# eimpute:
Efficiently IMPUTE Large Scale Incomplete Matrix

## Introdution

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.

## Software

A computationally efficient R package, **eimpute** is
developed for matrix completion.

### Installation

Install the stable version from CRAN:

`install.packages("eimpute")`

### Advantage

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
Moreover, **eimpute** also supports flexible data
standardization.

Compare **eimpute** and **softimpute** in
systhesis datasets \(X_{m \times m}\)
with \(p\) proportion missing
observations:

- \(m\) 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.

## References

Rahul Mazumder, Trevor Hastie and Rob Tibshirani (2010) Spectra
Regularization Algorithms for Learning Large Incomplete Matrices,
Journal of Machine Learning Research 11 (2010) 2287-2322

Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp (2011) Finding
Structure with Randomness: Probabilistic Algorithms for Constructing
Approximate Matrix Decompositions, SIAM Review Vol. 53, num. 2,
pp. 217-288

## Bug report

Send an email to Zhe Gao at gaozh8@mail.ustc.edu.cn