Vector Database

Normalize Elasticsearch

L1 norm

$$\text{l1 norm(x)} = \frac{x_j}{\sum_{i=1}^n{|x_i|}}$$

Ví dụ: x = [3, -2, 7]

$$|3| + |-2] + |7| = 12$$

$$\text{l1 norm(x)} = \left[\frac{3}{12}, \frac{-2}{12}, \frac{7}{12}\right] = [0.25, -0.167, 0.583]$$

l1 norm with python

from sklearn.preprocessing import normalize
X = [
    [3, -2, 7],
    [1, 6, 8],
    [1, 3, 3]
]
normalize(X, norm = 'l1')

L2 norm

$$\text{l2 norm(x)} = \frac{x_j}{\sqrt{\sum_{i=1}^n{x_i^2}}}$$

Ví dụ: x = [3, -2, 7]

$$\sqrt{3^2 + (-2)^2 + 7^2} = 7.874$$

$$\text{l2 norm(x)} = \left[\frac{3}{7.874}, \frac{-2}{7.874}, \frac{7}{7.874}\right] = [0.381, -0.254, 0.889]$$

l2 norm with python

from sklearn.preprocessing import normalize
X = [
    [3, -7, 2],
    [1, 6, 8],
    [1, 3, 3]
]
normalize(X, norm = 'l2')