Norms
Norms are mathematical concepts to measure the length of vector.
Norm is any function that satisfy following properties:
for all
, triangle inequality
for all scalar
Example of Norms
L^p Norm
norm is given as
So, is euclidean norm. Many times, square of norm is used. Many times denoted simply by . For vector
Many times used when difference between zero and non-zero elements are more important.
Max Norm
It is denoted by . It is simply the absolute value of element with largest magnitude.
Frobenius Norm
This is norm used for measure size of a matrix.
Properties:
norms are not differentiable at origin, because of using in the norm, which is not differentiable at origin.
For , isn't convex as it doesn't follow the triangle inequality. Using induces sparsity in the features.
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