## 6 Conclusions and Future Work  
Several top-K frequent regular pattern mining methods are introduced using a support threshold defined by users to determine the number of topmost frequent regular patterns. The top-K frequent regular patterns maintain the top-K list to record the topmost-K frequent regular patterns in descending support order during exploration of a search space. The top-K frequent regular patterns classically perform breadth-first traversal of the search space to generate the required patterns. In top-K frequent regular pattern mining, different support calculation procedures are adopted. However, the available methods have the following limitations: (1) top-K frequent regular pattern mining methods adopt a best-fit strategy for the patterns, perform excessive candidate pattern generation which is inessential for computing, and use no pruning methods to prune the unnecessary candidates before counting the support of the frequent regular itemsets, and (2) top-K frequent regular patterns are applied on offline-datasets, which are not feasible for the online datasets, which continuously remain in the updating stage.  
This paper has presented a novel top-K identical frequent regular pattern mining (TKIFRPM) method producing top-K identical frequent regular patterns from the online transactional and incremental datasets. The TKIFRPM maintains a novel performance-wise effective data structure with item support index tables (ISI-tables) to keep summarized information about the updated datasets. The mining operation can be launched at any time interval to discover top-K regular frequent patterns from the ISI-tables at any instant of time. The TKIFRPM explores the search space (arranged in an itemset enumeration tree) in recursive depth-first order. The TKIFRPM applies a novel progressive node's sub-tree pruning strategy to rapidly eliminate a complete infrequent sub-tree from the search space. Hence, the TKIFRPM is computationally efficient compared to the best-fit methods of top-K frequent regular pattern mining, since TKIFRPM does not perform support checking on the nodes of the infrequent subtrees, unlike other top-K frequent regular pattern mining methods. The experimental results have shown that the TKIFRPM method performs better than its counterpart methods (e.g., MTKPP) on the datasets following incremental updates.  
In the future, we expect to provide detailed comparisons of the proposed TKIFRPM method with other top-K frequent regular pattern mining methods (i.e., TR-CT, TKRIMPE, TFRC, etc.) using available large-sized online datasets to derive more accurate and widely acceptable results.  
Methodology, S.U.R.; Software, M.A.K., H.U.N. and S.A.; Validation, S.U.R. and M.A.K.; Investigation, S.U.R., H.U.N., S.A. and N.A.; Resources, N.A. and S.K.; Writing--original draft, S.U.R. and N.A.; Writing--review & editing, S.K.; Supervision, S.K.; Project administration, S.K.; Funding acquisition, N.A. All authors have read and agreed to the published version of the manuscript.  
This research has received no external funding.  
Not applicable.  
No new data were created.  
The authors of this paper would like to offer thanks for the research facilities provided by the Huaiyin Institute of Technology, China.  
The authors declare no conflict of interest.