# L-Norms as Loss Function

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In linear algebra, functional analysis, and related areas of mathematics, a norm (l-norms) is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

L1-Norm loss function is known as least absolute deviations (LAD).

It is basically minimizing the sum of the absolute differences between the target value and the estimated values .

L2-Norm loss function is known as least squares error (LSE).

It is basically minimizing the sum of the square of the differences between the target value and the estimated values

Differences between L1-L2 norm

The differences of L1-norm and L2-norm as a loss function are the following.

 L1-norm L2-norm Robust Not robust Unstable solution Stable solution Possible multiple solutions Only one solution

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