Before revision:  This paperproposes a novel method, called  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 .
After revision:  This paperproposes a novel method, 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 .