Polynomial feature expansion (Geron Ch 4, morie.fn grpoly)

[1, X, X^2, ..., X^d] per feature, powers only, no cross terms, so the column order is (bias), then all features at power 1, then all at power 2, and so on. powers entries are 0-based (feature, power) pairs with (0, 0) marking the bias.

Usage

morie_geron_polynomial_features(X, degree, include_bias = TRUE)

Arguments

X

Vector or (m, n) matrix.

degree

Highest power, at least 1.

include_bias

Prepend a column of ones.

Value

List with features, powers, n_features.

Examples

morie_geron_polynomial_features(X = c(1, 2, 3, 4, 5, 6, 7, 8), degree = 5L)
#> $features
#>      [,1] [,2] [,3] [,4] [,5]  [,6]
#> [1,]    1    1    1    1    1     1
#> [2,]    1    2    4    8   16    32
#> [3,]    1    3    9   27   81   243
#> [4,]    1    4   16   64  256  1024
#> [5,]    1    5   25  125  625  3125
#> [6,]    1    6   36  216 1296  7776
#> [7,]    1    7   49  343 2401 16807
#> [8,]    1    8   64  512 4096 32768
#> 
#> $powers
#> $powers[[1]]
#> [1] 0 0
#> 
#> $powers[[2]]
#> [1] 0 1
#> 
#> $powers[[3]]
#> [1] 0 2
#> 
#> $powers[[4]]
#> [1] 0 3
#> 
#> $powers[[5]]
#> [1] 0 4
#> 
#> $powers[[6]]
#> [1] 0 5
#> 
#> 
#> $n_features
#> [1] 6
#> 
#> $estimate
#>      [,1] [,2] [,3] [,4] [,5]  [,6]
#> [1,]    1    1    1    1    1     1
#> [2,]    1    2    4    8   16    32
#> [3,]    1    3    9   27   81   243
#> [4,]    1    4   16   64  256  1024
#> [5,]    1    5   25  125  625  3125
#> [6,]    1    6   36  216 1296  7776
#> [7,]    1    7   49  343 2401 16807
#> [8,]    1    8   64  512 4096 32768
#> 
#> $n
#> [1] 8
#>