Bivariate data peelings — peel

Use convex hulls (and eventually other peelings) to order bivariate data.

Usage

peel_hulls(
  x,
  y = NULL,
  num = NULL,
  by = 1L,
  breaks = c(0.5),
  cut = c("above", "below")
)

Arguments

x, y: coordinate vectors of points. This can be specified as two vectors x and y, a 2-column matrix x, a list x with two components, etc, see xy.coords.
num: A positive integer; the number of hulls to peel. Pass Inf for all hulls.
by: A positive integer; with what frequency to include consecutive hulls, pairs with num.
breaks: A numeric vector of fractions (between 0 and 1) of the data to contain in each hull; overridden by num.
cut: Character; one of "above" and "below", indicating whether each hull should contain at least or at most breaks of the data, respectively.

Value

A matrix with some or all of the following columns:

x,y: original coordinates
i: position in input matrix or vectors
hull: index of hull, starting from outermost
frac: value of breaks used to determine hull
prop: proportion of data within hull

Details

Methods for peeling bivariate data into concentric tiers generalize the univariate concept of rank to separate core versus peripheral cases (Green, 1981).

The code for peeling convex hulls was adapted from plothulls() in the aplpack package. Other peeling options should be implemented soon.

References

Green PJ (1981) "Peeling Bivariate Data". Interpreting Multivariate Data Chapter 1, 3–19. John Wiley & Sons, Ltd, ISBN 978-0-471-28039-2.

Examples

x <- mtcars$disp; y <- mtcars$mpg

# all hulls
peel_hulls(x, y, num = Inf)
#>           x    y  i hull    prop
#>  [1,] 400.0 19.2 25    1 0.71875
#>  [2,] 440.0 14.7 17    1 0.71875
#>  [3,] 472.0 10.4 15    1 0.71875
#>  [4,] 460.0 10.4 16    1 0.71875
#>  [5,] 167.6 17.8 11    1 0.71875
#>  [6,] 121.0 21.4 32    1 0.71875
#>  [7,] 108.0 22.8  3    1 0.71875
#>  [8,]  79.0 27.3 26    1 0.71875
#>  [9,]  71.1 33.9 20    1 0.71875
#> [10,] 360.0 18.7  5    2 0.46875
#> [11,] 360.0 14.3  7    2 0.46875
#> [12,] 350.0 13.3 24    2 0.46875
#> [13,] 275.8 15.2 14    2 0.46875
#> [14,] 145.0 19.7 30    2 0.46875
#> [15,] 120.1 21.5 21    2 0.46875
#> [16,]  75.7 30.4 19    2 0.46875
#> [17,]  78.7 32.4 18    2 0.46875
#> [18,] 258.0 21.4  4    3 0.25000
#> [19,] 351.0 15.8 29    3 0.25000
#> [20,] 301.0 15.0 31    3 0.25000
#> [21,] 167.6 19.2 10    3 0.25000
#> [22,] 140.8 22.8  9    3 0.25000
#> [23,] 120.3 26.0 27    3 0.25000
#> [24,]  95.1 30.4 28    3 0.25000
#> [25,] 318.0 15.5 22    4 0.09375
#> [26,] 304.0 15.2 23    4 0.09375
#> [27,] 225.0 18.1  6    4 0.09375
#> [28,] 160.0 21.0  2    4 0.09375
#> [29,] 146.7 24.4  8    4 0.09375
#> [30,] 275.8 17.3 13    5 0.00000
#> [31,] 275.8 16.4 12    5 0.00000
#> [32,] 160.0 21.0  1    5 0.00000

# every third hull
peel_hulls(x, y, num = Inf, by = 3)
#>           x    y  i hull    prop
#>  [1,] 400.0 19.2 25    1 0.71875
#>  [2,] 440.0 14.7 17    1 0.71875
#>  [3,] 472.0 10.4 15    1 0.71875
#>  [4,] 460.0 10.4 16    1 0.71875
#>  [5,] 167.6 17.8 11    1 0.71875
#>  [6,] 121.0 21.4 32    1 0.71875
#>  [7,] 108.0 22.8  3    1 0.71875
#>  [8,]  79.0 27.3 26    1 0.71875
#>  [9,]  71.1 33.9 20    1 0.71875
#> [10,] 318.0 15.5 22    4 0.09375
#> [11,] 304.0 15.2 23    4 0.09375
#> [12,] 225.0 18.1  6    4 0.09375
#> [13,] 160.0 21.0  2    4 0.09375
#> [14,] 146.7 24.4  8    4 0.09375

# tertile hulls, cut below
peel_hulls(x, y, breaks = seq(0, 1, length.out = 4))
#>           x    y  i hull      frac    prop
#>  [1,] 400.0 19.2 25    1 1.0000000 1.00000
#>  [2,] 440.0 14.7 17    1 1.0000000 1.00000
#>  [3,] 472.0 10.4 15    1 1.0000000 1.00000
#>  [4,] 460.0 10.4 16    1 1.0000000 1.00000
#>  [5,] 167.6 17.8 11    1 1.0000000 1.00000
#>  [6,] 121.0 21.4 32    1 1.0000000 1.00000
#>  [7,] 108.0 22.8  3    1 1.0000000 1.00000
#>  [8,]  79.0 27.3 26    1 1.0000000 1.00000
#>  [9,]  71.1 33.9 20    1 1.0000000 1.00000
#> [10,] 360.0 18.7  5    2 0.6666667 0.71875
#> [11,] 360.0 14.3  7    2 0.6666667 0.71875
#> [12,] 350.0 13.3 24    2 0.6666667 0.71875
#> [13,] 275.8 15.2 14    2 0.6666667 0.71875
#> [14,] 145.0 19.7 30    2 0.6666667 0.71875
#> [15,] 120.1 21.5 21    2 0.6666667 0.71875
#> [16,]  75.7 30.4 19    2 0.6666667 0.71875
#> [17,]  78.7 32.4 18    2 0.6666667 0.71875
#> [18,] 258.0 21.4  4    3 0.3333333 0.46875
#> [19,] 351.0 15.8 29    3 0.3333333 0.46875
#> [20,] 301.0 15.0 31    3 0.3333333 0.46875
#> [21,] 167.6 19.2 10    3 0.3333333 0.46875
#> [22,] 140.8 22.8  9    3 0.3333333 0.46875
#> [23,] 120.3 26.0 27    3 0.3333333 0.46875
#> [24,]  95.1 30.4 28    3 0.3333333 0.46875
#> [25,] 275.8 17.3 13    5 0.0000000 0.09375
#> [26,] 275.8 16.4 12    5 0.0000000 0.09375
#> [27,] 160.0 21.0  1    5 0.0000000 0.09375

# tertile hulls, cut above
peel_hulls(x, y, breaks = seq(0, 1, length.out = 4), cut = "below")
#>           x    y  i hull      frac    prop
#>  [1,] 400.0 19.2 25    1 1.0000000 1.00000
#>  [2,] 440.0 14.7 17    1 1.0000000 1.00000
#>  [3,] 472.0 10.4 15    1 1.0000000 1.00000
#>  [4,] 460.0 10.4 16    1 1.0000000 1.00000
#>  [5,] 167.6 17.8 11    1 1.0000000 1.00000
#>  [6,] 121.0 21.4 32    1 1.0000000 1.00000
#>  [7,] 108.0 22.8  3    1 1.0000000 1.00000
#>  [8,]  79.0 27.3 26    1 1.0000000 1.00000
#>  [9,]  71.1 33.9 20    1 1.0000000 1.00000
#> [10,] 258.0 21.4  4    3 0.6666667 0.46875
#> [11,] 351.0 15.8 29    3 0.6666667 0.46875
#> [12,] 301.0 15.0 31    3 0.6666667 0.46875
#> [13,] 167.6 19.2 10    3 0.6666667 0.46875
#> [14,] 140.8 22.8  9    3 0.6666667 0.46875
#> [15,] 120.3 26.0 27    3 0.6666667 0.46875
#> [16,]  95.1 30.4 28    3 0.6666667 0.46875
#> [17,] 318.0 15.5 10    4 0.3333333 0.25000
#> [18,] 304.0 15.2 12    4 0.3333333 0.25000
#> [19,] 225.0 18.1  4    4 0.3333333 0.25000
#> [20,] 160.0 21.0  2    4 0.3333333 0.25000
#> [21,] 146.7 24.4  6    4 0.3333333 0.25000