Matrix completion and extrapolation via kernel regression

TL;DR

This paper introduces a kernel ridge regression approach for matrix completion and extrapolation within RKHSs, providing a faster, low-complexity algorithm that improves accuracy, especially with noisy data, and supports online implementation.

Contribution

It presents a novel kernel ridge regression-based algorithm for MCEX that is faster, more accurate, and suitable for online use, leveraging prior information in RKHSs.

Findings

Faster than ALS and SGD methods.

Reduces recovery error, especially with noisy data.

Supports online implementation.

Abstract

Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is formulated as a kernel ridge regression. The resultant MCEX algorithm can also afford online implementation, while the class of kernel functions also encompasses several existing approaches to MC with prior information. Numerical tests on synthetic and real datasets show that the novel approach performs faster than widespread methods such as alternating least squares (ALS) or stochastic gradient descent (SGD), and that the recovery error is reduced, especially when dealing with noisy data.