I. Introduction
Behavior permeates all aspects of our lives, and how to understand a behavior, especially the nonoccurring behaviors (NOBs), is a crucial issue in the behavior informatics [1]–[4]. Negative sequential pattern (NSP) mining is one of few methods available for understanding NOB [5]. NSPs refer to frequent sequences with NOB and occurring behaviors (also called negative and positive behaviors in behavior and sequence analysis). Sometimes, NSPs play an important role in many real-world applications, such as intrusion detection systems (IDS), intelligent transport systems (ITS), network, health, and medical management systems, biomedical systems, risk management, and counter terrorism. For instance, in IDS, is a positive sequential pattern (PSP); is an NSP, where , , and denote the alarm information codes indicating the alarms a network device has issued, and and denote the device status. indicates that devices which usually issue alarm information , , and then are likely to have anomaly status , whereas indicates that devices which issue alarms and but NOT have a high probability of having normal status . In ITS, negative driving behavior patterns result in drivers failing to follow certain traffic rules which could cause serious traffic problems or even disasters. These situations cannot be handled by the identification of PSP alone.