maxDissim function

Maximum Dissimilarity Sampling

Functions to create a sub-sample by maximizing the dissimilarity between new samples and the existing subset.

maxDissim(
  a,
  b,
  n = 2,
  obj = minDiss,
  useNames = FALSE,
  randomFrac = 1,
  verbose = FALSE,
  ...
)

minDiss(u)

sumDiss(u)

Arguments

• a: a matrix or data frame of samples to start
• b: a matrix or data frame of samples to sample from
• n: the size of the sub-sample
• obj: an objective function to measure overall dissimilarity
• useNames: a logical: should the function return the row names (as opposed ot the row index)
• randomFrac: a number in (0, 1] that can be used to sub-sample from the remaining candidate values
• verbose: a logical; should each step be printed?
• ...: optional arguments to pass to dist
• u: a vector of dissimilarities

Returns

a vector of integers or row names (depending on useNames) corresponding to the rows of b that comprise the sub-sample.

Details

Given an initial set of m samples and a larger pool of n samples, this function iteratively adds points to the smaller set by finding with of the n samples is most dissimilar to the initial set. The argument obj

measures the overall dissimilarity between the initial set and a candidate point. For example, maximizing the minimum or the sum of the m dissimilarities are two common approaches.

This algorithm tends to select points on the edge of the data mainstream and will reliably select outliers. To select more samples towards the interior of the data set, set randomFrac to be small (see the examples below).

Examples

example <- function(pct = 1, obj = minDiss, ...)
{
  tmp <- matrix(rnorm(200 * 2), nrow = 200)

  ## start with 15 data points
  start <- sample(1:dim(tmp)[1], 15)
  base <- tmp[start,]
  pool <- tmp[-start,]
  
  ## select 9 for addition
  newSamp <- maxDissim(
                       base, pool, 
                       n = 9, 
                       randomFrac = pct, obj = obj, ...)
  
  allSamp <- c(start, newSamp)
  
  plot(
       tmp[-newSamp,], 
       xlim = extendrange(tmp[,1]), ylim = extendrange(tmp[,2]), 
       col = "darkgrey", 
       xlab = "variable 1", ylab = "variable 2")
  points(base, pch = 16, cex = .7)
  
  for(i in seq(along.with = newSamp))
    points(
           pool[newSamp[i],1], 
           pool[newSamp[i],2], 
           pch = paste(i), col = "darkred") 
}

par(mfrow=c(2,2))

set.seed(414)
example(1, minDiss)
title("No Random Sampling, Min Score")

set.seed(414)
example(.1, minDiss)
title("10 Pct Random Sampling, Min Score")

set.seed(414)
example(1, sumDiss)
title("No Random Sampling, Sum Score")

set.seed(414)
example(.1, sumDiss)
title("10 Pct Random Sampling, Sum Score")

References

Willett, P. (1999), "Dissimilarity-Based Algorithms for Selecting Structurally Diverse Sets of Compounds," Journal of Computational Biology, 6, 447-457.

See Also

dist

Author(s)

Max Kuhn max.kuhn@pfizer.com