  High utility sequential pattern mining (HUSPM) is a significant and valuable
activity in knowledge discovery and data analytics with many real-world
applications. In some cases, HUSPM can not provide an excellent measure to
predict what will happen. High utility sequential rule mining (HUSRM) discovers
high utility and high confidence sequential rules, allowing it to solve the
problem in HUSPM. All existing HUSRM algorithms aim to find high-utility
partially-ordered sequential rules (HUSRs), which are not consistent with
reality and may generate fake HUSRs. Therefore, in this paper, we formulate the
problem of high utility totally-ordered sequential rule mining and propose two
novel algorithms, called TotalSR and TotalSR+, which aim to identify all high
utility totally-ordered sequential rules (HTSRs). TotalSR creates a utility
table that can efficiently calculate antecedent support and a utility prefix
sum list that can compute the remaining utility in O(1) time for a sequence. We
also introduce a left-first expansion strategy that can utilize the
anti-monotonic property to use a confidence pruning strategy. TotalSR can also
drastically reduce the search space with the help of utility upper bounds
pruning strategies, avoiding much more meaningless computation. In addition,
TotalSR+ uses an auxiliary antecedent record table to more efficiently discover
HTSRs. Finally, there are numerous experimental results on both real and
synthetic datasets demonstrating that TotalSR is significantly more efficient
than algorithms with fewer pruning strategies, and TotalSR+ is significantly
more efficient than TotalSR in terms of running time and scalability.
