Remove Correlated Attributes (RapidMiner Studio Core)

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.