IEEE Power & Energy Magazine - May/June 2022 - 20

Mathematically, the word norm can be used to describe
the distance of a vector from the origin. Minimizing the sum
of squared errors is equivalent to minimizing the Euclidean
distance of the error vector from the origin, which is
called the Euclidean norm, 2-norm, or L2 norm. Similarly,
minimizing the sum of absolute errors is equivalent to minimizing
the Manhattan distance of the error vector from the
origin, which is called the Manhattan norm, 1-norm, or L1
norm. The regression analysis that minimizes the L1 norm
of the error vector is called L1 regression, or least absolute
deviation regression.
Starting from least squares regression, we can also obtain
several extensions that are well within the field of AI. For
example, in addition to minimizing the sum of squared
errors, adding a penalty (regularization) to reduce the magnitude

IEEE Power & Energy Magazine - May/June 2022

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