Noisy matrix completion on a novel neural network framework

Abstract

A novel matrix completion algorithm based on the iterative application of neural networks is presented. It is shown that Bayesian regularization provides proper protection against overfitting, more so than early-stopping or a combination of both. The flexibility to increase the size of the hidden layer provides a better description of increasingly nonlinear relationships between the known and missing values in the data with a limited loss in generalization ability. The proposed neural network algorithm provides a more accurate estimation of missing values than current matrix completion algorithms based on iterative regression approaches or PCA applications for many datasets with fractions of missing values from 5 to 40%. The neural network algorithm performs particularly well on datasets where the number of observations significantly exceeds the number of features.