Deep Manifold Transformation for Nonlinear Dimensionality Reduction
This work addresses a key limitation in unsupervised dimensionality reduction for data exploration, though it appears incremental as it builds on existing deep neural network approaches with added constraints.
The paper tackles the problem of existing manifold learning methods failing to preserve geometric, topological, and distributional structures in nonlinear dimensionality reduction, proposing a deep manifold transformation framework that outperforms leading methods in structure preservation.
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.