A critical parameter in NMF algorithms is the
factorization rank \(r\). It defines the number of
basis effects used to approximate the target matrix.
Function nmfEstimateRank helps in choosing an
optimal rank by implementing simple approaches proposed
in the literature.
Note that from version 0.7, one can equivalently
call the function nmf with a range of
ranks.
In the plot generated by plot.NMF.rank, each curve
represents a summary measure over the range of ranks in
the survey. The colours correspond to the type of data to
which the measure is related: coefficient matrix, basis
component matrix, best fit, or consensus matrix.
nmfEstimateRank(x, range,
method = nmf.getOption("default.algorithm"), nrun = 30,
model = NULL, ..., verbose = FALSE, stop = FALSE) # S3 method for NMF.rank
plot (x, y = NULL,
what = c("all", "cophenetic", "rss", "residuals", "dispersion", "evar",
"sparseness", "sparseness.basis", "sparseness.coef", "silhouette",
"silhouette.coef", "silhouette.basis", "silhouette.consensus"),
na.rm = FALSE, xname = "x", yname = "y",
xlab = "Factorization rank", ylab = "",
main = "NMF rank survey", ...)
nmfEstimateRank returns a S3 object (i.e. a list)
of class NMF.rank with the following elements:
a data.frame containing the
quality measures for each rank of factorizations in
range. Each row corresponds to a measure, each
column to a rank.
a list of
consensus matrices, indexed by the rank of factorization
(as a character string).
a list of
the fits, indexed by the rank of factorization (as a
character string).
For nmfEstimateRank a target object to be
estimated, in one of the format accepted by interface
nmf.
For plot.NMF.rank an object of class
NMF.rank as returned by function
nmfEstimateRank.
a numeric vector containing the ranks
of factorization to try. Note that duplicates are removed
and values are sorted in increasing order. The results
are notably returned in this order.
A single NMF algorithm, in one of the
format accepted by the function nmf.
a numeric giving the number of run to
perform for each value in range.
model specification passed to each
nmf call. In particular, when x is a
formula, it is passed to argument data of
nmfModel to determine the target matrix --
and fixed terms.
toggle verbosity. This parameter only
affects the verbosity of the outer loop over the values
in range. To print verbose (resp. debug) messages
from each NMF run, one can use .options='v' (resp.
.options='d') that will be passed to the function
nmf.
logical flag for running the estimation
process with fault tolerance. When TRUE, the
whole execution will stop if any error is raised. When
FALSE (default), the runs that raise an error will
be skipped, and the execution will carry on. The summary
measures for the runs with errors are set to NA values,
and a warning is thrown.
For nmfEstimateRank, these are extra
parameters passed to interface nmf. Note that the
same parameters are used for each value of the rank. See
nmf.
For plot.NMF.rank, these are extra graphical
parameter passed to the standard function plot.
See plot.
reference object of class NMF.rank, as
returned by function nmfEstimateRank. The measures
contained in y are used and plotted as a
reference. It is typically used to plot results obtained
from randomized data. The associated curves are drawn in
red (and pink), while those from x
are drawn in blue (and green).
a character vector whose elements
partially match one of the following item, which
correspond to the measures computed by
summary on each -- multi-run -- NMF result:
‘all’, ‘cophenetic’, ‘rss’,
‘residuals’, ‘dispersion’, ‘evar’,
‘silhouette’ (and more specific *.coef, *.basis,
*.consensus), ‘sparseness’ (and more specific
*.coef, *.basis). It specifies which measure must be
plotted (what='all' plots all the measures).
single logical that specifies if the rank
for which the measures are NA values should be removed
from the graph or not (default to FALSE). This is
useful when plotting results which include NAs due to
error during the estimation process. See argument
stop for nmfEstimateRank.
legend labels for the curves
corresponding to measures from x and y
respectively
x-axis label
y-axis label
main title
Given a NMF algorithm and the target matrix, a common way of estimating \(r\) is to try different values, compute some quality measures of the results, and choose the best value according to this quality criteria. See Brunet et al. (2004) and Hutchins et al. (2008).
The function nmfEstimateRank allows to perform
this estimation procedure. It performs multiple NMF runs
for a range of rank of factorization and, for each,
returns a set of quality measures together with the
associated consensus matrix.
In order to avoid overfitting, it is recommended to run
the same procedure on randomized data. The results on the
original and the randomised data may be plotted on the
same plots, using argument y.
Brunet J, Tamayo P, Golub TR and Mesirov JP (2004). "Metagenes and molecular pattern discovery using matrix factorization." _Proceedings of the National Academy of Sciences of the United States of America_, *101*(12), pp. 4164-9. ISSN 0027-8424, <URL: http://dx.doi.org/10.1073/pnas.0308531101>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/15016911>.
Hutchins LN, Murphy SM, Singh P and Graber JH (2008). "Position-dependent motif characterization using non-negative matrix factorization." _Bioinformatics (Oxford, England)_, *24*(23), pp. 2684-90. ISSN 1367-4811, <URL: http://dx.doi.org/10.1093/bioinformatics/btn526>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/18852176>.
# roxygen generated flag
options(R_CHECK_RUNNING_EXAMPLES_=TRUE)
if( !isCHECK() ){
set.seed(123456)
n <- 50; r <- 3; m <- 20
V <- syntheticNMF(n, r, m)
# Use a seed that will be set before each first run
res <- nmfEstimateRank(V, seq(2,5), method='brunet', nrun=10, seed=123456)
# or equivalently
res <- nmf(V, seq(2,5), method='brunet', nrun=10, seed=123456)
# plot all the measures
plot(res)
# or only one: e.g. the cophenetic correlation coefficient
plot(res, 'cophenetic')
# run same estimation on randomized data
rV <- randomize(V)
rand <- nmfEstimateRank(rV, seq(2,5), method='brunet', nrun=10, seed=123456)
plot(res, rand)
}
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