# Deep Recursive Embedding for High-Dimensional Data

arXiv: https://arxiv.org/abs/2104.05171 · HTML: https://mlsanity.com/paper/2104.05171/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 12 Apr 2021.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [Deep Learning of Representations: Looking Forward](https://mlsanity.com/paper/1305.0445/) (2013)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Approximated and User Steerable tSNE for Progressive Visual Analytics](https://mlsanity.com/paper/1512.01655/) (2015)
- [t-SNE-CUDA: GPU-Accelerated t-SNE and its Applications to Modern Data](https://mlsanity.com/paper/1807.11824/) (2018)
- [Deep Learning Multidimensional Projections](https://mlsanity.com/paper/1902.07958/) (2019)
- [Divide and Conquer: Leveraging Intermediate Feature Representations for Quantized Training of Neural Networks](https://mlsanity.com/paper/1906.06033/) (2019)

## Built on by (most cited first, 2 of 2)

- [A Robust and Efficient Boundary Point Detection Method by Measuring Local Direction Dispersion](https://mlsanity.com/paper/2312.04065/) (2023)
- [On Out-of-sample Embedding in UMAP](https://mlsanity.com/paper/2606.04451/) (2026)

## Abstract (arXiv)

t-distributed stochastic neighbor embedding (t-SNE) is a well-established visualization method for complex high-dimensional data. However, the original t-SNE method is nonparametric, stochastic, and often cannot well prevserve the global structure of data as it emphasizes local neighborhood. With t-SNE as a reference, we propose to combine the deep neural network (DNN) with the mathematical-grounded embedding rules for high-dimensional data embedding. We first introduce a deep embedding network (DEN) framework, which can learn a parametric mapping from high-dimensional space to low-dimensional embedding. DEN has a flexible architecture that can accommodate different input data (vector, image, or tensor) and loss functions. To improve the embedding performance, a recursive training strategy is proposed to make use of the latent representations extracted by DEN. Finally, we propose a two-stage loss function combining the advantages of two popular embedding methods, namely, t-SNE and uniform manifold approximation and projection (UMAP), for optimal visualization effect. We name the proposed method Deep Recursive Embedding (DRE), which optimizes DEN with a recursive training strategy and two-stage losse. Our experiments demonstrated the excellent performance of the proposed DRE method on high-dimensional data embedding, across a variety of public databases. Remarkably, our comparative results suggested that our proposed DRE could lead to improved global structure preservation.