## 2 Descriptive Patterns
### Pattern Interestingness  
From the contingency table for a class association pattern \(X\wedge C\) (Figure 2), measures of pattern interestingness can be computed [24]. Interestingness measures guide the pattern discovery towards patterns that are of potential interest and should be presented. They can be used during pattern mining to prune uninteresting pattern candidates or during post-processing to rank or select patterns. The issue of identifying interesting association patterns has been extensively studied, and a large number of interestingness measures have been proposed. [PERSON] et al. [28] analyzed 21 interestingness measures for association analysis; the survey of [PERSON] and [PERSON] [24] covered 38 measures; while [PERSON] et al. [29] studied 61 measures. In this paper, we consider seven interestingness measures that have been used in characteristic pattern mining; the measures and their definitions are listed in Table 1.  
* Typicality: The measure of typicality evaluates relative pattern frequency in the target class, i.e., the proportion of examples in class \(C\) that are covered by pattern \(X\). The measure was originally proposed to quantify disjunctive patterns which together completely cover a class [30], but is here applied to evaluate individual characteristic patterns. * Utility: The utility measure was proposed in order to rank as more interesting those patterns which are more specifically related to the target class than to other classes [22]. The measure returns a positive value when pattern and class cannot be considered statistically independent, i.e., when \(P(X\wedge C)>P(X)\times P(C)\). Utility is weighted by pattern frequency (scaled by \(a\)), favoring more general patterns with higher relative frequency \(P(X)\) (for \(a>0\)). * Novelty: Similarly to utility, novelty (applied to characteristic patterns in [31]) is based on comparing the joint and individual probabilities of a pattern and a class: it returns a positive value when the co-occurrence of pattern and class is more frequent, measured by \(P(X\wedge C)\), than expected given the individual probabilities \(P(X)\) and \(P(C)\). Novelty can be rewritten as weighted relative accuracy, \(P(X)\times[P(C|X)-P(C)]\), combining generality of the pattern with added value of the class probability given the pattern [32]. Figure 2: Contingency table for a class association pattern \(X\wedge C\). Laplace estimate: The Laplace estimate has been used as an alternative to novelty for assessing characteristic patterns [31]. The measure quantifies the pattern's frequency in the target class relative to its frequency in the complete dataset. The value of the Laplace estimate is maximal if all examples covered by the pattern are examples of the target class. Due to the constant summands (1 in the numerator and 2 in the denominator), the measure implicitly penalizes less frequent patterns with smaller \(n(X)\) and \(n(X\wedge C)\)[33]. * Relative risk: The measure of relative risk has been employed to select among typical patterns those patterns which are more predictive of the target class [21]. Relative risk assesses the conditional probability of the class \(C\) given the pattern \(X\) against the class probability in the case of the pattern being absent. * IC\({}^{++}\): The IC\({}^{++}\) measure [34] not only considers the pattern's absence in the target class, but also in the background, with \(\
eg X\) observed in the target class rather than background suggesting \(C\) to be less plausible. Different from utility and novelty, the IC\({}^{++}\) measure, increasing with higher \(P(C)\), is biased towards frequent classes rather than frequent patterns. * F1 score: As a further measure, we borrow the F1 score from predictive data mining, which is designed to balance recall \(P(X|C)\) and precision \(P(C|X)\) by calculating their harmonic mean.