[R] Idea/package to "linearize a curve" along the diagonal?

Jeff Newmiller jdnewmil at dcn.davis.ca.us
Mon Mar 12 07:15:45 CET 2012

It is possible that I do not see what you mean, but it seems like the following code does what you want. The general version of this is likely to be rather more difficult to do, but in theory the inverse function seems like what you are trying to accomplish.

x <- 1:20
y <- x^2 + rnorm(20)

y.lm <- lm( y ~ I(x^2) + x )
plot( x, y )
lines( x, predict( y.lm ) )

qa <- coef(y.lm)["I(x^2)"]
qb <- coef(y.lm)["x"]
qc <- coef(y.lm)["(Intercept)"]

# define inverse of known model
f1 <- function( y ) { ( sqrt( 4*qa*( y -qc ) + qb^2 ) - qb ) / ( 2*qa ) }
f2 <- function( y ) { -( sqrt( 4*qa*( y -qc ) + qb^2 ) + qb ) / ( 2*qa ) }

plot( x, f1( y ) ) 

Jeff Newmiller                        The     .....       .....  Go Live...
DCN:<jdnewmil at dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live Go...
                                      Live:   OO#.. Dead: OO#..  Playing
Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
/Software/Embedded Controllers)               .OO#.       .OO#.  rocks...1k
Sent from my phone. Please excuse my brevity.

Emmanuel Levy <emmanuel.levy at gmail.com> wrote:

>Dear Jeff,
>I'm sorry but I do not see what you mean. It'd be great if you could
>let me know in more details what you mean whenever you can.
>On 12 March 2012 00:07, Jeff Newmiller <jdnewmil at dcn.davis.ca.us>
>> Aren't you just reinventing the inverse of a function?
>> Jeff Newmiller                        The     .....       .....  Go
>> DCN:<jdnewmil at dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live
>>                                      Live:   OO#.. Dead: OO#..
> Playing
>> Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
>> /Software/Embedded Controllers)               .OO#.       .OO#.
> rocks...1k
>> Sent from my phone. Please excuse my brevity.
>> Emmanuel Levy <emmanuel.levy at gmail.com> wrote:
>>>I am trying to normalize some data. First I fitted a principal curve
>>>(using the LCPM package), but now I would like to apply a
>>>transformation so that the curve becomes a "straight diagonal line"
>>>the plot.  The data used to fit the curve would then be normalized by
>>>applying the same transformation to it.
>>>A simple solution could be to apply translations only (e.g., as done
>>>after a fit using loess), but here rotations would have to be applied
>>>as well. One could visualize this as the "stretching of a curve",
>>>i.e., during such an "unfolding" process, both translations and
>>>rotations would need to be applied.
>>>Before I embark on this (which would require me remembering long
>>>forgotten geometry principles) I was wondering if you can think of
>>>packages or tricks that could make my life simpler?
>>>Thanks for any input,
>>>Below I provide an example - the black curve is to be "brought" along
>>>the diagonal, and all data points normal to a "small segment" (of the
>>>black curve) would undergo the same transformation as it - what
>>>"small" is remains to be defined though.
>>>    tmp=rnorm(2000)
>>>    X.1 = 5+tmp
>>>    Y.1 = 5+ (5*tmp+rnorm(2000))
>>>    tmp=rnorm(1000)
>>>    X.2 = 9+tmp
>>>    Y.2 = 40+ (1.5*tmp+rnorm(1000))
>>>    X.3 = 7+ 0.5*runif(500)
>>>    Y.3 = 15+20*runif(500)
>>>    X = c(X.1,X.2,X.3)
>>>    Y = c(Y.1,Y.2,Y.3)
>>>    lpc1 = lpc(cbind(X,Y), scaled=FALSE, h=c(1,1) )
>>>    plot(lpc1)
>>>R-help at r-project.org mailing list
>>>PLEASE do read the posting guide
>>>and provide commented, minimal, self-contained, reproducible code.

More information about the R-help mailing list