Normalización L2, also known as Euclidean normalization, is a mathematical technique used primarily in the field of aprendizaje automático and procesamiento de datos. The purpose of L2 normalization is to scale data vectors to have a unit norm, which helps improve the performance and convergence of various algorithms, particularly those involving distance calculations, such as máquinas de vectores de soporte and k-vecinos más cercanos.
The L2 norm of a vector is calculated as the square root of the sum of the squares of its components. In formulaic terms, for a vector x = [x1, x2, ..., xn], the L2 norm is expressed as:
||x||2 = sqrt(x1^2 + x2^2 + ... + xn^2)
The L2 normalization process involves dividing each component of the vector by its L2 norm, resulting in a new vector y defined as:
y = x / ||x||2
This transformation ensures that the resulting vector y has a length of 1, making it easier to compare different data points in a consistent manner. L2 normalization is particularly useful in contexts where the scale of the input features varies significantly, as it mitigates the influence of larger magnitude features on the outcome of machine learning models.
Beyond its applications in machine learning, L2 normalization is also widely used in various mathematical and computational contexts, including optimization problems and preprocesamiento de datos tasks. By ensuring that data is uniformly scaled, L2 normalization contributes to the stability and reliability of computational algorithms.