Introduction
Matrix completion is a procedure for imputing the missing elements in matrices by using the information of observed elements. This procedure can be visualized as:
Matrix completion has attracted a lot of attention, it is widely applied in:
- tabular data imputation: recover the missing elements in data table;
- recommend system: estimate users’ potantial preference for items pending purchased;
- image inpainting: inpaint the missing elements in digit images.
A computationally efficient R package, eimpute is developed for matrix completion. In eimpute, matrix completion problem is solved by iteratively performing low-rank approximation and data calibration, which enjoy two admirable advantages:
- unbiased low-rank approximation for incomplete matrix
- less time consumption via truncated SVD
Compare eimpute and softimpute in systhesis datasets \(X_{m \times m}\) with \(p\) proportion missing observations. The square matrix \(X_{m \times m}\) is generated by \(X = UV + \epsilon\), where \(U\) and \(V\) are \(m \times r\), \(r \times n\) matrices whose entries are \(i.i.d.\) sampled standard normal distribution, \(\epsilon \sim N(0, r/3)\).
- \(m\) is chosen as 1000, 2000, 3000, 4000
- \(p\) is chosen as 0.1, 0.5, 0.9.
In high dimension case, als method in softimpute is a little faster than eimpute in low proportion of missing observations, as the proportion of missing observations increase, rsvd method in eimpute have a better performance than softimpute in time cost and test error. Compare with two method in **eimpute*, rsvd method is better than tsvd in time cost.