SPMF documentation > Calculate the standardization of time series

This example explains how to calculate the standardization of time series using the SPMF open-source data mining library.

How to run this example?

What is the calculation of the standardization of a time series?

Standardization is an operation that is often used to normalize a time series. Let there be a time series (a list of data points). Let V and W be the mean and standard deviation of the values in the time series, respectively. The standardization of a time series is obtained by replacing each data point Z by (Z-V)/ (W). This has for effect or normalizing the time series with respect to the mean and standard deviation. However, note that unlike the min max normalization, standardization does not ensure that data points of the resulting time series are in the [0,1] interval.

What is the input of this algorithm?

The input is one or more time series. A time series is a sequence of floating-point decimal numbers (double values). A time-series can also have a name (a string).

Time series are used in many applications. An example of time series is the price of a stock on the stock market over time. Another example is a sequence of temperature readings collected using sensors.

For this example, consider the following time series:

Name Data points
ECG1 3,2,8,9,8,9,8,7,6,7,5,4,2,7,9,8,5

This example time series database is provided in the file contextMovingAverage.txt of the SPMF distribution.

In SPMF, to read a time-series file, it is necessary to indicate the "separator", which is the character used to separate data points in the input file. In this example, the "separator" is the comma ',' symbol.

What is the output?

The output is the standardization of the time series received as input. Let there be a time series (a list of data points). Let V and W be the mean and standard deviation of the values in the time series, respectively. The standardization of a time series is obtained by replacing each data point Z by (Z-V)/ (W).

For example, the result is:

Name Data points
ECG1_STDDZ -1.4196563543775027,-1.8506234619563875,0.7351791835169211,1.166146291095806,0.7351791835169211,1.166146291095806,0.7351791835169211,0.3042120759380364,-0.1267550316408484,0.3042120759380364,-0.5577221392197332,-0.988689246798618,-1.8506234619563875,0.3042120759380364,1.166146291095806,0.7351791835169211,-0.5577221392197332

To see the result visually, it is possible to use the SPMF time series viewer, described in another example of this documentation. In the following figure, the original time series is displayed (top) and its standardization (bottom).

Input file format

The input file format is defined as follows. It is a text file. The text file contains one or more time series. Each time series is represented by two lines in the input file. The first line contains the string "@NAME=" followed by the name of the time series. The second line is a list of data points, where data points are floating-point decimal numbers separated by a separator character (here the ',' symbol).

For example, the input file of the previous example, named contextMovingAverage.txt is defined as follows:

@NAME=ECG2
3,2,8,9,8,9,8,7,6,7,5,4,2,7,9,8,5

Consider the first two lines. It indicates that the first time series name is "ECG2" and that it consits of the data points: 3,2,8,9,8,9,8,7,6,7,5,4,2,7,9,8, and 5. Then, three other time series are provided in the same file, which follows the same format.

But note that it is possible to have more than one time series per file. For example, this is another input file called contextSax.txt, which contains 4 time series.

@NAME=ECG1
1,2,3,4,5,6,7,8,9,10
@NAME=ECG2
1.5,2.5,10,9,8,7,6,5
@NAME=ECG3
-1,-2,-3,-4,-5
@NAME=ECG4
-2.0,-3.0,-4.0,-5.0,-6.0

Output file format

The output file format is the same as the input format. For example, there is the result of this example:

@NAME=ECG2_STDDZ
-1.4196563543775027,-1.8506234619563875,0.7351791835169211,1.166146291095806,0.7351791835169211,1.166146291095806,0.7351791835169211,0.3042120759380364,-0.1267550316408484,0.3042120759380364,-0.5577221392197332,-0.988689246798618,-1.8506234619563875,0.3042120759380364,1.166146291095806,0.7351791835169211,-0.5577221392197332

Notes

Beside the stantardization, SPMF offers other operations for normalization such as the "min max normalization"

Where can I get more information about the standardization?

The standardization is a basic operation for analyzing time series. It is described in many websites and books.

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