backtransformPrincipalCurve: Reverse transformation of principal-curve fit
In aroma.light: Light-Weight Methods for Normalization and Visualization of Microarray Data using Only Basic R Data Types

Description Usage Arguments Details Value Target dimension Subsetting dimensions See Also Examples

Reverse transformation of principal-curve fit.

## S3 method for class 'matrix'
backtransformPrincipalCurve(X, fit, dimensions=NULL, targetDimension=NULL, ...)
## S3 method for class 'numeric'
backtransformPrincipalCurve(X, ...)

`X`	An NxK `matrix` containing data to be backtransformed.
`fit`	An MxL principal-curve fit object of class `principal_curve` as returned by `fitPrincipalCurve`(). Typically L = K, but not always.
`dimensions`	An (optional) subset of of D dimensions all in [1,L] to be returned (and backtransform).
`targetDimension`	An (optional) index specifying the dimension in [1,L] to be used as the target dimension of the `fit`. More details below.
`...`	Passed internally to `smooth.spline`.

Each column in X ("dimension") is backtransformed independently of the others.

The backtransformed NxK (or NxD) matrix.

By default, the backtransform is such that afterward the signals are approximately proportional to the (first) principal curve as fitted by fitPrincipalCurve(). This scale and origin of this principal curve is not uniquely defined. If targetDimension is specified, then the backtransformed signals are approximately proportional to the signals of the target dimension, and the signals in the target dimension are unchanged.

Argument dimensions can be used to backtransform a subset of dimensions (K) based on a subset of the fitted dimensions (L). If K = L, then both X and fit is subsetted. If K <> L, then it is assumed that X is already subsetted/expanded and only fit is subsetted.

fitPrincipalCurve()

# Consider the case where K=4 measurements have been done
# for the same underlying signals 'x'.  The different measurements
# have different systematic variation
#
#   y_k = f(x_k) + eps_k; k = 1,...,K.
#
# In this example, we assume non-linear measurement functions
#
#   f(x) = a + b*x + x^c + eps(b*x)
#
# where 'a' is an offset, 'b' a scale factor, and 'c' an exponential.
# We also assume heteroscedastic zero-mean noise with standard
# deviation proportional to the rescaled underlying signal 'x'.
#
# Furthermore, we assume that measurements k=2 and k=3 undergo the
# same transformation, which may illustrate that the come from
# the same batch. However, when *fitting* the model below we
# will assume they are independent.

# Transforms
a <- c(2, 15, 15,   3)
b <- c(2,  3,  3,   4)
c <- c(1,  2,  2, 1/2)
K <- length(a)

# The true signal
N <- 1000
x <- rexp(N)

# The noise
bX <- outer(b,x)
E <- apply(bX, MARGIN=2, FUN=function(x) rnorm(K, mean=0, sd=0.1*x))

# The transformed signals with noise
Xc <- t(sapply(c, FUN=function(c) x^c))
Y <- a + bX + Xc + E
Y <- t(Y)



# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# Fit principal curve
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# Fit principal curve through Y = (y_1, y_2, ..., y_K)
fit <- fitPrincipalCurve(Y)

# Flip direction of 'lambda'?
rho <- cor(fit$lambda, Y[,1], use="complete.obs")
flip <- (rho < 0)
if (flip) {
  fit$lambda <- max(fit$lambda, na.rm=TRUE)-fit$lambda
}

L <- ncol(fit$s)

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# Backtransform data according to model fit
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# Backtransform toward the principal curve (the "common scale")
YN1 <- backtransformPrincipalCurve(Y, fit=fit)
stopifnot(ncol(YN1) == K)


# Backtransform toward the first dimension
YN2 <- backtransformPrincipalCurve(Y, fit=fit, targetDimension=1)
stopifnot(ncol(YN2) == K)


# Backtransform toward the last (fitted) dimension
YN3 <- backtransformPrincipalCurve(Y, fit=fit, targetDimension=L)
stopifnot(ncol(YN3) == K)


# Backtransform toward the third dimension (dimension by dimension)
# Note, this assumes that K == L.
YN4 <- Y
for (cc in 1:L) {
  YN4[,cc] <- backtransformPrincipalCurve(Y, fit=fit,
                                  targetDimension=1, dimensions=cc)
}
stopifnot(identical(YN4, YN2))


# Backtransform a subset toward the first dimension
# Note, this assumes that K == L.
YN5 <- backtransformPrincipalCurve(Y, fit=fit,
                               targetDimension=1, dimensions=2:3)
stopifnot(identical(YN5, YN2[,2:3]))
stopifnot(ncol(YN5) == 2)


# Extract signals from measurement #2 and backtransform according
# its model fit.  Signals are standardized to target dimension 1.
y6 <- Y[,2,drop=FALSE]
yN6 <- backtransformPrincipalCurve(y6, fit=fit, dimensions=2,
                                               targetDimension=1)
stopifnot(identical(yN6, YN2[,2,drop=FALSE]))
stopifnot(ncol(yN6) == 1)


# Extract signals from measurement #2 and backtransform according
# the the model fit of measurement #3 (because we believe these
# two have undergone very similar transformations.
# Signals are standardized to target dimension 1.
y7 <- Y[,2,drop=FALSE]
yN7 <- backtransformPrincipalCurve(y7, fit=fit, dimensions=3,
                                               targetDimension=1)
stopifnot(ncol(yN7) == 1)
stopifnot(cor(yN7, yN6) > 0.9999)