In pattern mining, the main challenge is the exponential explosion of the set
of patterns. Typically, to solve this problem, a constraint for pattern
selection is introduced. One of the first constraints proposed in pattern
mining is support (frequency) of a pattern in a dataset. Frequency is an
anti-monotonic function, i.e., given an infrequent pattern, all its
superpatterns are not frequent. However, many other constraints for pattern
selection are not (anti-)monotonic, which makes it difficult to generate
patterns satisfying these constraints. In this paper we introduce the notion of
projection-antimonotonicity and $\theta$-$\Sigma\o\phi\iota\alpha$ algorithm
that allows efficient generation of the best patterns for some nonmonotonic
constraints. In this paper we consider stability and $\Delta$-measure, which
are nonmonotonic constraints, and apply them to interval tuple datasets. In the
experiments, we compute best interval tuple patterns w.r.t. these measures and
show the advantage of our approach over postfiltering approaches.
KEYWORDS: Pattern mining, nonmonotonic constraints, interval tuple data

该论文介绍了在模式挖掘中，使用投影反单调性和 θ−Σοφια 算法可以有效生成满足非单调限制条件的最佳模式，并利用稳定性和 Δ- 度量应用于区间元组数据集，计算最佳模式，并显示其优势。