Differentiation (Time Series)
SynopsisThis operators calculates the differentiated values for the selected time series attributes.
There are three differentiation methods provided and additionally a lag can be added. The differentiated values can either be added as new attributes or they override the existing attributes.
This operator works only on numerical time series.
- example set (IOObject)
The ExampleSet which contains the time series data as attributes.
- example set (IOObject)
The ExampleSet after applying the differentation. In case of overwrite attributes is true original time series attributes are overwritten, if not new attributes with the differentiated values are added. For the name of the new attributes a postfix, specified by the new attributes postfix parameter, is added to the name of the original attributes. Other attributes are not changed.
This parameter allows you to select the filter for the time series attributes selection filter; the method you want to select the attributes which holds the time series values. Only numeric attributes can be selected as time series attributes. The different filter types are:
- all: This option selects all attributes of the ExampleSet to be time series attributes. This is the default option.
- single: This option allows the selection of a single time series attribute. The required attribute is selected by the attribute parameter.
- subset: This option allows the selection of multiple time series attributes through a list (see parameter attributes). If the meta data of the ExampleSet is known all attributes are present in the list and the required ones can easily be selected.
- regular_expression: This option allows you to specify a regular expression for the time series attribute selection. The regular expression filter is configured by the parameters regular expression, use except expression and except expression.
- value_type: This option allows selection of all the attributes of a particular type to be time series attributes. It should be noted that types are hierarchical. For example real and integer types both belong to the numeric type. The value type filter is configured by the parameters value type, use value type exception, except value type.
- block_type: This option allows the selection of all the attributes of a particular block type to be time series attributes. It should be noted that block types may be hierarchical. For example value_series_start and value_series_end block types both belong to the value_series block type. The block type filter is configured by the parameters block type, use block type exception, except block type.
- no_missing_values: This option selects all attributes of the ExampleSet as time series attributes which do not contain a missing value in any example. Attributes that have even a single missing value are not selected.
- numeric_value_filter: All numeric attributes whose examples all match a given numeric condition are selected as time series attributes. The condition is specified by the numeric condition parameter.
The required attribute can be selected from this option. The attribute name can be selected from the drop down box of the parameter if the meta data is known.Range:
The required attributes can be selected from this option. This opens a new window with two lists. All attributes are present in the left list. They can be shifted to the right list, which is the list of selected time series attributes.Range:
Attributes whose names match this expression will be selected. The expression can be specified through the edit and preview regular expression menu. This menu gives a good idea of regular expressions and it also allows you to try different expressions and preview the results simultaneously.Range:
If enabled, an exception to the first regular expression can be specified. This exception is specified by the except regular expression parameter.Range:
This option allows you to specify a regular expression. Attributes matching this expression will be filtered out even if they match the first expression (expression that was specified in regular expression parameter).Range:
This option allows to select a type of attribute. One of the following types can be chosen: numeric, integer, real.Range:
If enabled, an exception to the selected type can be specified. This exception is specified by the except value type parameter.Range:
The attributes matching this type will be removed from the final output even if they matched the before selected type, specified by the value type parameter. One of the following types can be selected here: numeric, integer, real.Range:
This option allows to select a block type of attribute. One of the following types can be chosen: value_series, value_series_start, value_series_end.Range:
If enabled, an exception to the selected block type can be specified. This exception is specified by the except block type parameter.Range:
The attributes matching this block type will be removed from the final output even if they matched the before selected type by the block type parameter. One of the following block types can be selected here: value_series, value_series_start, value_series_end.Range:
The numeric condition used by the numeric condition filter type. A numeric attribute is selected if all examples match the specified condition for this attribute. For example the numeric condition '> 6' will keep all numeric attributes having a value of greater than 6 in every example. A combination of conditions is possible: '> 6 && < 11' or '<= 5 || < 0'. But && and || cannot be used together in one numeric condition. Conditions like '(> 0 && < 2) || (>10 && < 12)' are not allowed because they use both && and ||.Range:
If this parameter is set to true the selection is reversed. In that case all attributes not matching the specified condition are selected as time series attributes. Special attributes are not selected independent of the invert selection parameter as along as the include special attributes parameter is not set to true. If so the condition is also applied to the special attributes and the selection is reversed if this parameter is checked.Range:
Special attributes are attributes with special roles. These are: id, label, prediction, cluster, weight and batch. Also custom roles can be assigned to attributes. By default special attributes are not selected as time series attributes irrespective of the filter conditions. If this parameter is set to true, special attributes are also tested against conditions specified and those attributes are selected that match the conditions.Range:
This parameter indicates if the original time series attributes are overwritten by the resulting time series. If this parameter is set to false, the resulting new time series are added as new attributes to the ExampleSet. The name of these new attributes will be the name of the original time series with a postfix added. The postfix is specified by the parameter new attributes postfix.Range:
If overwrite attributes is false, this parameter specifies the postfix which is added to the names of the original time series to create the new attribute names.Range:
This parameter defines the amount of lag that is used when calculating the differentiated values. Hence the differentiated value z(i) is calculated as the differentation between y(i) and y(i-lag). Larger lags can be very helpful to remove seasonal effects from time series data. For the first lag values of the differentiated time series, the differentation is not defined, hence the first lag values are set to missing values.Range:
With this parameter the used differentiation method can be selected.
- substraction: The differentiated value is calculated as z(i) = y(i)-y(i-lag).
- ratio: The differentiated value is calculated as z(i) = y(i) / y(i-lag).
- direction: The differentiated value is 1 if y(i) > y(i-lag), 0 if y(i) = y(i-lag) and -1 if y(i) < y(i-lag)
Comparing differentiation methods
In this tutorial process the effects of differentiating of a sinus signal are demonstrated.
Differentiate Monthly Milk Production Data
This tutorial process demonstrate the use of the lag parameter. The Monthly Milk Production data set is retrieved from the Samples/Time Series folder. The Differentiation of the time series with lag 1 results in the increase in production from month to month. A Differentiation with lag 12 results in the increase in production from year to year, removing the seasonal effects visible in the differentiated time series with lag 1.