evolving software
The algorithm ensures that the mean of all elements in the output vector is approximately zero. The mean 
of all elements 
of a vector can be calculated by:
The algorithm performs a transformation of input vector x into the (normalized) output vector x’:
yielding the output vector property:
This normalization procedure ensures that all elements of an input vector are transformed proportionally into an output vector with predefined upper and lower limits:
The following parameters are required for the calculation:
The algorithm performs a transformation of input vector x into the (normalized) output vector x’:
Normalization procedures are mathematical transformations of quantities (time series, vectors). In this type of operation, a vector is transformed from one value domain into another value domain in such a way that the output vector features certain statistical properties such as certain limit values, a certain variance, standard deviation or even a desired average.
A straightforward example for the necessity of such a transformation is the representation of a real time series in a chart. Suppose we want to represent the development of the price of a stock over a certain period by means of a chart. Within the period to be represented, the price fluctuates between $113.29 and $241.05. For generating our chart, we have an empty graph of 640×480 pixels. The system of coordinates in the case of computer output devices such as printers or displays is based on natural numbers, since these devices assemble the images from indivisible pixels. As a result, it is not possible to represent the price of $113.29 exactly on such a device, even if – as in our case – the value domain of the price lies within the value domain of the pixel coordinates. Two transformations would be desirable for the representation of this chart: