Matrix Coherence and the Nystrom Method

08/09/2014
by   Ameet Talwalkar, et al.
0

The Nystrom method is an efficient technique used 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, connecting 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/04/2010

On the Estimation of Coherence

Low-rank matrix approximations are often used to help scale standard mac...
research
02/12/2013

Coherence and sufficient sampling densities for reconstruction in compressed sensing

We give a new, very general, formulation of the compressed sensing probl...
research
10/06/2021

A Weighted Generalized Coherence Approach for Sensing Matrix Design

As compared to using randomly generated sensing matrices, optimizing the...
research
07/14/2014

On the Power of Adaptivity in Matrix Completion and Approximation

We consider the related tasks of matrix completion and matrix approximat...
research
04/18/2019

On Low-rank Trace Regression under General Sampling Distribution

A growing number of modern statistical learning problems involve estimat...
research
06/26/2016

Fast Methods for Recovering Sparse Parameters in Linear Low Rank Models

In this paper, we investigate the recovery of a sparse weight vector (pa...
research
06/29/2016

Small coherence implies the weak Null Space Property

In the Compressed Sensing community, it is well known that given a matri...

Please sign up or login with your details

Forgot password? Click here to reset