Constructs Unique Attribute Pattern Map for Binary Data

Computes the powers of 2 from \(0\) up to \(K - 1\) for \(K\)-dimensional attribute pattern.

attribute_bijection(K)

Arguments

K	Number of Attributes.

Value

A vec with length \(K\) detailing the power's of 2.

Details

The bijection vector generated is \(\mathbf v = (2^{K-1},2^{K-2},\dots,1)^\top\). With the bijection vector, there is a way to map the binary latent class with \(c=\mathbf\alpha_c^\top\mathbf v\in\{0, 1,\dots, 2^{K}-1\}\). For example, for \(K = 2\), \(\mathbf v=(2, 1)^\top\) and the integer representations for attribute profiles \(\mathbf \alpha_0=(0,0)^\top\), \(\mathbf \alpha_1=(0,1)^\top\), \(\mathbf \alpha_2=(1, 0)^\top\), and \(\mathbf \alpha_3=(1,1)^\top\) are \(c\) = 0, 1, 2, and 3, respectively.

See also

attribute_inv_bijection()

Author

Steven Andrew Culpepper and James Joseph Balamuta

Examples

## Construct an attribute bijection for binary data ----
bijection_k3 = attribute_bijection(3)

bijection_k3
#>      [,1]
#> [1,]    4
#> [2,]    2
#> [3,]    1