Scale for 3d plotting

Source: R/l_plot3D.R

l_scale3D scales its argument in a variety of ways used for 3D visualization.

l_scale3D(x, center = TRUE, method = c("box", "sphere"))

Arguments

x

the matrix or data.frame whose columns are to be scaled. Any NA entries will be preserved but ignored in calculations. x must have exactly 3 columns for method = "sphere".
center

either a logical value or numeric-alike vector of length equal to the number of columns of x, where ‘numeric-alike’ means that as.numeric(.) will be applied successfully if is.numeric(.) is not true.
method

the scaling method to use. If method = "box" (the default) then the columns are scaled to have equal ranges and, when center = TRUE, to be centred by the average of the min and max; If method = "sphere" then x must be three dimensional. For sphering, on each of the original 3 dimensions x is first centred (mean centred when center = TRUE) and scaled to equal standard deviation on. The V matrix of the singular value decomposition (svd) is applied to the right resulting in uncorrelated variables. Coordinates are then divided by (non-zero as tested by !all.equal(0, .)) singular values. If x contains no NAs, the resulting coordinates are simply the U matrix of the svd.

Value

a data.frame whose columns are centred and scaled according to the given arguments. For method = "sphere"), the three variable names are x1, x2, and x3.

See also

l_plot3D, scale, and prcomp.

Other three-dimensional plotting functions: l_plot3D()

Examples


##### Iris data
#
# All variables (including Species as a factor)
result_box <- l_scale3D(iris)
head(result_box, n = 3)

#>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> 1   -0.2777778  0.12500000   -0.4322034  -0.4583333    -0.5
#> 2   -0.3333333 -0.08333333   -0.4322034  -0.4583333    -0.5
#> 3   -0.3888889  0.00000000   -0.4491525  -0.4583333    -0.5
apply(result_box, 2, FUN = range)

#>      Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> [1,]         -0.5        -0.5         -0.5        -0.5    -0.5
#> [2,]          0.5         0.5          0.5         0.5     0.5
# Note mean is not zero.
apply(result_box, 2, FUN = mean)

#> Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species 
#>  -0.07129630  -0.05944444  -0.03254237  -0.04194444   0.00000000 


# Sphering only on 3D data.
result_sphere <- l_scale3D(iris[, 1:3], method = "sphere")
head(result_sphere, n = 3)

#>            x1          x2           x3
#> 1 -0.10665359 -0.03635358 -0.039744517
#> 2 -0.09153699  0.06124692 -0.080344512
#> 3 -0.11208702  0.03517574 -0.009633385
apply(result_sphere, 2, FUN = range)

#>              x1         x2         x3
#> [1,] -0.1423020 -0.2338372 -0.1627308
#> [2,]  0.1737036  0.2262592  0.2203348
# Note mean is numerically zero.
apply(result_sphere, 2, FUN = mean)

#>            x1            x2            x3 
#> -2.074395e-17  3.842760e-18  1.056550e-16 


#  With NAs
x <- iris
x[c(1, 3), 1] <- NA
x[2, 3] <- NA

result_box <- l_scale3D(x)
head(result_box, n = 5)

#>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> 1           NA  0.12500000   -0.4322034  -0.4583333    -0.5
#> 2   -0.3333333 -0.08333333           NA  -0.4583333    -0.5
#> 3           NA  0.00000000   -0.4491525  -0.4583333    -0.5
#> 4   -0.4166667 -0.04166667   -0.4152542  -0.4583333    -0.5
#> 5   -0.3055556  0.16666667   -0.4322034  -0.4583333    -0.5
apply(result_box, 2, FUN = function(x) {range(x, na.rm = TRUE)})

#>      Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> [1,]         -0.5        -0.5         -0.5        -0.5    -0.5
#> [2,]          0.5         0.5          0.5         0.5     0.5

# Sphering only on 3D data.
result_sphere <- l_scale3D(x[, 1:3], method = "sphere")
# Rows having had any NA are all NA after sphering.
head(result_sphere, n = 5)

#>           x1          x2          x3
#> 1         NA          NA          NA
#> 2         NA          NA          NA
#> 3         NA          NA          NA
#> 4 -0.1097604 -0.05847447 0.021141688
#> 5 -0.1188225  0.04803699 0.001622979
# Note with NAs mean is no longer numerically zero.
# because centring was based on all non-NAs in each column
apply(result_sphere, 2, FUN = function(x) {mean(x, na.rm = TRUE)})

#>            x1            x2            x3 
#>  0.0012171739 -0.0002142758  0.0019700846