Efficiently Impute Large Scale Incomplete Matrix

Efficiently impute large scale matrix with missing values via its unbiased low-rank matrix approximation. Our main approach is Hard-Impute algorithm proposed in < https://www.jmlr.org/papers/v11/mazumder10a.html>, which achieves highly computational advantage by truncated singular-value decomposition.

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 [email protected]