  Mining frequent sequential patterns consists in extracting recurrent
behaviors, modeled as patterns, in a big sequence dataset. Such patterns inform
about which events are frequently observed in sequences, i.e. what does really
happen. Sometimes, knowing that some specific event does not happen is more
informative than extracting a lot of observed events. Negative sequential
patterns (NSP) formulate recurrent behaviors by patterns containing both
observed events and absent events. Few approaches have been proposed to mine
such NSPs. In addition, the syntax and semantics of NSPs differ in the
different methods which makes it difficult to compare them. This article
provides a unified framework for the formulation of the syntax and the
semantics of NSPs. Then, we introduce a new algorithm, NegPSpan, that extracts
NSPs using a PrefixSpan depth-first scheme and enabling maxgap constraints that
other approaches do not take into account. The formal framework allows for
highlighting the differences between the proposed approach wrt to the methods
from the literature, especially wrt the state of the art approach eNSP.
Intensive experiments on synthetic and real datasets show that NegPSpan can
extract meaningful NSPs and that it can process bigger datasets than eNSP
thanks to significantly lower memory requirements and better computation times.
