Discretisation functions

Description

These are the helper functions called by do_disc (which is the function normally applied by an opm user). discrete converts continuous numeric characters to discrete ones. best_cutoff determines the best cutoff for dividing a numeric matrix into two categories by minimising within-group discrepancies. That is, for each combination of row group and column maximise the number of contained elements that are in the category in which most of the elements within this combination of row group and column are located.

Usage

  ## S4 method for signature 'matrix,character'
best_cutoff(x, y, ...) 
  ## S4 method for signature 'matrix,factor'
best_cutoff(x, y, combined = TRUE, lower = min(x, na.rm = TRUE),
    upper = max(x, na.rm = TRUE), all = FALSE) 

  ## S4 method for signature 'array'
discrete(x, ...) 
  ## S4 method for signature 'data.frame'
discrete(x, ..., as.labels = NULL, sep = " ")
  ## S4 method for signature 'numeric'
discrete(x, range, gap = FALSE,
    output = c("character", "integer", "logical", "factor", "numeric"),
    middle.na = TRUE, states = 32L, ...) 

Arguments

Details

One of the uses of discrete is to create character data suitable for phylogenetic studies with programs such as PAUP* and RAxML. These accept only discrete characters with at most 32 states, coded as 0 to 9 followed by A to V. For the full export one additionally needs phylo_data. The matrix method is just a wrapper that takes care of the matrix dimensions, and the data-frame method is a wrapper for that method.

The term ‘character’ as used here has no direct connection to the eponymous mode or class of R. Rather, the term is borrowed from taxonomic classification in biology, where, technically, a single ‘character’ is stored in one column of a data matrix if each organism is stored in one row. Characters are the quasi-independent units of evolution on the one hand and of phylogenetic reconstruction (and thus taxonomic classification) on the other hand.

The scoring function to be maximised by best_cutoff is calculated as follows. All values in x are divided into those larger then the cutoff and those at most large as the cutoff. For each combination of group and matrix column the frequencies of the two categories are determined, and the respective larger ones are summed up over all combinations. This value is then divided by the frequency over the entire matrix of the more frequent of the two categories. This is done to avoid trivial solutions with minimal and maximal cutoffs, causing all values to be placed in the same category.

Value

discrete generates a double, integer, character or logical vector or factor, depending on output. For the matrix method, a matrix composed of a vector as produced by the numeric method, the original dimensions and the original dimnames attributes of x.

If combined is TRUE, best_cutoff yields either a matrix or a vector: If all is TRUE, a two-column matrix with (i) the cutoffs examined and (ii) the resulting scores. If all is FALSE, a vector with the entries ‘maximum’ (the best cutoff) and ‘objective’ (the score it achieved). If combined is FALSE, either a list of matrices or a matrix. If all is TRUE, a list of matrices structures like the single matrix returned if combined is TRUE. If all is FALSE, a matrix with two columns called ‘maximum’ ‘objective’, and one row per level of y.

References

Dougherty, J., Kohavi, R., Sahami, M. 1995 Supervised and unsupervised discretisation of continuous features. In: Prieditis, A., Russell, S. (eds.) Machine Learning: Proceedings of the fifth international conference.

Ventura, D., Martinez, T. R. 1995 An empirical comparison of discretisation methods. Proceedings of the Tenth International Symposium on Computer and Information Sciences, p. 443–450.

Wiley, E. O., Lieberman, B. S. 2011 Phylogenetics: Theory and Practice of Phylogenetic Systematics. Hoboken, New Jersey: Wiley-Blackwell.

Bunuel, L. 1972 Le charme discret de la bourgeoisie. France/Spain, 96 min.

See Also

base::cut stats::optimize

Other discretization-functions: do_disc

Examples

# Treat everything between 3.4 and 4.5 as ambiguous
(x <- discrete(1:5, range = c(3.5, 4.5), gap = TRUE))

## [1] "0" "0" "0" "?" "1"
## attr(,"cutoffs")
## [1] 3.5 4.5

stopifnot(x == c("0", "0", "0", "?", "1"))

# Treat everything between 3.4 and 4.5 as intermediate
(x <- discrete(1:5, range = c(3.5, 4.5), gap = TRUE, middle.na = FALSE))

## [1] "0" "0" "0" "1" "2"
## attr(,"cutoffs")
## [1] 3.5 4.5

stopifnot(x == c("0", "0", "0", "1", "2"))

# Boring example: real and possible range as well as the number of states
# to code the data have a 1:1 relationship
(x <- discrete(1:5, range = c(1, 5), states = 5))

## [1] "0" "1" "2" "3" "4"

stopifnot(identical(x, as.character(0:4)))

# Now fit the data into a potential range twice as large, and at the
# beginning of it
(x <- discrete(1:5, range = c(1, 10), states = 5))

## [1] "0" "0" "1" "1" "2"

stopifnot(identical(x, as.character(c(0, 0, 1, 1, 2))))

# Matrix and data-frame methods
x <- matrix(as.numeric(1:10), ncol = 2)
(y <- discrete(x, range = c(3.4, 4.5), gap = TRUE))

##      [,1] [,2]
## [1,] "0"  "1" 
## [2,] "0"  "1" 
## [3,] "0"  "1" 
## [4,] "?"  "1" 
## [5,] "1"  "1" 
## attr(,"cutoffs")
## [1] 3.4 4.5

stopifnot(identical(dim(x), dim(y)))
(yy <- discrete(as.data.frame(x), range = c(3.4, 4.5), gap = TRUE))

##      V1  V2 
## [1,] "0" "1"
## [2,] "0" "1"
## [3,] "0" "1"
## [4,] "?" "1"
## [5,] "1" "1"
## attr(,"cutoffs")
## [1] 3.4 4.5

stopifnot(y == yy)

# K-means based discretisation of PM data (prefer do_disc() for this)
x <- extract(vaas_4, as.labels = list("Species", "Strain"),
  in.parens = FALSE)
(y <- discrete(x, range = TRUE, gap = TRUE))[, 1:3]

##                                Negative Control Dextrin D-Maltose
## Escherichia coli DSM18039      "0"              "?"     "0"      
## Escherichia coli DSM30083T     "?"              "1"     "1"      
## Pseudomonas aeruginosa DSM1707 "0"              "0"     "0"      
## Pseudomonas aeruginosa 429SC1  "0"              "0"     "0"

stopifnot(c("0", "?", "1") %in% y)

## best_cutoff()
x <- matrix(c(5:2, 1:2, 7:8), ncol = 2)
grps <- c("a", "a", "b", "b")

# combined optimisation
(y <- best_cutoff(x, grps))

##   maximum objective 
##  3.673825  2.000000

stopifnot(is.numeric(y), length(y) == 2) # two-element numeric vector
stopifnot(y[["maximum"]] < 4, y[["maximum"]] > 3, y[["objective"]] == 2)
plot(best_cutoff(x, grps, all = TRUE), type = "l")

# separate optimisation
(y <- best_cutoff(x, grps, combined = FALSE))

##    maximum objective
## a 2.652523         2
## b 6.347592         2

stopifnot(is.matrix(y), dim(y) == c(2, 2)) # numeric matrix
stopifnot(y["a", "objective"] == 2, y["b", "objective"] == 2)
(y <- best_cutoff(x, grps, combined = FALSE, all = TRUE))

## $a
##      cutoff score
## [1,]    1.5     1
## [2,]    3.0     2
## [3,]    4.5     1
## 
## $b
##      cutoff score
## [1,]    2.5     1
## [2,]    5.0     2
## [3,]    7.5     1

plot(y$a, type = "l")

plot(y$b, type = "l")