The differences between the TP/FP convex hulls for q g and q c measures may seem small and insignificant, but in reality it is not so. The majority of interesting subgroups (this claim is supported also by patterns A1–C1 selected by the domain expert) are subgroups with a small false positive rate which lie in the range in which qo works better. In addition, for subgroups with FP = 0 the true positive rate in our examples was about two times larger for subgroups induced with go than with gc . Furthermore, note that for stages A and B there are two out of five subgroups (A2 and C1) which lie in the gap between the TP/FP
convex hulls. If the qc measure instead of qo measure were used in the experiments with CHD domain, at least subgroup A2 could not have been detected.

## 5. Related Work

This section provides comparisons and links to related work in subgroup discovery, measures of interestingness, evaluation measures and visualization.

## 5.1  Subgroup Discovery

The need for user interactivity in subgroup discovery is addressed by Wrobel S. et al. (1996),
describing a system developed in the KESO European research project (Knowledge Extraction for Statistical Offices) and in the systems EXPLORA (Klösgen, 1996) and MIDOS
(Wrobel, 1997, 2001). EXPLORA treats the learning task as a single relation problem, i.e.,
all the data are assumed to be available in one table (relation), whereas MIDOS extends this task to multi-relation databases, which is related to a number of other learning tasks (De Raedt & Dehaspe, 1997; Mannila & Toivonen, 1996; Wrobel & Džeroski, 1995), mostly in the field of Inductive Logic Programming (Džeroski & Lavrač, 2001; Lavrač & Džeroski, 1994).

The most important features of EXPLORA and MIDOS, related to this paper, concern the use of heuristics for subgroup discovery; the measures of interestingness and the search heuristics are outlined in separate sections below. A related approach to our approach to rule subset selection, presented in Section 2.3, is Gebhardt's (1991) work on subgroup suppression.

Note that some approaches to association rule induction can also be used for subgroup discovery.  For instance, the APRIORI-C algorithm (Jovanoski & Lavrač, 2001), which applies association rule induction to classification rule induction, outputs classification rules with guaranteed support and confidence with respect to a target class. If a rule satisfies also a user-defined significance threshold, an induced APRIORI-C rule is an independent 'chunk' of knowledge about the target class, which can be viewed as a subgroup description with guaranteed significance, support and confidence.  Similarly, the confirmation rule concept, introduced by Gamberger and Lavrač (2000) and used as a basis for the subgroup discovery algorithm in this paper, utilizes the minimal support requirement as a measure whi must be satisfied by every rule in order to be included in the induced confirmation rule set.

Both above mentioned approaches to subgroup discovery exploit the information about class membership. One of the main reasons why these approaches are of interest for subgroup discovery is that, unlike the classical classification rule induction algorithms such as CN2 (Clark & Niblett, 1989) and AQ (Michalski, Mozetic, Hong, & Lavrac, 1986), they do not use the covering algorithm. In covering algorithms only the first few induced rules may