(d,τ)-robustness: A pattern α is (d, τ)-robust if d is the maximum number of items that can be removed from α for the resulting pattern to remain a τ-core pattern of α • For a (d,τ)-robust pattern α, it has core patterns • A colossal pattern tends to have a large number of core patterns • Pattern distance: For patterns α and β, the pattern distance of α and β is defined to be • If two patterns α and β are both core patterns of a same pattern, they would be bounded by a “ball” of a radius specified by their core ratio τ • Once we identify one core pattern, we will be able to find all the other core patterns by a bounding ball of radius r(τ) Ω(2d ) α β α β α β D D D D Dist ∪ ( , ) =1− ∩ Dist(α,β ) ≤1− 2 /τ 1 −1 = r(τ ) Robustness of Colossal Patterns翻译解释概念

这段文字主要在讨论关于频繁模式挖掘中的巨型模式的强健性和核心模式的概念。其中，作者引入了(d,τ)-robustness的概念，即如果从模式α中最多删除d个项，得到的模式仍然是α的τ-core模式，则称模式α是(d,τ)-robust的。对于(d,τ)-robust的模式，它们往往具有许多的核心模式。而巨型模式则往往具有更多的核心模式，这意味着它们更加强健和普适。此外，作者还提到了模式之间的距离概念，即用来衡量两个模式之间的相似度。如果两个模式都是同一个模式的核心模式，那么它们之间的距离可以用一个半径为r(τ)的球来界定。通过识别一个核心模式，可以通过半径为r(τ)的球找到所有其他核心模式。