Spectral Clustering Based on Local PCA
This work addresses clustering challenges in multi-manifold data, offering an incremental improvement over standard spectral methods.
The authors tackled the problem of spectral clustering in multi-manifold settings by proposing a method based on local PCA, which resolves intersections and was evaluated on simulated data sets with theoretical guarantees.
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.