  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. 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.
