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29/07/2018 by Benjamin Stein

Normalization to Zero Mean

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:

[Read more…]

Filed Under: Time Series Analysis

28/07/2018 by Benjamin Stein

Normalization into an Interval

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:

  • Upper limit: Lmax
  • Lower limit: Lmin
  • Highest value in x: xmax
  • Smallest value in x: xmin

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

[Read more…]

Filed Under: Time Series Analysis

27/07/2018 by Benjamin Stein

Normalization

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:

  1. The prices (real numbers) would have to be converted to the natural numbers of the system of coordinates of the output device in such a way that the proportions are preserved as precisely as possible.
  2. Since we shall want to utilize as much of the available output area as possible for the representation, the domain [113.29, 241.05] should also be scaled to the coordinate domain [0, 480].

[Read more…]

Filed Under: Time Series Analysis

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Recent Posts

  • Normalization to Euclidean Norm 1
  • Normalization to Sum 1
  • Normalization to Zero Mean and Unit Standard Deviation
  • Normalization to Zero Mean
  • Normalization into an Interval

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  • Neural Networks
  • Time Series Analysis

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