A way to compare measures in association rule mining

Association rule mining is used to find statistically significant rules of the form ”if a then b”, a→ b, where a and b are two distinct events. Today there exists a lot of different measures that are used to find these rules. Generally these measures try to compare the conditional probability, p(b|a), related to the rule a → b with marginal probability of b, p(b), and see how much they deviate from each other. For example, as a difference p(b|a) − p(b). Some measures have normalizing factors, but they are all measuring the strength of dependence between two events in some way. Currently there exists no good way of comparing the goodness of these measures. Therefore we will introduce a way of doing so, the comparison method we introduce may not be perfect, but we hope that this paper may shine some light onto some of the problems that exists when trying to compare different measures with each other. We will also defined a simple new measure for measuring rules. The reason for creating this measure is that there are cases when a measure is indicating a very strong rule, but we still only have a 50 % chance of predicting the correct outcome, this is called equilibrium. In the cases where we are not only interested in deviation from independence, but also deviation from equilibrium, no good measures exist today. Our measure will therefore takes the equilibrium into account as well as the independence. Ett sätt att jämföra m̊att inom kundkorgsanalys Sammanfattning Kundkorgsanalys g̊ar ut p̊a att hitta regler p̊a formen ”om a s̊a b”, a→ b, där a och b är tv̊a separata händelser. Det finns i dag redan flertalet olika mått för att hitta dessa regler. Generellt sett s̊a jämför dessa mått den betingade sannolikheten, p(b|a), med sannolikheten för b, p(b), helt enkelt skillnaden p(b|a) − p(b). En del mått har en normaliseringsfaktor, men alla mått mäter p̊a n̊agot sätt hur stor avvikelsen fr̊an oberoende är. Det existerar inget bra sätt att mäta och utvärdera dessa mått. Därför introducerar vi ett nytt sätt att göra det, metoden är l̊angt ifr̊an perfekt, men vi hoppas att den kan p̊avisa n̊agra av problemen som finns med att jämföra dessa mått med varandra. Vi har ocks̊a definerat ett nytt mått för att mäta dessa regler och anledningen är att ibland indikerar ett m̊att p̊a en stark regel, men man har änd̊a bara 50 % chans att förutsp̊a rätt utfall, detta kallas jämnvikt. I de fall vi inte bara är intresserade av avvikelse fr̊an oberoende utan ocks̊a intresserade av avvikelse fr̊an den här jämnvikten s̊a existerar det inget bra mått i dagsläget. Popular science summary Association rule mining is the field of statistics where you try to find rules on the form ”if a then b’ where a and b are two events. For example, a store owner might be interested in how to organize the store to maximize sales. So she may want to find strong rules like ”if (buying) flash-light then (buying) batteries” that she can use to reorganize the store accordingly. Today there exist a lot of measures that are used to identify what a strong rule is, but no good way of comparing these measures. In this paper we will therefore introduce a way of comparing these measures. We have also defined a new measure and compare it with some of the existing measures by our new comparison method. The results show that there are many challenges in comparing different measures, our method have some flaws and can only be said to be conceptually correct. The results also show that our method ranks the existing measures to be more stable.