Norm knowledge points of machine learning - Code World

Norm knowledge points of machine learning

Others 2022-04-21 22:08:05 views: 0

1-norm:

$||x||_1 = \sum_{i=1}^N|x_i|$ , that is, the sum of the absolute values of the vector elements, matlab calls the function norm(x, 1)

2-norm:

$||\textbf{x}||_2 =\sqrt{\sum_{i=1}^Nx_i^2}$ , Euclid norm (Euclidean norm, commonly used to calculate the length of the vector), that is, the square sum of the absolute values of the vector elements and then the square root, matlab calls the function norm(x, 2).

$\infty$ - Norm: $||\textbf{x}||_\infty = \max_{i}|x_i|$ , that is, the maximum value in the absolute value of all vector elements, matlab calls the function norm(x, inf).

$-\infty$ - Norm: $||\textbf{x}||_{-\infty}=\min_i|x_i|$

, that is, the minimum value among the absolute values of all vector elements, and matlab calls the function norm(x, -inf).

p-norm: $||\textbf{x}||_p = (\sum_{i=1}^N|x_i|^p)^{\frac{1}{p}}$
, that is, the 1/p power of the sum of the absolute value of the vector elements to the p power, matlab calls the function norm(x, p).

Other matrix norm, etc., refer to the link below

Link: https://www.zhihu.com/question/20473040/answer/102907063

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