A Growing Self-Organizing Network for Reconstructing Curves and Surfaces

TL;DR

This paper introduces a new growing self-organizing network designed to accurately and stably reconstruct the topological structure of known-dimensional input manifolds, enhancing manifold learning applications.

Contribution

It presents a novel self-organizing network that guarantees effective and stable recovery of the input manifold's topology when the manifold's dimension is known.

Findings

The network effectively reconstructs the topology of input manifolds.

It demonstrates stability in topological recovery.

The approach improves manifold learning accuracy.

Abstract

Self-organizing networks such as Neural Gas, Growing Neural Gas and many others have been adopted in actual applications for both dimensionality reduction and manifold learning. Typically, in these applications, the structure of the adapted network yields a good estimate of the topology of the unknown subspace from where the input data points are sampled. The approach presented here takes a different perspective, namely by assuming that the input space is a manifold of known dimension. In return, the new type of growing self-organizing network presented gains the ability to adapt itself in way that may guarantee the effective and stable recovery of the exact topological structure of the input manifold.