Matrix Coherence and the Nystrom Method

Abstract

The Nystrom method is an efficient technique to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this assumption to the concept of matrix coherence and connect matrix coherence to the performance of the Nystrom method. Making use of related work in the compressed sensing and the matrix completion literature, we derive novel coherence-based bounds for the Nystrom method in the low-rank setting. We then present empirical results that corroborate these theoretical bounds. Finally, we present more general empirical results for the full-rank setting that convincingly demonstrate the ability of matrix coherence to measure the degree to which information can be extracted from a subset of columns.

References in corpus (2)

• Sparsity and Incoherence in Compressive Sampling
• The Power of Convex Relaxation: Near-Optimal Matrix Completion

Cited by in corpus (5)

• The Effect of Coherence on Sampling from Matrices with Orthonormal Columns, and Preconditioned Least Squares Problems
• SketchyCoreSVD: SketchySVD from Random Subsampling of the Data Matrix
• Compressive PCA for Low-Rank Matrices on Graphs
• On the Estimation of Coherence
• Fast Fourier-Based Generation of the Compression Matrix for Deterministic Compressed Sensing