Partition Measures for Data Mining

Abstract

We investigate a number of measures associated with partitions. The first of these is congruence measures, which are used to calculate the similarity between two partitions. We provide a number of examples of this type of measure. Another class of measures we investigate are prognostication measures. This measure, closely related to a concept of containment between partitions, are useful in indicating how well knowledge of an objects class in one partition predicts its class in a second partitioning. Finally we introduce a measure of the non-specificity of a partition. This measures a feature of a partition related to the generality of the constituent classes of the partition. A common task in machine learning is developing rules that allow us to predict the class of an object based upon the value of some features of the object. The more narrowly we categorize the features in the rules the better we can predict an objects classification. However counterbalancing this is the fact that to many narrow feature categories are difficult for human experts to cognitively manage, this introduces a fundamental issue in data mining. We shown how the combined use of our measures prognostication and non-specificity allow us navigate this issue.