L2 Normalization (Unit Vector)

Scales the vector so that its Euclidean norm (L2 norm) is 1. This technique is often used in text mining and high-dimensional clustering, and is related to spatial sign prepkitocessing in robust statistics.

Usage

norm_l2(x, na.rm = TRUE)

Arguments

x

A numeric vector.

na.rm

Logical. Remove NAs for norm calculation? Default is TRUE.

Value

A numeric vector with an L2 norm of 1.

Details

Formula: \(x' = \frac{x}{\sqrt{\sum x^2}}\)

References

Serneels, S., De Nages, E., & Van Espen, P. J. (2006). Spatial sign prepkitocessing: a simple way to impart moderate robustness to multivariate estimators. Journal of Chemical Information and Modeling, 46(3), 1402-1409. doi:10.1021/ci050498u

Han, J., Kamber, M., & Pei, J. (2011). Data mining: concepts and techniques (3rd ed.). Morgan Kaufmann.

Examples

# Convert a vector to unit length
x <- c(3, 4)
norm_l2(x) # Returns c(0.6, 0.8)
#> [1] 0.6 0.8