# Remove Correlated Attributes (AI Studio Core)

## Synopsis

This operator removes correlated attributes from an ExampleSet. The correlation threshold is specified by the user. Correlation is a statistical technique that can show whether and how strongly pairs of attributes are related.## Description

A correlation is a number between -1 and +1 that measures the degree of association between two attributes (call them X and Y). A positive value for the correlation implies a positive association. In this case large values of X tend to be associated with large values of Y and small values of X tend to be associated with small values of Y. A negative value for the correlation implies a negative or inverse association. In this case large values of X tend to be associated with small values of Y and vice versa.

Suppose we have two attributes X and Y, with means X' and Y' respectively and standard deviations S(X) and S(Y) respectively. The correlation is computed as summation from 1 to n of the product *(X(i)-X').(Y(i)-Y') * and then dividing this summation by the product *(n-1).S(X).S(Y)* where *n* is the total number of examples and *i* is the increment variable of summation. There can be other formulas and definitions but let us stick to this one for simplicity.

As discussed earlier a positive value for the correlation implies a positive association. Suppose that an X value was above average, and that the associated Y value was also above average. Then the product *(X(i)-X').(Y(i)-Y')* would be the product of two positive numbers which would be positive. If the X value and the Y value were both below average, then the product above would be of two negative numbers, which would also be positive. Therefore, a positive correlation is evidence of a general tendency that large values of X are associated with large values of Y and small values of X are associated with small values of Y.

As discussed earlier a negative value for the correlation implies a negative or inverse association. Suppose that an X value was above average, and that the associated Y value was instead below average. Then the product *(X(i)-X').(Y(i)-Y')* would be the product of a positive and a negative number which would make the product negative. If the X value was below average and the Y value was above average, then the product above would also be negative. Therefore, a negative correlation is evidence of a general tendency that large values of X are associated with small values of Y and small values of X are associated with large values of Y.

This operator can be used for removing correlated or uncorrelated attributes depending on the setting of parameters specially the *filter relation* parameter. The procedure is quadratic in number of attributes i.e. for *m* attributes an *m x m* matrix of correlations is calculated. Please note that this operator might fail in some cases when the attributes should be filtered out. For example, it might not be able to remove for example all negative correlated attributes because for the complete *m x m* - matrix of correlation the correlations will not be recalculated and hence not checked if one of the attributes of the current pair was already marked for removal. This means that for three attributes X, Y, and Z that it might be that Y was already ruled out by the negative correlation with X and is now not able to rule out Z any longer. The used correlation function in this operator is the Pearson correlation. In order to get more stable results the original, random, and reverse order of attributes is available.

Correlated attributes are usually removed because they are similar in behavior and will have similar impact in prediction calculations, so keeping attributes with similar impacts is redundant. Removing correlated attributes saves space and time of calculation of complex algorithms. Moreover, it also makes processes easier to design, analyze, understand and comprehend.

## Input

- example set input (Data Table)
This input port expects an ExampleSet. It is the output of the Filter Examples operator in the attached Example Process. The output of other operators can also be used as input.

## Output

- example set output (Data Table)
The (un-)correlated attributes are removed from the ExampleSet and this ExampleSet is delivered through this output port.

- original (Data Table)
The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.

## Parameters

- correlationThis parameter specifies the correlation for filtering attributes. A correlation is a number between -1 and +1 that measures the degree of association between two attributes (call them X and Y). A positive value for the correlation implies a positive association. In this case large values of X tend to be associated with large values of Y and small values of X tend to be associated with small values of Y. A negative value for the correlation implies a negative or inverse association. In this case large values of X tend to be associated with small values of Y and vice versa. Range: real
- filter_relationCorrelations of two attributes are compared at a time. One of the two attributes is removed if their correlation fulfills the relation specified by this parameter. Range: selection
- attribute_orderThe algorithm takes this attribute order to calculate correlations and for filtering the attributes. Range: selection
- use_absolute_correlationThis parameter indicates if the absolute value of the correlations should be used for comparison. Range: boolean

## Tutorial Processes

### Removing correlated attributes from the Sonar data set

The 'Sonar' data set is loaded using the Retrieve operator. A breakpoint is inserted here so that you can view the ExampleSet before further operators are applied on it. You can see that the 'Sonar' data set has 60 numerical attributes. The Correlation Matrix operator is applied on it. This operator is applied so that you can view the correlation matrix of the 'Sonar' data set otherwise this operator was not required here. The Remove Correlated Attributes operator is applied on the 'Sonar' data set. The correlation parameter is set to 0.8. The filter relation parameter is set to 'greater' and the attribute order parameter is set to 'original'. Run the process and you will see in the Results Workspace that 19 out of 60 numerical attributes of the 'Sonar' data set have been removed. Now have a look at the correlation matrix generated by the Correlation Matrix operator. You can see that most of the attributes with correlations above 0.8 have been removed from the data set. Some such attributes are not removed because this operator might fail in some cases when the attributes should be filtered out. It might not be able to remove all correlated attributes because for the complete m x m matrix of correlation the correlations will not be recalculated and hence not checked if one of the attributes of the current pair was already marked for removal. Change the value of the attribute order parameter to 'random' and run the process again. Compare these results with the previous ones. This time a different set of attributes is removed from the data set. So, the order in which correlation operator is applied may change the output.