This algorithm transforms the input vector proportionally into an output vector with a Euclidean norm of 1:

The algorithm performs a transformation of input vector **x** into the (normalized) output vector **x’**:

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This algorithm transforms the input vector proportionally into an output vector with a Euclidean norm of 1:

The algorithm performs a transformation of input vector **x** into the (normalized) output vector **x’**:

This normalization algorithm performs a transformation that results in an output vector where all elements sum up to 1.

The algorithm performs a transformation of input vector **x** into the (normalized) output vector **x’**:

The use of this normalization algorithm ensures that all elements of the input vector are transformed into the output vector in such a way that the mean of the output vector is approximately Zero, while the standard deviation (as well as the variance) are in a range close to unity.

We calculate the mean of all elements of a vector as:

The standard deviation can be expressed as:

The use of this formula depends on a pre-calculated . From a programmer’s point of view, the following equivalent formula would be computationally less expensive, since it requires only one iteration over the input vector:

We transform the input vector **x** into the (normalized) output vector **x’** by applying the following algorithm:

yielding for the output vector the conditions:

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