Norm
NormIt is a basic function in mathematics. It is often used to measure the length or size of a vector in a vector space (or matrix). For the norm of model parameters, it can be used as a regularization function.
Properties of norms
In functional analysis, it is defined in a normed linear space and satisfies certain conditions, namely
1) Non-negativity;
2) Homogeneity;
3) Triangle inequality.
The essence of norm is distance, and it is a function with the concept of "length". It is often used in linear algebra, functional analysis and related mathematical fields. Its purpose is to achieve comparison. Norm converts incomparable vectors into comparable real numbers.
Several common norms:
- L0 norm: refers to the number of non-zero elements in the vector.
- L1 norm: refers to the sum of the absolute values of each element in the vector.
- L2 norm: used to improve the overfitting problem in machine learning.
- Nuclear norm: refers to the sum of the singular values of a matrix.
- Frobenius norm: A matrix norm often used in numerical linear algebra.