Negative sequential patterns (NSPs) capture more informative and actionable knowledge than classic positive sequential patterns (PSPs) due to the involvement of both occurring and nonoccurring behaviors and events, which can contribute to many relevant applications. However, NSP mining is nontrivial, as it involves fundamental challenges requiring distinct theoretical foundations and is not directly addressable by PSP mining. In the very limited research reported on NSP mining, a negative element constraint (NEC) is incorporated to only consider the NSPs composed of specific forms of elements (containing either positive or negative items), which results in many valuable NSPs being missed. Here, we loosen the NEC (called loose negative element constraint (LNEC)) to include partial negative elements containing both positive and negative items, which enables the discovery of more flexible patterns but incorporates significant new learning challenges, such as representing and mining complete NSPs. Accordingly, we formalize the LNEC-based NSP mining problem and propose a novel vertical NSP mining framework , VM-NSP, to efficiently mine the complete set of NSPs by a vertical representation (VR) of each sequence. An efficient bitmap-based vertical NSP mining algorithm , bM-NSP, introduces a bitmap hash table--based VR and a prefix-based negative sequential candidate generation strategy to optimize the discovery performance. VM-NSP and its implementation bM-NSP form the first VR-based approach for complete NSP mining with LNEC. Theoretical analyses and experiments confirm the performance superiority of bM-NSP on synthetic and real-life datasets w.r.t. diverse data factors, which substantially expands existing NSP mining methods toward flexible NSP discovery.

中文翻译：

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虚拟机-NSP

由于涉及发生和未发生的行为和事件，负序列模式 (NSP) 比经典正序列模式 (PSP) 捕获更多信息和可操作的知识，这有助于许多相关应用。然而，NSP 挖掘并非微不足道，因为它涉及需要不同理论基础的基本挑战，并且 PSP 挖掘无法直接解决。在关于 NSP 挖掘的非常有限的研究中，引入了负元素约束 (NEC) 以仅考虑由特定形式的元素（包含正项或负项）组成的 NSP，这导致许多有价值的 NSP 被遗漏。在这里，我们放松了 NEC（称为松散的负元素约束(LNEC)) 包括包含正面和负面项目的部分负面元素，这使得发现更灵活的模式成为可能，但也包含了重要的新学习挑战，例如表示和挖掘完整的 NSP。因此，我们形式化了基于 LNEC 的 NSP 挖掘问题，并提出了一种新的垂直 NSP 挖掘框架，VM-NSP，通过每个序列的垂直表示（VR）有效地挖掘完整的 NSP 集。一个高效的基于位图的垂直NSP挖掘算法, bM-NSP, 引入了基于位图哈希表的 VR 和基于前缀的负序候选生成策略来优化发现性能。VM-NSP 及其实现 bM-NSP 形成了第一个基于 VR 的方法，用于使用 LNEC 进行完整的 NSP 挖掘。理论分析和实验证实了 bM-NSP 在合成数据集和真实数据集上具有不同数据因素的性能优势，这大大扩展了现有的 NSP 挖掘方法向灵活的 NSP 发现方向发展。