Affine Normalization of a Numeric Vector (Zero-Centered Min-Max Scaling)

Transforms a numeric vector by centering it at zero and scaling it so that the minimum value becomes -1. Specifically, the affine normalization is defined as:

Usage

calc_affine_normalization(x)

Arguments

x

A numeric vector to be normalized. This vector may contain NA values.

Value

A numeric vector of the same length as x that has been affine normalized.

Details

$$x_{\text{scaled}} = \frac{x - \mu}{\mu - \min(x)}$$

where \(\mu\) is the mean of x.

The transformation produces a vector with a mean that is approximately zero (ignoring NA values), a minimum of -1, and a maximum above zero if the original maximum exceeds the mean.

The function computes the mean and minimum of x with na.rm = TRUE. If the mean equals the minimum (or is nearly equal within machine precision), the function issues a warning and returns a vector of NA values to avoid division by zero.

Examples

# Example vector with NA values
x <- c(3, 5, 7, NA, 10, 12)

# Apply affine normalization
normalized_x <- calc_affine_normalization(x)

# The normalized vector should have a mean of approximately zero,
# a minimum of -1, and a maximum above zero (if the original maximum exceeds the mean).