README

The R package rsvddpd is an acronym for Robust Singular Value Decomposition using Density Power Divergence. As the name suggests, the package mainly concerns with a special function for performing SVD in a robust way in presence of outliers. The details of the algorithm can be found in the paper https://arxiv.org/abs/2109.10680.

Installation

# install.packages("devtools")
devtools::install_github("subroy13/rsvddpd")

Use the following to install the development version with manuals and vignettes, which provides useful information about the structure of the function.

devtools::install_github("subroy13/rsvddpd", build_opts = c("--no-resave-data"), build_manual = TRUE, build_vignettes = TRUE)

Examples

library(rsvddpd)

X <- matrix(1:20, nrow = 4, ncol = 5)
svd(X)
#> $d
#> [1] 5.352022e+01 2.363426e+00 4.870683e-15 7.906968e-16
#> 
#> $u
#>            [,1]       [,2]        [,3]       [,4]
#> [1,] -0.4430188 -0.7097424 -0.52426094  0.1585890
#> [2,] -0.4798725 -0.2640499  0.81721984  0.1793091
#> [3,] -0.5167262  0.1816426 -0.06165685 -0.8343851
#> [4,] -0.5535799  0.6273351 -0.23130204  0.4964870
#> 
#> $v
#>             [,1]        [,2]       [,3]       [,4]
#> [1,] -0.09654784  0.76855612 -0.6000256  0.1704800
#> [2,] -0.24551564  0.48961420  0.5577664 -0.5560862
#> [3,] -0.39448345  0.21067228  0.2312115  0.1606664
#> [4,] -0.54345125 -0.06826963  0.2643802  0.6650059
#> [5,] -0.69241905 -0.34721155 -0.4533325 -0.4400661

As you can see, the first two singular values are 53.5 and 2.36, and the third and fourth singular values are very small positive reals.

Let us see what happens when you contaminate just one entry of the matrix by a large value say 100.

X[2, 3] <- 100
svd(X)
#> $d
#> [1] 1.070340e+02 3.617861e+01 2.200002e+00 1.851858e-15
#> 
#> $u
#>            [,1]       [,2]         [,3]          [,4]
#> [1,] -0.1472125 -0.4893994  0.816938282  2.672612e-01
#> [2,] -0.9548191  0.2971284  0.005940614 -1.110223e-16
#> [3,] -0.1753739 -0.5614500 -0.105644232 -8.017837e-01
#> [4,] -0.1894546 -0.5974754 -0.566935489  5.345225e-01
#> 
#> $v
#>             [,1]       [,2]         [,3]          [,4]
#> [1,] -0.03121244 -0.1097166 -0.798115312  3.357170e-01
#> [2,] -0.08603093 -0.2591083 -0.524844308 -6.516983e-01
#> [3,] -0.94371346  0.3306537 -0.008548386  1.387779e-16
#> [4,] -0.19566792 -0.5578918  0.021697699  6.122270e-01
#> [5,] -0.25048641 -0.7072836  0.294968703 -2.962457e-01

Note that, the first singular value changes drastically, being 107, while second and third singular values 36.1 and 2.2 respectively. However, such error is very common in practice, and can pose serious problem in many statistical estimation techniques. rSVDdpd solves the problem as shown in the following code.

rSVDdpd(X, alpha = 0.3)
#> $d
#> [1] 5.355990e+01 2.358915e+00 1.492008e-01 6.694858e-11
#> 
#> $u
#>           [,1]       [,2]       [,3]          [,4]
#> [1,] 0.4426825 -0.7124356  0.4743827  2.672615e-01
#> [2,] 0.4810583 -0.2588203 -0.8376126  2.697441e-07
#> [3,] 0.5163450  0.1804013  0.2408039 -8.017834e-01
#> [4,] 0.5531753  0.6268197  0.1240144  5.345228e-01
#> 
#> $v
#>            [,1]        [,2]       [,3]          [,4]
#> [1,] 0.09646637  0.77032520  0.2174706 -5.827481e-01
#> [2,] 0.24532578  0.49133794  0.2200041  7.031679e-01
#> [3,] 0.39606323  0.20319890 -0.8954575  5.552961e-07
#> [4,] 0.54304936 -0.06663662  0.2250709  2.214907e-01
#> [5,] 0.69191099 -0.34562390  0.2276043 -3.419085e-01

Author

Getting help

If you encounter a clear bug, please file an issue with a minimal reproducible example on GitHub.