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#' Diffusion Maps
#'
#' An S4 Class implementing Diffusion Maps
#'
#' Diffusion Maps uses a diffusion probability matrix to robustly
#' approximate a manifold.
#'
#'
#' @template dimRedMethodSlots
#'
#' @template dimRedMethodGeneralUsage
#'
#' @section Parameters:
#' Diffusion Maps can take the following parameters:
#' \describe{
#' \item{d}{a function transforming a matrix row wise into a
#' distance matrix or \code{dist} object,
#' e.g. \code{\link[stats]{dist}}.}
#' \item{ndim}{The number of dimensions}
#' \item{eps}{The epsilon parameter that determines the
#' diffusion weight matrix from a distance matrix \code{d},
#' \eqn{exp(-d^2/eps)}, if set to \code{"auto"} it will
#' be set to the median distance to the 0.01*n nearest
#' neighbor.}
#' \item{t}{Time-scale parameter. The recommended value, 0,
#' uses multiscale geometry.}
#' \item{delta}{Sparsity cut-off for the symmetric graph Laplacian,
#' a higher value results in more sparsity and faster calculation.
#' The predefined value is 10^-5.}
#' }
#'
#' @section Implementation:
#' Wraps around \code{\link[diffusionMap]{diffuse}}, see there for
#' details. It uses the notation of Richards et al. (2009) which is
#' slightly different from the one in the original paper (Coifman and
#' Lafon, 2006) and there is no \eqn{\alpha} parameter.
#' There is also an out-of-sample extension, see examples.
#'
#'
#' @references
#' Richards, J.W., Freeman, P.E., Lee, A.B., Schafer,
#' C.M., 2009. Exploiting Low-Dimensional Structure in
#' Astronomical Spectra. ApJ 691,
#' 32. doi:10.1088/0004-637X/691/1/32
#'
#' Coifman, R.R., Lafon, S., 2006. Diffusion maps. Applied and
#' Computational Harmonic Analysis 21,
#' 5-30. doi:10.1016/j.acha.2006.04.006
#'
#' @examples
#' if(requireNamespace("diffusionMap", quietly = TRUE)) {
#' dat <- loadDataSet("3D S Curve", n = 300)
#' emb <- embed(dat, "DiffusionMaps")
#'
#' plot(emb, type = "2vars")
#'
#' # predicting is possible:
#' samp <- sample(floor(nrow(dat) / 10))
#' emb2 <- embed(dat[samp])
#' emb3 <- predict(emb2, dat[-samp])
#'
#' plot(emb2, type = "2vars")
#' points(getData(emb3))
#' }
#' @include dimRedResult-class.R
#' @include dimRedMethod-class.R
#' @family dimensionality reduction methods
#' @export DiffusionMaps
#' @exportClass DiffusionMaps
DiffusionMaps <- setClass(
"DiffusionMaps",
contains = "dimRedMethod",
prototype = list(
stdpars = list(d = stats::dist,
ndim = 2,
eps = "auto",
t = 0,
delta = 1e-5),
fun = function (data, pars,
keep.org.data = TRUE) {
chckpkg("diffusionMap")
meta <- data@meta
orgdata <- if (keep.org.data) data@data else NULL
indata <- data@data
distmat <- pars$d(indata)
if (pars$eps == "auto")
pars$eps <- diffusionMap::epsilonCompute(distmat)
diffres <- diffusionMap::diffuse(
D = distmat,
t = pars$t,
eps.val = pars$eps,
neigen = pars$ndim,
maxdim = pars$ndim,
delta = pars$delta
)
outdata <- as.matrix(diffres$X)
appl <- function(x) {
appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame()
proj <- if (inherits(x, "dimRedData")) x@data else x
if (ncol(proj) != ncol(data@data))
stop("x must have the same number of dimensions ",
"as the original data")
dd <- sqrt(pdist2(proj, indata))
appl.res <-
diffusionMap::nystrom(diffres, dd, sigma = diffres$epsilon)
dimnames(appl.res) <- list(
rownames(x), paste0("diffMap", seq_len(ncol(outdata)))
)
new("dimRedData", data = appl.res, meta = appl.meta)
}
colnames(outdata) <- paste0("diffMap", seq_len(ncol(outdata)))
return(new(
"dimRedResult",
data = new("dimRedData",
data = outdata,
meta = meta),
org.data = orgdata,
apply = appl,
has.apply = TRUE,
has.org.data = keep.org.data,
method = "diffmap",
pars = pars
))
},
requires = c("diffusionMap"))
)
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