided by well-established objectives such as Kullback-Leibler (KL) divergence minimization. We further propose a recursive strategy, called deep recursive embedding (DRE), to make use of the latent data representations for boosted embedding performance. We exemplify the flexibility of DRE by different architectures and loss functions, and benchmarked our method against the two most popular embedding methods, namely, t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP). The proposed DRE method can map out-of-sample data and scale to extremely large datasets. Experiments on a range of public datasets demonstrated improved embedding performance in terms of local and global structure preservation, compared with other state-of-The-Art embedding methods. Code is available at https://github.com/tao-Aimi/DeepRecursiveEmbedding.

Original languageEnglish
Pages (from-to)1237-1248
JournalIEEE Transactions on Visualization and Computer Graphics
Volume28
Issue number2
DOIs
Publication statusPublished - 2021

Keywords

  • Data visualization
  • deep embedding network
  • deep recursive embedding
  • Feature extraction
  • Manifolds
  • Standards
  • t-distributed stochastic neighbor embedding
  • Tools
  • Training
  • uniform manifold approximation and projection
  • Unsupervised learning
  • unsupervised learning

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