## 4 Results
### Distribution of Completeness and Discriminant Power for Different Interestingness Measures  
Figure 3 shows graphically the variation in completeness and discriminant power over the top \(k\) (\(k=30\)) patterns for each of the studied interestingness measures, in the two case studies of comparing songs by different Plains tribes and of comparing different song types within Chippewa music. The box and whisker plots in Figure 3 show for each measure a box around the first and third quartile, with whiskers from the minimum to maximum completeness or discriminant power. The plots reveal differences between the interestingness measures in balancing completeness and discriminant power. At the same time, overall similar behavior of the measures relative to each other can be observed in both case studies, suggesting that the principal observations can be generalized across datasets. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Attribute** & **Definition** & \multicolumn{2}{c}{**\# of Values**} \\  & & **Case Study 1** & **Case Study 2** \\ \hline \hline tonality & third above keynote & 5 & 3 \\ firstNoteReKey & first tone relative to keynote & 17 & 14 \\ lastNoteReKey & last tone relative to keynote & 7 & 6 \\ lastNoteReCompass & last tone relative to compass of song & 4 & 2 \\ material & tone material & 16 & 13 \\ accidentals & chromatic alterations of tones & 6 & 3 \\ structure & relation between contiguous accented tones & 4 & 3 \\ firstProgression & direction of first progression & 2 & 2 \\ firstMetricPos & part of measure on which song begins & 3 & 3 \\ firstMeasure & rhythm (meter) of first measure & 13 & 10 \\ meterChange & change of time (measure-lengths) & 3 & 3 \\ rhythmicUnits & rhythmic units & 3 & 3 \\ tempoVoiceAccomp & tempo relation voice/ rhythmic accompaniment & – & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Music content features based on [PERSON]’s quantitative analyses. Unsurprisingly, patterns ranked high by the typicality measure are located high in the completeness space but predominantly low with respect to discriminant power. In the first case  
Figure 3: Distribution of completeness and discriminant power for the top 30 patterns mined with different pattern interestingness measures (minimum association support 3%, maximum pattern size 4). Numbers in brackets indicate the rank of the maximally complete resp. discriminant pattern. study, the comparison of tribes, the maximum completeness (indicated by the highest ranked pattern according to typicality) is also reached by the IC\({}^{++}\) measure where it is found on rank five. In the second case study, the comparison of Chippewa song types, additionally utility (with higher \(a\)), novelty, and F1 score also include the maximally complete pattern among the top 30 patterns, in the case of utility (with \(a=1\)) on rank one. For the utility measure, generally, the bias towards more frequent patterns with higher \(a\) favors more complete patterns, while low \(a\) leads to more discriminant patterns. The remaining measures proposed for discovering characteristic patterns seek to increase discriminant power, frequently at the cost of lower completeness. The Laplace estimate generally appears to favor highly discriminant patterns, while relative risk shows a larger variance especially in the first case study, reaching relatively high, but also relatively low completeness values for some among the top ranked patterns. Novelty, like utility biased towards more frequent patterns, achieves higher completeness than Laplace and utility (with \(a=0\)) and predominantly higher discriminant power than IC\({}^{++}\) and utility (with higher \(a\)). These findings are in line with alternative uses of these measures: Laplace has proven successful in associative classification using patterns [44]. The measure is similar to confidence in association rule mining, which was proposed as a measure for discriminant as opposed to characteristic pattern induction in early work on data mining and knowledge discovery [20].