Frequent tree mining asks us to enumerate tree patterns that occur frequently in a database of rooted trees. This problem is motivated by tree-structured data in bioinformatics, such as glycans and pseudoknot-free RNA secondary structures. A direct enumeration of all frequent trees is often highly redundant, because every subtree of a frequent tree is again frequent. Closed and maximal frequent trees are standard ways to reduce this redundancy, but their enumeration can still be computationally hard.
In this paper, we study the effect of bounding the height of the input trees. This is a natural restriction for rooted trees, since the height is the depth of the hierarchy. We ask whether closed/maximal frequent tree mining remains hard when every input tree has a small height. Our results show that the answer depends sharply on the model. For rooted unordered trees of height at most 2, we give a polynomial-delay algorithm for enumerating closed frequent trees. On the other hand, for rooted ordered trees of height at most 2, we show that an output-polynomial time algorithm for enumerating closed frequent trees would imply an output-polynomial time algorithm for Dualization. For maximal frequent tree enumeration, we prove that no output-polynomial time algorithm exists unless P = NP already for rooted ordered trees of height at most 2 and for rooted unordered trees of height at most 3.
Thus, even very small height bounds do not make the enumeration problems easy in general. At the same time, the unordered closed case of height at most 2 admits polynomial-delay enumeration. These results give a height-based classification of the complexity of closed and maximal frequent tree mining on shallow rooted trees.
Ramp: Fast Frequent Itemset Mining with Efficient Bit-Vector Projection Technique
National University of Computer and Emerging Sciences（国家计算机与新兴科学大学）
基于位向量表示的频繁项集挖掘方法对于密集数据集是非常有效的，但对于稀疏数据集，由于缺乏有效的位向量投影技术，挖掘效率很低。在本文中，我们提出了一种新的有效的位向量投影技术，稀疏和密集的数据集。为了检验我们的位向量投影技术的效率，我们提出了一个新的频繁项集挖掘算法Ramp（Real Algorithm for Mining Patterns）。在基准数据集上将Ramp算法与目前最好的频繁项集挖掘算法（全频繁项集、最大频繁项集和闭频繁项集）进行了性能比较。在稀疏数据集和密集数据集上的不同实验结果表明，使用Ramp挖掘频繁项集的速度比目前最好的算法都要快，这表明了位向量投影思想的有效性。我们还提出了一个新的本地最大频繁项集传播和最大项集超集检查方法FastLMFI，建立在我们的PBR位向量投影技术。我们不同的计算实验表明，使用FastLMFI的项集最大值检查是快速和有效的比以前将已知的渐进聚焦方法。
频繁项集挖掘是数据采掘中的一个基本问题，在关联分析、分类等数据采掘任务中发挥着重要作用。然而，在一些应用中，例如推荐系统和社交网络，人们更感兴趣的是找出数据库中与某些用户指定的项集（查询项集）一起出现最频繁的项。在本文中，我们解决这个问题，提出了一个新的挖掘任务命名为top-k共现项目挖掘，其中k是所需的项目数被发现。然后，我们引入了一种特殊的数据结构Pi-Tree（Prefix itemset Tree）来维护项目集的信息。基于Pi-Tree，提出了两种挖掘top-k共现项的算法：PT（Pi-Tree-based algorithm）和PT-TA（Pi-Tree-based algorithm with TA pruning），并结合了几种新的搜索空间修剪策略以提高挖掘效率。PT和PT-TA的性能进行了评估，对四个建议的基线算法在合成和真实的数据库。大量的实验表明，PT不仅在执行时间上大大优于其他算法，而且具有良好的可扩展性。
