Performance Analysis of Spectral Clustering on Compressed, Incomplete and Inaccurate Measurements

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and partially observed signals respectively. We combine the distance preserving measurements of compressed sensing and matrix completion with the power of robust spectral clustering. Our analysis provides rigorous bounds on how small errors in the affinity matrix can affect the spectral coordinates and clusterability. This work generalizes the current perturbation results of two-class spectral clustering to incorporate multi-class clustering with k eigenvectors. We thoroughly track how small perturbation from using compressed sensing and matrix completion affect the affinity matrix and in succession the spectral coordinates. These perturbation results for multi-class clustering require an eigengap between the kth and (k + 1)th eigenvalues of the affinity ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Blake Hunter, Thomas Strohmer
• Keywords: Affinity Matrix, Compressed Sensing, CORR 2010, Education, Matrix