Fit a principal curve in K dimensions

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Description

Fit a principal curve in K dimensions.

Usage

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## S3 method for class 'matrix'
fitPrincipalCurve(X, ..., verbose=FALSE)

Arguments

X

An NxK matrix (K>=2) where the columns represent the dimension.

...

Other arguments passed to principal.curve.

verbose

A logical or a Verbose object.

Value

Returns a principal.curve object (which is a list). See principal.curve for more details.

Missing values

The estimation of the normalization function will only be made based on complete observations, i.e. observations that contains no NA values in any of the channels.

Author(s)

Henrik Bengtsson

References

[1] Hastie, T. and Stuetzle, W, Principal Curves, JASA, 1989.
[2] H. Bengtsson, A. Ray, P. Spellman and T.P. Speed, A single-sample method for normalizing and combining full-resolutioncopy numbers from multiple platforms, labs and analysis methods, Bioinformatics, 2009.

See Also

backtransformPrincipalCurve(). principal.curve.

Examples

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# Simulate data from the model y <- a + bx + x^c + eps(bx)
J <- 1000
x <- rexp(J)
a <- c(2,15,3)
b <- c(2,3,4)
c <- c(1,2,1/2)
bx <- outer(b,x)
xc <- t(sapply(c, FUN=function(c) x^c))
eps <- apply(bx, MARGIN=2, FUN=function(x) rnorm(length(b), mean=0, sd=0.1*x))
y <- a + bx + xc + eps
y <- t(y)

# Fit principal curve through (y_1, y_2, y_3)
fit <- fitPrincipalCurve(y, verbose=TRUE)

# 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
}


# Backtransform (y_1, y_2, y_3) to be proportional to each other
yN <- backtransformPrincipalCurve(y, fit=fit)

# Same backtransformation dimension by dimension
yN2 <- y
for (cc in 1:ncol(y)) {
  yN2[,cc] <- backtransformPrincipalCurve(y, fit=fit, dimensions=cc)
}
stopifnot(identical(yN2, yN))


xlim <- c(0, 1.04*max(x))
ylim <- range(c(y,yN), na.rm=TRUE)


# Pairwise signals vs x before and after transform
layout(matrix(1:4, nrow=2, byrow=TRUE))
par(mar=c(4,4,3,2)+0.1)
for (cc in 1:3) {
  ylab <- substitute(y[c], env=list(c=cc))
  plot(NA, xlim=xlim, ylim=ylim, xlab="x", ylab=ylab)
  abline(h=a[cc], lty=3)
  mtext(side=4, at=a[cc], sprintf("a=%g", a[cc]),
        cex=0.8, las=2, line=0, adj=1.1, padj=-0.2)
  points(x, y[,cc])
  points(x, yN[,cc], col="tomato")
  legend("topleft", col=c("black", "tomato"), pch=19,
                    c("orignal", "transformed"), bty="n")
}
title(main="Pairwise signals vs x before and after transform", outer=TRUE, line=-2)


# Pairwise signals before and after transform
layout(matrix(1:4, nrow=2, byrow=TRUE))
par(mar=c(4,4,3,2)+0.1)
for (rr in 3:2) {
  ylab <- substitute(y[c], env=list(c=rr))
  for (cc in 1:2) {
    if (cc == rr) {
      plot.new()
      next
    }
    xlab <- substitute(y[c], env=list(c=cc))
    plot(NA, xlim=ylim, ylim=ylim, xlab=xlab, ylab=ylab)
    abline(a=0, b=1, lty=2)
    points(y[,c(cc,rr)])
    points(yN[,c(cc,rr)], col="tomato")
    legend("topleft", col=c("black", "tomato"), pch=19,
                      c("orignal", "transformed"), bty="n")
  }
}
title(main="Pairwise signals before and after transform", outer=TRUE, line=-2)

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