[R] finding peaks in a simple dataset with R

[Marc Kirchner]

> 
> I wonder if we shouldn't polish that a bit and add to R's
> standard 'utils' package.
> 

Hm, I figured out there are (at least) two versions out there, one being
the "original" idea and a modification. 

=== Petr Pikal in 2001 (based on Brian Ripley's idea)==
peaks <- function(series, span=3) {
	z <- embed(series, span)
	result <- max.col(z) == 1 + span %/% 2
	result
}

versus

=== Petr Pikal in 2004 ==
peaks2<-function(series,span=3) {
	z <- embed(series, span)
	s <- span%/%2
	v<- max.col(z) == 1 + s
	result <- c(rep(FALSE,s),v)
	result <- result[1:(length(result)-s)]
	result
} 

Comparison shows
> peaks(c(1,4,1,1,6,1,5,1,1),3)
[1]  TRUE FALSE FALSE  TRUE FALSE  TRUE FALSE
which is a logical vector for elements 2:N-1 and

> peaks2(c(1,4,1,1,6,1,5,1,1),3)
[1] FALSE  TRUE FALSE FALSE  TRUE FALSE  TRUE
which is a logical vector for elements 1:N-2.

As I would expect to "lose" (span-1)/2 elements on each side 
of the vector, to me the 2001 version feels more natural.

Also, both "suffer" from being non-deterministic in the 
multiple-maxima-case (the two 4s here)

> peaks(c(1,4,4,1,6,1,5,1,1),3)
[1] FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE
> peaks(c(1,4,4,1,6,1,5,1,1),3)
[1]  TRUE  TRUE FALSE  TRUE FALSE  TRUE FALSE
> peaks(c(1,4,4,1,6,1,5,1,1),3)
[1] FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE
> peaks(c(1,4,4,1,6,1,5,1,1),3)
[1] FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE

which also persits for span > 3 (without the 6 then, of course):

> peaks(c(1,4,4,1,1,1,5,1,1),5)
[1]  TRUE FALSE FALSE FALSE  TRUE
> peaks(c(1,4,4,1,1,1,5,1,1),5)
[1] FALSE FALSE FALSE FALSE  TRUE
> peaks(c(1,4,4,1,1,1,5,1,1),5)
[1]  TRUE FALSE FALSE FALSE  TRUE

This could (should?) be fixed by modifying the call to max.col()
	result <- max.col(z, "first") == 1 + span %/% 2;

Just my two cents,
Marc

-- 
========================================================
Dipl. Inform. Med. Marc Kirchner
Interdisciplinary Centre for Scientific Computing (IWR)
Multidimensional Image Processing
INF 368
University of Heidelberg
D-69120 Heidelberg
Tel: ++49-6221-54 87 97
Fax: ++49-6221-54 88 50
marc.kirchner at iwr.uni-heidelberg.de

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