Nonlinear dimensionality reduction (NLDR) plays an important role in feature extraction and visualization of high dimensional data . It transforms patterns of interest, or manifolds, in datato regions in a lower-dimensional latent space. When the manifolds are highly complicated, the NLDR transformation has to provide sufficient nonlinearity for downstream tasks. This paperproposes a novel method, called%DIFDELCMD < {\em %%%  deep manifold transformation (DMT) , to tackle this problem. As a multi-layer neural network, DMT can support a higher degree of nonlinearity than single-layer methods. Continuation strategy is applied during training to address the local minimum problem common in manifold learning algorithms. Such a learned DMT network can generalize to unseen data whereas traditional manifold learning methods only provide an embedding of the trainingdata . Extensive experiments , comparisons, and ablation studies demonstrate that DMT can deliver results superior to UMAP and t-SNE, and other leading manifold-based NLDR methods  .
Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional structures of data . %DIFDELCMD < {\em %%% In this paper, we propose a deep manifold learning framework, called deep manifold transformation (DMT) for unsupervised NLDR and embedding learning. DMT enhances deep neural networks by using cross-layer local geometry-preserving (LGP) constraints. The LGP constraints constitute the loss for deep manifold learning and serve as geometric regularizers for NLDR network training . Extensive experiments on synthetic and real-world data demonstrate that DMT networks outperform existing leading manifold-based NLDR methods in terms of preserving the structures of data .
R
Nonlinear
Manifold learning-based encoders have been playing important roles in nonlinear
R
plays an important role in feature extraction and visualization of high dimensional data
for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional structures of data
D
It transforms patterns of interest, or manifolds, in datato regions in a lower-dimensional latent space. When the manifolds are highly complicated, the NLDR transformation has to provide sufficient nonlinearity for downstream tasks. This paperproposes a novel method, called
A
In this paper, we propose a deep manifold learning framework, called
R
, to tackle this problem. As a multi-layer neural network, DMT can support a higher degree of nonlinearity than single-layer methods. Continuation strategy is applied during training to address the local minimum problem common in manifold learning algorithms. Such a learned DMT network can generalize to unseen data whereas traditional manifold learning methods only provide an embedding of the trainingdata
for unsupervised NLDR and embedding learning. DMT enhances deep neural networks by using cross-layer local geometry-preserving (LGP) constraints. The LGP constraints constitute the loss for deep manifold learning and serve as geometric regularizers for NLDR network training
R
, comparisons, and ablation studies
on synthetic and real-world data
R
can deliver results superior to UMAP and t-SNE, and other
networks outperform existing
A
in terms of preserving the structures of data