Multi-dimensional scaling projection of samples,
using a distance matrix as an input.
The MDS algorithm is not the classical MDS
(cmdscale alike, aka Torgerson's algorithm),
but is the SMACOF algorithm for metric distances that are not
necessarily euclidean.
After having obtained the projections on the nDim dimensions,
we always apply svd decomposition to visualize as first axes the ones that
contain the most variance of the projected dataset in nDim dimensions.
Instead of being provided directly by the user, the nDim parameter can
otherwise be found iteratively by finding the minimum nDim parameter that
allows the projection to reach a target pseudo RSquare.
If this is the case, the maxDim parameter is used to avoid
looking for too big projection spaces.
computeMetricMDS(
pwDist,
nDim = NULL,
seed = NULL,
targetPseudoRSq = 0.95,
maxDim = 128,
...
)(nSamples rows, nSamples columns),
previously calculated pairwise distances between samples,
must be provided as a full symmetric square matrix, with 0. diagonal
number of dimensions of projection, as input to SMACOF algorithm
if not provided, will be found iteratively using targetPseudoRSq
seed to be set when launching SMACOF algorithm
(e.g. when init is set to "random" but not only)
target pseudo RSquare to be reached
(only used when nDim is set to NULL)
in case nDim is found iteratively,
maximum number of dimensions the search procedure is allowed to explore
additional parameters passed to SMACOF algorithm
a list with six elements:
$pwDist the initial pair-wise distance (same as input)
$proj the final configuration, i.e. the projected data matrix
(nSamples rows, nDim columns) in nDim dimensions
$projDist the distance matrix of projected data
stress the global stress loss function final value
obtained from the SMACOF algorithm
spp the stress per point obtained from the SMACOF algorithm, i.e.
the contribution of each point to the stress loss function
$RSq R squares, for each d, from 1 to nDim:
the (pseudo) R square when taking all dims from 1 to d.
$GoF Goodness of fit, for each d, from 1 to nDim:
the goodness of fit indicator (b/w 0 and 1) when taking all dims from 1 to d.
Note pseudo R square and goodness of fit indicators are essentially the
same indicator, only the definition of total sum of squares differ:
for pseudo RSq: TSS is calculated using the mean pairwise distance as minimum
for goodness of fit: TSS is calculated using 0 as minimum
library(CytoPipeline)
data(OMIP021Samples)
# estimate scale transformations
# and transform the whole OMIP021Samples
transList <- estimateScaleTransforms(
ff = OMIP021Samples[[1]],
fluoMethod = "estimateLogicle",
scatterMethod = "linearQuantile",
scatterRefMarker = "BV785 - CD3")
OMIP021Trans <- CytoPipeline::applyScaleTransforms(
OMIP021Samples,
transList)
# As there are only 2 samples in OMIP021Samples dataset,
# we create artificial samples that are random combinations of both samples
ffList <- c(
flowCore::flowSet_to_list(OMIP021Trans),
lapply(3:5,
FUN = function(i) {
aggregateAndSample(
OMIP021Trans,
seed = 10*i,
nTotalEvents = 5000)[,1:22]
}))
fsNames <- c("Donor1", "Donor2", paste0("Agg",1:3))
names(ffList) <- fsNames
fsAll <- as(ffList,"flowSet")
flowCore::pData(fsAll)$type <- factor(c("real", "real", rep("synthetic", 3)))
flowCore::pData(fsAll)$grpId <- factor(c("D1", "D2", rep("Agg", 3)))
# calculate all pairwise distances
pwDist <- pairwiseEMDDist(fsAll,
channels = c("FSC-A", "SSC-A"),
verbose = FALSE)
# compute Metric MDS object with explicit number of dimensions
mdsObj <- computeMetricMDS(pwDist, nDim = 4, seed = 0)
dim <- nDim(mdsObj) # should be 4
#' # compute Metric MDS object by reaching a target pseudo RSquare
mdsObj2 <- computeMetricMDS(pwDist, seed = 0, targetPseudoRSq = 0.999)