# Integration (Time Series)

## Synopsis

This operators calculates the integrated values for the selected time series attributes.## Description

There are six integration methods provided.
See the parameter *integration method* for an overview.
The operator provides the option to *skip invalid values* within integration.
The integrated values can either be added as new attributes or they override the existing attributes.

If the *index attribute* is provided the index values are taken into account when calculating the integrated values.
If the index attribute is a date time attribute, the index values are converted in seconds when calculating the integrated values.

This operator works only on numerical time series.

## Input

- example set (Data table)
The ExampleSet which contains the time series data as attributes.

## Output

- example set (Data table)
The ExampleSet after applying the integration. 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.

## Parameters

- attribute filter type
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.

- attribute
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.

- attributes
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.

- regular expression
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. - use except expression
If enabled, an exception to the first regular expression can be specified. This exception is specified by the

*except regular expression*parameter. - except regular expression
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). - value type
This option allows to select a type of attribute. One of the following types can be chosen: numeric, integer, real.

- use value type exception
If enabled, an exception to the selected type can be specified. This exception is specified by the

*except value type*parameter. - except value type
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. - block type
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.

- use block type exception
If enabled, an exception to the selected block type can be specified. This exception is specified by the

*except block type*parameter. - except block type
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. - numeric condition
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 ||.

- invert selection
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. - include special attributes
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.

- has indices
This parameter indicates if there is an index attribute associated with the time series. If this parameter is set to true, the index attribute has to be selected.

- indices attribute
If the parameter

*has indices*is set to true, this parameter defines the associated index attribute. It can be either a date, date_time or numeric value type attribute. The attribute name can be selected from the drop down box of the parameter if the meta data is known. - sort time series
If this parameter is selected, the input time series will be sorted, according to the selected

*indices attribute*, before the time series operation is applied on. If it is not selected and the input time series is not sorted, a corresponding User Error is thrown.Keep in mind that the indices values still needs to be unique. If the values are non-unique a corresponding User Error is thrown.

- overwrite attributes
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*. - new attributes postfix
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. - skip invalid values
This parameter specifies if invalid values are skipped within integration otherwise all values following are invalid as well.

- integration method
This parameter specifies the integration method. For the following notation: The integrated time series is given by z(x_i) with i in [0,n] which enumerates the index values x_i (if no index attribute is specified, the x_i are 1,2,3,...), while n is the number of samples and the selected time series for integration is given by y(x_i).

- cumulative sum: The integrated value is given by z(x_i) = z(x_(i-1))+y(x_i).
- left Riemann sum: The integrated value is given by z(x_i) = sum_(i=1) y(x_i)*(x_i-x_(i-1)).
- right Riemann sum: The integrated value is given by z(x_i) = sum_(i=1) y(x_(i-1)*(x_i-x_(i-1)).
- upper Riemann sum: The integrated value is given by z(x_i) = sum_(i=1) max([y(x_i),y(x_(i-1)])*(x_i-x_(i-1)).
- lower Riemann sum: The integrated value is given by z(x_i) = sum_(i=1) min([y(x_i),y(x_(i-1)])*(x_i-x_(i-1)).
- trapezoidal rule:
The integrated value is given by z(x_i) = sum_(i=1) *
*(**y(x_i)+y(x_(i-1))**)**/2*(x_i-x_(i-1)).

## Tutorial Processes

### Comparing integration methods

In this tutorial process the different integration methods are used on different time series - time series involving invalid values to demonstrate the function of the *skip invalid values* parameter and a time series with date time index.