Negative sequence analysis (NSA)  refers to the analysis and discovery of important yet negative (including nonoccurring, unobserved, hidden or inaction) sequential entities, events, behaviors, or situations that are associated with each other and with positive (occurring, observed) ones. NSA is a useful method for non-occurring behavior analysis .
A typical research topic is to discover negative sequential patterns (NSP) , which involves negation and negative couplings (negative dependency , negative correlation, etc.) between the entities, events, behaviors or situations. NSP mining [1,3] is to discover frequent interesting patterns consisting of negative elements and subsequences. Arguably, NSPs are usually more informative and useful than positive sequential patterns (PSPs) as they can disclose non-occurring but important behaviors. NSA and NSP mining involve critical challenges, including modeling negation and negative elements with diverse formats and combinations; negative patterns mixed with negative items and elements in sophisticated combinations; various negative containment scenarios; and different couplings between negative and positive items, elements, and patterns; a large search space; and high computational cost.
Typical research topics in NSA and NSP mining include but are not limited to:
- Element/Pattern relation analysis: Analyze the couplings including dependency, correlation, association, and implicit relations between elements and between patterns for NSA and NSP mining, and discovering impact-targeted, impact-reversed, impact-contrasted patterns, pair patterns, cluster patterns, implicit rules; e.g., [11-14,21];
- Frequentist-based NSP mining: Frequentist theories and downward closure (Apriori) property are the foundation of such methods, frequency-based statistics including support and confidence of negative candidates and NSPs are calculated for their search and sequence/subset selection to obtain frequent NSPs, e.g., [5-11];
- Set theory-based NSP learning: The set theory is used to represent PSP and NSP relations, the negative sequence containment problem is converted to PSP and then conduct PSP-based NSA, e.g., [3,17-20];
- Approximate NSP mining: Approximation methods like genetic algorithms, sampling, inference, and fuzzy set are used to approximate and select NSPs, e.g. ;
- Impact-targeted NSP mining: Discover NSP leading to impact (e.g., debt, fraud) [7,10]
- Representation-based NSP mining: Build representation of negative elements, sequences and candidates and then discover NSPs from the representations, e.g., vertical representations  and graph representation ;
- Interactions with negative feedbacks: Model sequential interactions with negative feedback (non-occurring or missing ations or unselections) 
- Actionable NSP mining: It is to discover actionable NSPs that are representative, highly probable and diverse to represent the whole original NSP collection, but not redundant and similar, and are discriminative and informative for suggesting decision-making actions, e.g., [10,11,21];
- High-utility NSP mining: It is to evaluate and select NSPs per the utility of NSPs by measuring item utility, element utility, sequence utility, and database utility, etc.
- Other topics: Including top-k NSP mining, constraint-based NSP mining, graph-based NSP mining , network-based NSA, etc.
 Wei Wang and Longbing Cao. Negative Sequence Analysis: A Review and the Supplementary, ACM Computing Surveys, 52(2): 32:1-32:39 (2019). BibTeX.
 Longbing Cao, Philip S. Yu, Vipin Kumar. Nonoccurring Behavior Analytics: A New Area. IEEE Intelligent Systems 30(6): 4-11 (2015). BibTeX.
 Longbing Cao, Xiangjun Dong and Zhigang Zheng. e-NSP: Efficient Negative Sequential Pattern Mining, Artificial Intelligence, 235: 156-182, http://dx.doi.org/10.1016/j.artint.2016.03.001, 2016. Download e-NSP codes and example; Download NegSeq codes and example BibTeX.
 J. Borcea, P. Br¨and´en, and T. Liggett, “Negative dependence and the geometry of polynomials,” Journal of the American Mathematical Society, vol. 22, no. 2, pp. 521–567, 2009.
 Zhigang Zheng, Yanchang Zhao, Ziye Zuo, Longbing Cao. Negative-GSP: An Efficient Method for Mining Negative Sequential Patterns, AusDM 2009: 63-67. BibTeX.
 Yanchang Zhao, Huaifeng Zhang, Shanshan Wu, Jian Pei,Longbing Cao, Chengqi Zhang and Hans Bohlscheid. Debt Detection in Social Security by Sequence Classification Using Both Positive and Negative Patterns, ECML/PKDD2009, 648-663, 2009. BibTeX.
 Yanchang Zhao, Huaifeng Zhang, Longbing Cao, Chengqi Zhang and Hans Bohlscheid. Mining Both Positive and Negative Impact-Oriented Sequential Rules From Transactional Data, PAKDD2009, pp.656-663. BibTeX.
 Zhigang Zheng, Wei Wei, Chunming Liu, Wei Cao, Longbing Cao, Maninder Bhatia. An effective contrast sequential pattern mining approach to taxpayer behavior analysis, World Wide Web 19(4): 633-651 (2016). BibTeX.
 N. P. Lin, H.-J. Chen, and W.-H. Hao, “Mining negative sequential patterns,” in ICACS’2007, 2007, pp. 654–658.
 Longbing Cao. Zhao Y., Zhang, C. Mining Impact-Targeted Activity Patterns in Imbalanced Data, IEEE Trans. on Knowledge and Data Engineering, 20(8): 1053-1066, 2008. BibTeX.
 Longbing Cao. Combined Mining: Analyzing Object and Pattern Relations for Discovering and Constructing Complex but Actionable Patterns, WIREs Data Mining and Knowledge Discovery, 3(2): 140-155, 2013. BibTeX.
 Longbing Cao. Coupling Learning of Complex Interactions, Journal of Information Processing and Management, 51(2): 167-186 (2015). BibTeX.
 Longbing Cao, Yuming Ou, Philip S Yu. Coupled Behavior Analysis with Applications (KDD2010 extension), IEEE Trans. on Knowledge and Data Engineering, 24(8): 1378-1392 (2012). BibTeX.
 Shoujin Wang, Longbing Cao. Inferring Implicit Rules by Learning Explicit and Hidden Item Dependency. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(3): 935-946, 2020.
 Zhigang Zheng, Yanchang Zhao, Ziye ZuoLongbing Cao, Huaifeng Zhang, Yanchang Zhao, Chengqi Zhang. An Efficient GA-Based Algorithm for Mining Negative Sequential Patterns, PAKDD2010, 262-273. BibTeX.
 T. Guyet and R. Quiniou, “Negpspan: Efficient extraction of negative sequential patterns with embedding constraints,” Data Min. Knowl. Discov., vol. 34, no. 2, pp. 563–609, 2020.
 Xiangjun Dong, Yongshun Gong and Longbing Cao. F-NSP+: A fast negative sequential patterns mining method with self-adaptive data storage, Pattern Recognition, 2018. BibTeX.
 Xiangjun Dong, Ping Qiu, Jinhu Lü, Longbing Cao, Tiantian Xu. Mining Top-k Useful Negative Sequential Patterns via Learning, IEEE Trans. Neural Netw. Learning Syst. 30(9): 2764-2778 (2019). BibTeX.
 Xiangjun Dong, Yongshun Gong, Longbing Cao. e-RNSP: An Efficient Method for Mining Repetition Negative Sequential Patterns, IEEE Trans. Cybern. 50(5): 2084-2096, 2020.
 Xiangjun Dong, Zhigang Zhao, Longbing Cao, Yanchang Zhao, Chengqi Zhang, Jinjiu Li, Wei Wei, Yuming Ou. e-NSP: Efficient Negative Sequential Pattern Mining Based on Identified Positive Patterns Without Database Rescanning, CIKM 2011, 825-830. BibTeX.
 Wei Wang and Longbing Cao. Explicit and Implicit Pattern Relation Analysis for Discovering Actionable Negative Sequences, IEEE Trans Neural Netw Learn Syst., 1 – 15, 2022.
 Wei Wang and Longbing Cao. Interactive Sequential Basket Recommendation by Learning Basket Couplings and Positive/Negative Feedback, ACM Transactions on Information Systems, 39(3): 1-26, 2021. BibTeX
 Wei Wang and Longbing Cao. VM-NSP: Vertical Negative Sequential Pattern Mining with Loose Negative Element Constraints, ACM Transactions on Information Systems, 39(2): 1-27, 2021. BibTeX
 Ping Qiu, Yongshun Gong, Yuhai Zhao, Longbing Cao, Chengqi Zhang, Xiangjun Dong. An Efficient Method for Modeling Nonoccurring Behaviors by Negative Sequential Patterns With Loose Constraints, IEEE Trans Neural Netw Learn Syst, 10.1109/TNNLS.2021.3063162, 2021