Normalization (machine learning)

L2 normalization equation: x_i' = x_i / ||x||_2

L2 normalization is a technique used to scale vectors in machine learning. The equation x_i' = x_i / ||x||_2 represents this process, where x_i' is the normalized vector, x_i is the original vector, and ||x||_2 is the L2 norm of the vector x.

Example

Consider a vector x = [3, 4]. The L2 norm ||x||_2 is calculated as √(3² + 4²) = 5. Thus, the L2 normalized vector x' = [3/5, 4/5] = [0.6, 0.8].

L2 normalization ensures that vectors have a unit norm, which can improve the performance of machine learning algorithms and facilitate better convergence during training.

Related concepts

Matrix norm

L1 norm of a vector is the sum of absolute values of its components

Batch normalization

Batch normalization formula: Y = (X - μ) / σ * γ + β

Dot product

Dot product = sum of products of corresponding entries

Quadratic equation

Quadratic equation standard form: ax² + bx + c = 0

Lagrangian L(x,λ) = f(x) - λg(x)

L(x,λ) = f(x) - λ(g(x) - c)

Regression analysis

Linear regression equation: ŷ = β0 + β1X

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