feemparafac forwards its arguments to
parafac from the multiway package,
optionally rescales the result and attaches a few attributes.
Resulting objects of class feemparafac can be accessed using
methods presented below.
feemparafac(
X, ..., const = rep('nonneg', 3), ctol = 1e-6,
rescale = 3, retries = 10, subset = TRUE, envir = NULL
)
# S3 method for feemparafac
plot(x, type = c("image", "lines"), ...)
# S3 method for feemparafac
coef(
object, type = c(
"all", "scores", "loadings", "surfaces",
"emission", "excitation", "samples"
), ...
)
# S3 method for feemparafac
fitted(object, ...)
# S3 method for feemparafac
residuals(object, ...)
# S3 method for feemparafac
reorder(x, neworder, like, ...)
# S3 method for feemparafac
rescale(x, mode, newscale, absorb, like, ...)
An object of classes feemparafac and parafac with the
following attributes added:
A copy of the X argument.
A copy of the subset argument.
A copy of the envir argument.
The time it took to compute the decomposition as an object of
class proc_time. Only the time taken to run
multiway::parafac (including the
retries, if the decomposition failed) is included. The time
taken to rescale the scores should be negligible.
rownames are added from the original data cube
to the A, B, C components of the list returned
by parafac.
Use feemcube on the return value to access the original
data cube.
A lattice plot object. Its print or plot
method will draw the plot on an appropriate plotting device.
A data.frame or a list of them (only if
type is “all”). See the description of the type
argument for more information.
A feemcube object comparable to X as it was
decomposed by parafac, ignoring the scaling.
A feemcube object equal to \(
\mathbf{X} - \hat{\mathbf{X}}
\), with an additional
class feem.resid set. Objects of this class are plotted with
a different default palette, see plot.feem.resid.
A FEEM cube object. The per-sample factors will be multiplied by
attr(X, 'scales') stored in it.
If envir is NULL (by default), this should be just a
value. If envir is given, this should be a name of the value
to get from the environment.
Passed as-is to parafac.
Forwarded to the respective multiway functions.
No other parameters are allowed.
A character vector of length 3 specifying the constraints for all
modes of X, passed to parafac.
Defaults to non-negativity. See const for more
information.
The stopping criterion used by parafac. When
a step results in an absolute change in
\(R^2\) below ctol, the algorithm
stops.
Rescale the resulting factors to leave all the variance in the given
mode: emission, excitation, or sample (default). Set to NA
to disable.
Retry for given number of tries until
parafac returns a successfully fitted model
or stops due to the iteration number limit. Raise a fatal error if
all tries were unsuccessful.
An integer or logical vector choosing the samples from X, as
in feemparafac(X[,,subset], ...). Defaults to the whole cube.
An environment to look up X in.
An object returned by feemparafac.
Given a fitted PARAFAC model:
$$ X_{i,j,k} = \sum_r A_{i,r} B_{j,r} C_{k,r} $$
With \(\mathbf{A}\) corresponding to fluorescence emission loadings, \(\mathbf{B}\) corresponding to fluorescence excitation loadings, and \(\mathbf{C}\) corresponding to the scores of the components in different samples, the following plots can be produced:
Plot the factors (“loadings”) as a series of pseudo-colour images of outer products \( \mathbf{a}_r \times \mathbf{b}_r^\top \)
Plot the factors \(\mathbf a_r\) and \(\mathbf b_r\) as functions of wavelengths, with each pair of factors on a different panel.
Fitted PARAFAC coefficients can be returned in the following forms:
Return the contents of \(\mathbf{A}\),
\(\mathbf{B}\) or \(\mathbf{C}\),
respectively, as a data.frame with three
columns, the first one (named wavelength or
sample) containing the independent variable
(\(\lambda_\mathrm{em}\) /
\(\lambda_\mathrm{ex}\) /
sample name or number),
the second one (named value) containing the values and
the third one (named factor) containing the factor numbers.
Same as samples.
Same as “emission” and “excitation” combined using
rbind, with a fourth column (mode)
added, naming the kinds of loadings.
A list with names “emission”, “excitation”,
“samples” containing results of
coef(object, "emission"), coef(object, "excitation"),
coef(object, "samples"), respectively.
A data.frame containing the columns
emission, excitation (containing the wavelengths),
intensity (containing the values of the outer product
\(
\mathbf{a}_r \times \mathbf{b}_r^\top
\)),
and factor (containing the factor numbers \(r\)).
A permutation of integers between \(1\) and ncol(x$A) (the
number of components) specifying the new order of factors.
Forwarded to reorder.parafac. Incompatible
with the like argument.
A feemparafac object.
In reorder, the factors in x will be reordered to
match the factors in like according to the smallest of the
cosine similarities (congru) for the
emission and excitation wavelengths.
In rescale, every factor matrix
\(\mathbf{A}\) from x that was specified in
mode will be multiplied by scaling factors
\(\mathbf{c}\) so in order to minimise
\(
\| \mathbf{A}_\mathtt{like}
- \mathrm{diag}(\mathbf c) \mathbf{A}_\mathtt{x} \|^2
\).
The modes to rescale, with "A", "B", "C"
corresponding to emission, excitation, and samples, respectively.
When like is specified, defaults to c("A", "B").
Forwarded to rescale.parafac.
The desired root-mean-square for each column of the modes being
rescaled.
Forwarded to rescale.parafac. Incompatible
with the like argument.
The mode that should absorb the inverse rescaling coefficients.
When like is specified, defaults to "C".
Forwarded to rescale.parafac.
feemparafac tries hard to guarantee the convergence flag to be
0 (normal convergence) or 1 (iteration number limit
reached), but never 2 (a problem with the constraints). A fatal
error is raised if repeated runs of parafac do
not return a (semi-)successfully fitted model.
After the PARAFAC decomposition is calculated, the scores are
multiplied by the scales attribute of the X object,
making them represent the cube with scaling undone. Use
feemscale(remember = FALSE) if you don't want to undo
the scaling.
The output option is fixed to "best" value. Obtaining
a list of alternative solutions can therefore be achieved by running:
replicate(n, feemparafac(..., nstart = 1), simplify = FALSE)
The subset and envir options are useful to repeatedly
perform PARAFAC on different subsets of the same FEEM cube, e.g. in
jack-knifing or split-half analysis. Since feemparafac keeps
a reference to the its X and envir arguments, the use
of subset should ensure that the same FEEM cube is referenced
from multiple feemparafac objects instead of creating copies
of its subsets. Additionally, environment objects are not duplicated
on save or load, so storing
X in an environment and passing it to multiple invocations of
feemparafac will save a lot of memory when the results are
serialised together.
plot.feemparafac provides sane defaults for lattice
options such as xlab, ylab, as.table,
auto.key, type, cuts, col.regions, but
they can be overridden.
albatross:::.Rdreference('Bro1997')
The parafac class structure;
write.openfluor, feemcube for methods
specific to values returned from this function.
The rescale generic is re-exported from the
multiway package.
data(feems)
cube <- feemscale(feemscatter(cube, c(24, 14)), na.rm = TRUE)
(factors <- feemparafac(cube, nfac = 3, ctol = 1e-4))
plot(factors, 'image')
plot(factors, 'line')
head(coef(factors, 'loadings'))
str(coef(factors, 'all'))
str(feemcube(factors)) # original cube is retained
plot(fitted(factors))
plot(resid(factors))
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