"Association rules parameters"

sshilderman

Hi all,

What are the gain theta, laplace and ps parameters?

I couldn't find any info about it.

 

Thank you.

valerius_kaiser

Laplace function is similar to confidence: laplace(X->Y) = (supp(X->Y) +1)/(supp(X) +k)

Whereby k is a constant with the value k > 1. The value of lapülace meet the unequality1/(1+k) < laplace < 2/(1+k). The value for k will be often set to the class count, that is for binary classification k=2. The default value for  for the rule calculation in Rapid Miner software is k = 1.

Gain function (Fukuda, 1996) is similar to the confidence too: gain(X->Y)= supp(X->Y) - theta*supp(X), whereby the theta value is variable in the interval (0,1). The value range of the gain is between theta and 1-theta.

But you can see in the documentation of RapidMiner, that the theta lies in the interval (-Infinity, +Infinity) and that the default value for theta for the operator " Create Association Rules" in the RapidMiner is 2. It can be that the RapidMiner uses some function to map interval (0,1) to interval (-Infinity, +Infinity), for example by means of the function theta_RM = tan(PI(theta-1/2)).

The value gain(X->Y) = 0 indicates that every theta-th transaction that contains X, also contains Y. Values over/below 0 symbolize a stromnger/weaker connection between X and Y than specified by theta.

The ps function (Piatetsky-Shapiro, 1991) is identical to the gain function for theta = supp(Y). This assumes that the support of a rule should be higher than the expected support for statistical independence.. Values between 0 and 1 reflect a positive relationship, negative values to -1 reflect a negative relationship between X and Y