  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.
