select rows by criteria

On Thu, Mar 01, 2012 at 04:27:45AM -0800, syrvn wrote:

Hello,

I am stuck with selecting the right rows from a data frame. I think the
problem is rather how to select them
then how to implement the R code.

Consider the following data frame:

df <- data.frame(ID = c(1,2,3,4,5,6,7,8,9,10), value =
c(34,12,23,25,34,42,48,29,30,27))

What I want to achieve is to select 7 rows (values) so that the mean value
of those rows are closest
to the value of 35 and the remaining 3 rows (values) are closest to 45.
However, each value is only
allowed to be sampled once!

Hi.

If some 3 rows have mean close to 45, then they have sum close
to 3*45, so the remaining 7 rows have sum close to

  sum(df$value) - 3*45 # [1] 169

and they have mean close to 169/7 = 24.14286. In other words,
the two criteria cannot be optimized together.

For this reason, let me choose the criterion on 3 rows.
The closest solution may be found as follows.

  # generate all triples and compute their means
  tripleMeans <- colMeans(combn(df$value, 3))

  # select the index of the triple with mean closest to 35
  indClosest <- which.min(abs(tripleMeans - 35))

  # generate the indices, which form the closest triple in df$value
  tripleInd <- combn(1:length(df$value), 3)[, indClosest]
  tripleInd # [1] 1 3 7

  # check the mean of the triple
  mean(df$value[tripleInd]) # [1] 35

This code constructs all triples. If it is used for k-tuples
for a larger k and for a set of n values, its complexity
will be proportional to choose(n, k), so it will be large
even for moderate n, k. It is hard to provide a significant
speed up, since some variants of "knapsack problem", which
is NP-complete, may be reduced to your question. Consequently,
it is, in general, NP-complete.