optspace {vegan} | R Documentation |
optspace: algorithm for matrix reconstruction from a partially revealed set
Description
This function was adapted from the original source code in the
Roptspace R package (version 0.2.3; MIT License) by Raghunandan
H. Keshavan, Andrea Montanari, Sewoong Oh (2010). See
ROptSpace::OptSpace
for more information. Let's assume an ideal
matrix M
with (m\times n)
entries with rank r
and we
are given a partially observed matrix M\_E
which contains many
missing entries. Matrix reconstruction - or completion - is the task
of filling in such entries. optspace is an efficient algorithm that
reconstructs M
from |E|=O(rn)
observed elements with
relative root mean square error (RMSE)
RMSE \le
C(\alpha)\sqrt{nr/|E|}
.
Usage
optspace(x, ropt = 3, niter = 5, tol = 1e-5, verbose = FALSE)
Arguments
x |
An |
ropt |
|
niter |
Maximum number of iterations allowed. |
tol |
Stopping criterion for reconstruction in Frobenius norm. |
verbose |
a logical value; |
Details
This implementation removes the trimming step of the original
Roptspace::OptSpace
code in order to leave feature filtering to the
user. Some of the defaults have been adjusted to better reflect
ecological data. The implementation has been adjusted for ecological
applications as in Martino et al. (2019). The imputed matrix (M) in
the optspace output includes matrix reconstruction (XSY'), with
subsequent centering for the columns and rows.
Value
Returns a named list containing:
X |
an |
S |
an |
Y |
an |
dist |
a vector containing reconstruction errors at each successive iteration. |
M |
an |
Author(s)
Leo Lahti and Cameron Martino, with adaptations of the method
implemented in Roptspace::OptSpace
by Keshavan et
al. (2010).
References
Keshavan, R. H., Montanari, A., Oh, S. (2010). Matrix Completion From a Few Entries. IEEE Transactions on Information Theory 56(6):2980–2998.
Martino, C., Morton, J.T., Marotz, C.A., Thompson, L.R., Tripathi, A., Knight, R. & Zengler, K. (2019) A novel sparse compositional technique reveals microbial perturbations. mSystems 4, 1.
Examples
data(varespec)
# rclr transformation with no matrix completion for the 0/NA entries
x <- decostand(varespec, method = "rclr", impute = FALSE)
# Add matrix completion
xc <- optspace(x, ropt = 3, niter = 5, tol = 1e-5, verbose = FALSE)$M