Deep Manifold Transformation for Nonlinear Dimensionality Reduction

• URL: http://arxiv.org/abs/2010.14831v3
• Date: Mon, 3 May 2021 15:24:11 GMT
• Title: Deep Manifold Transformation for Nonlinear Dimensionality Reduction
• Authors: Stan Z. Li, Zelin Zang, Lirong Wu
• Abstract summary: 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. 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.
• Score: 37.7499958388076
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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