Angle constrained path to cluster multiple manifolds

TL;DR

This paper introduces a simple angle-constrained path method for clustering intersected manifolds, extending Isomap's capabilities to handle manifold intersections effectively.

Contribution

A novel, straightforward algorithm that uses angle constraints to cluster intersected manifolds, improving upon existing methods for manifold clustering.

Findings

Performs comparably to state-of-the-art methods on simulated data

Effective in clustering intersected manifolds

Simpler than previous approaches

Abstract

In this paper, we propose a method to cluster multiple intersected manifolds. The algorithm chooses several landmark nodes randomly and then checks whether there is an angle constrained path between each landmark node and every other node in the neighborhood graph. When the points lie on different manifolds with intersection they should not be connected using a smooth path, thus the angle constraint is used to prevent connecting points from one cluster to another one. The resulting algorithm is implemented as a simple variation of Dijkstras algorithm used in Isomap. However, Isomap was specifically designed for dimensionality reduction in the single-manifold setting, and in particular, can-not handle intersections. Our method is simpler than the previous proposals in the literature and performs comparably to the best methods, both on simulated and some real datasets.