A Metric-based Principal Curve Approach for Learning One-dimensional Manifold
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Abstract (arXiv)
Principal curve is a well-known statistical method oriented in manifold learning using concepts from differential geometry. In this paper, we propose a novel metric-based principal curve (MPC) method that learns one-dimensional manifold of spatial data. Synthetic datasets Real applications using MNIST dataset show that our method can learn the one-dimensional manifold well in terms of the shape.
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References · 9
- 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
- 2020Geoopt: Riemannian Optimization in PyTorchcited by 114
- 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 94
- 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
- 2016Fr'echet Regression for Random Objects with Euclidean Predictorscited by 57
- 2020Geometrically Enriched Latent Spacescited by 45
- 2020Wasserstein Regressioncited by 35
- 2016A Locally Adaptive Normal Distributioncited by 23
- 2023Invertible Kernel PCA with Random Fourier Featurescited by 6
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