Semantics of negative sequential patterns

In the field of pattern mining, a negative sequential pattern is specified by means of a sequence consisting of events to occur and of other events, called negative events, to be absent. For instance, containment of the pattern $\langle a\ \neg b\ c\rangle$ arises with an occurrence of a and a subsequent occurrence of c but no occurrence of b in between. This article is to shed light on the ambiguity of such a seemingly intuitive notation and we identify eight possible semantics for the containment relation between a pattern and a sequence. These semantics are illustrated and formally studied, in particular we propose dominance and equivalence relations between them. Also we prove that support is anti-monotonic for some of these semantics. Some of the results are discussed with the aim of developing algorithms to extract efficiently frequent negative patterns.

[1]  David Pearce,et al.  Stable reasoning , 2017, J. Appl. Non Class. Logics.

[2]  Ramakrishnan Srikant,et al.  Fast Algorithms for Mining Association Rules in Large Databases , 1994, VLDB.

[3]  Ming-Yen Lin,et al.  Mining Negative Sequential Patterns for E-commerce Recommendations , 2008, 2008 IEEE Asia-Pacific Services Computing Conference.

[4]  Giuseppe De Giacomo,et al.  Linear Temporal Logic and Linear Dynamic Logic on Finite Traces , 2013, IJCAI.

[5]  Longbing Cao,et al.  e-NSP: Efficient negative sequential pattern mining , 2016, Artif. Intell..

[6]  John F. Roddick,et al.  Sequential pattern mining -- approaches and algorithms , 2013, CSUR.

[7]  Ming-Tat Ko,et al.  Discovering time-interval sequential patterns in sequence databases , 2003, Expert Syst. Appl..

[8]  Yongshun Gong,et al.  e-NSPFI: Efficient Mining Negative Sequential Pattern from Both Frequent and Infrequent Positive Sequential Patterns , 2017, Int. J. Pattern Recognit. Artif. Intell..

[9]  Philip S. Yu,et al.  Nonoccurring Behavior Analytics: A New Area , 2015, IEEE Intelligent Systems.

[10]  Thomas Guyet,et al.  NegPSpan: efficient extraction of negative sequential patterns with embedding constraints , 2018, Data Mining and Knowledge Discovery.

[11]  Longbing Cao,et al.  Negative Sequence Analysis , 2019, ACM Comput. Surv..

[12]  Heikki Mannila,et al.  A database perspective on knowledge discovery , 1996, CACM.

[13]  Jianliang Xu,et al.  E-msNSP: Efficient Negative Sequential Patterns Mining Based on Multiple Minimum Supports , 2017, Int. J. Pattern Recognit. Artif. Intell..