A Metric-based Principal Curve Approach for Learning One-dimensional Manifold

TL;DR

This paper introduces a metric-based principal curve method for effectively learning one-dimensional manifolds in spatial data, demonstrating strong performance on synthetic and real datasets like MNIST.

Contribution

The paper proposes a novel metric-based principal curve approach that improves manifold learning by accurately capturing one-dimensional structures in data.

Findings

Successfully learns one-dimensional manifolds in synthetic data

Effectively captures manifold shape in MNIST dataset

Outperforms traditional methods in shape approximation

Abstract

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.