Normalization using sklearn

by Amrita Mitra | Nov 16, 2022 | AI, Machine Learning and Deep Learning, Data Preprocessing, Machine Learning Using Python, Python Scikit-learn

What is a vector norm?

The length of a vector is referred to as the vector’s magnitude or the vector norm. There can be several types of norms. The vector norm |x|_p is defined as:

${|x|}_{p}=(\sum_{i}{|x_{i}|}^{p})^{1/p}\ for\ p=1,2,3,...$

For p = 1, we get L¹ norm and that is defined as:

${|x|}_{1}=\sum_{i}{|x_{i}|}$

For p = 2, we get L² norm and that is defined as:

${|x|}_{2}=(\sum_{i}{|x_{i}|}^{2})^{1/2}$

For example, if v=(1, 2, 3), then L¹ norm of v is |1| + |2| + |3| = 6. And the L² norm of v is:

$\sqrt{1^2+2^2+3^2}=\sqrt{14}$

Similarly, L³ norm of v will be:

${|x|}_{3}=(\sum_{i}{|x_{i}|}^{3})^{1/3}=\sqrt[3]{1^3+2^3+3^3}=6^{2/3}$

And when p=∞, the vector norm is called vector max norm, and it is defined as:

${|x|}_{\infty}=\max_{i}{|x_{i}|}$

So, for our example vector v = (1, 2, 3), the vector max norm will be: …

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by Amrita Mitra | October 3, 2023 | Featured, Linear Algebra | 0 Comments

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by Amrita Mitra | October 3, 2023 | Featured, Linear Algebra | 0 Comments

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by Amrita Mitra | October 3, 2023 | Featured, Linear Algebra | 0 Comments

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by Amrita Mitra | October 3, 2023 | Featured, Linear Algebra | 0 Comments

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by Amrita Mitra | October 3, 2023 | Featured, Linear Algebra | 0 Comments

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by Amrita Mitra | October 3, 2023 | Featured, Linear Algebra | 0 Comments

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