Matrix completion methods

[mortonjt]

We'll want to have a handful of methods that seem appropriate to benchmark. Still need to finalize the following list

• [ ] Principal Components Pursuit
• [ ] Aitchison matrix norm?
• [ ] ?
• [ ] ?

[cameronmartino]

Compiled an inclusive list of state of the art methods to narrow down. The list based on the work/benchmarks for RNA-seq/Genechip/image-processing matrix completion.

- Categories of methods to use

• [ ] Global algorithms, homogenous data, work well with large amounts of missing data

Correlation information is derived from the entire data matrix. They assume the existence of a global covariance structure among all genes or samples in the expression matrix. (Liew et al. 2011)

• [ ] Local algorithms, heterogenous data with dominant local similarity, work well with smaller amounts of missing data

exploit only local similarity structure in the data set for missing value imputation. Only a subset of genes that exhibits high correlation with the gene containing the missing values is used to compute the missing values in the gene. (Liew et al. 2011)

• [ ] Hybrids, decided weighted combinations of global and local methods

Captures both global and local correlation information in the data. For example in LinCmb, the missing values are estimated by a convex combination of the estimates of five different imputation methods (both global and local) (Liew et al. 2011)

• [ ] Knowledge assisted approach

Domain knowledge or external information is integrated into the estimation process (Liew et al. 2011)

- Methods to Consider (no particular order)

• [ ] Unknown values to zero (current method)

• [ ] Row average method (Base Benchmark)

• [ ] PCP (L1) rank reduction + Aitchison matrix norm (novel compositional, will read up on the norm)

• [ ] Nonparametric Imputation [Fernandez et al. 2003] (Compositional)

• [ ] LRGeomCG Riemannian [Vandereycken (2013)] (Global)

• [ ] RMAMR Augmented Lagrangian [Ye et al. (2015)] (Global)

• [ ] Gene expression prediction method, (modified PCP method) [Kapur et al. 2016] (Global)

• [ ] bi-BPCA [Meng, et al. 2014] (local)

• [ ] Bicluster-based least square [Cheng et al. (2012)] (Local)

• [ ] EMDI [Pan et al. 2011] (Hybrid)

• [ ] POCS [Gan et al. 2006] (Knowledge assisted)