Mining Colossal Frequent Patterns • F. Zhu, X. Yan, J. Han, P. S. Yu, and H. Cheng, “Mining Colossal Frequent Patterns by Core Pattern Fusion”, ICDE'07. • We have many algorithms, but can we mine large (i.e., colossal) patterns? ― such as just size around 50 to 100? Unfortunately, not! • Why not? ― the curse of “downward closure” (向下封闭) of frequent patterns • The “downward closure” property • Any sub-pattern of a frequent pattern is frequent. • Example. If (a1, a2, …, a100) is frequent, then a1, a2, …, a100, (a1, a2), (a1, a3), …, (a1, a100), (a1, a2, a3), … are all frequent! There are about 2100 such frequent itemsets! • No matter using breadth-first search (e.g., Apriori) or depth-first search (FPgrowth), we have to examine so many patterns • Thus the downward closure property leads to explosion!翻译成中文，解释

《挖掘巨大频繁模式：核心模式融合》一文中提到，我们有很多算法可以挖掘频繁模式，但是我们能否挖掘大型的（即巨大的）模式，例如大小在50到100之间的模式呢？不幸的是，我们不能！为什么不行呢？因为频繁模式的“向下封闭性”导致了这个问题。向下封闭性是指，任何频繁模式的子模式都是频繁的。例如，如果(a1，a2，…，a100)是频繁的，那么a1，a2，…，a100，(a1，a2)，(a1，a3)，…，(a1，a100)，(a1，a2，a3)，…等都是频繁的！这样的频繁项集大约有2100个！不管是使用广度优先搜索（例如Apriori）还是深度优先搜索（FPgrowth），我们都必须检查这么多的模式。因此，向下封闭性导致了模式爆炸的问题。