A Metric-based Principal Curve Approach for Learning One-dimensional Manifold
This work addresses manifold learning for spatial data, but it appears incremental as it builds on existing principal curve methods with a metric-based adaptation.
The authors tackled the problem of learning one-dimensional manifolds from spatial data by proposing a metric-based principal curve method, demonstrating its effectiveness on synthetic datasets and the MNIST dataset in terms of shape learning.
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.