Spectral Clustering Based on Local PCA

TL;DR

This paper introduces a spectral clustering method that leverages local PCA to better distinguish intersecting manifolds, providing theoretical guarantees and demonstrating effectiveness on simulated data.

Contribution

The paper presents a novel spectral clustering algorithm based on local PCA that can resolve intersections, with theoretical analysis and empirical validation.

Findings

Algorithm successfully resolves intersecting manifolds.

Theoretical guarantees established for simplified variants.

Effective performance demonstrated on simulated datasets.

Abstract

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the principal subspaces in the neighborhoods, and then applies spectral clustering. As opposed to standard spectral methods based solely on pairwise distances between points, our algorithm is able to resolve intersections. We establish theoretical guarantees for simpler variants within a prototypical mathematical framework for multi-manifold clustering, and evaluate our algorithm on various simulated data sets.