## 6 Conclusions  
This study presented a comparative analysis of the Apriori and FP-Growth algorithms for association rule mining using an e-commerce transactional dataset. The algorithms were implemented using RapidMiner and evaluated through a series of experiments under varying support and confidence thresholds. Statistical analyses, including ANOVA, Kruskal-Wallis, Pearson's correlation, and linear regression analyses, were performed using SPSS to assess algorithm performance and distributional behavior.  
The results highlight the superior efficiency and scalability of FP-Growth, particularly at lower support thresholds. Its compact FP-tree structure and recursive pattern mining strategy allow it to outperform Apriori in execution time and rule generation capacity. Apriori, while conceptually simpler and suitable for smaller datasets, demonstrated a noticeable decline in performance as support thresholds increased.  
Key findings include the following:  
* FP-Growth consistently generated more frequent itemsets and executed significantly faster than Apriori, especially for larger search spaces.
* Apriori's performance degraded more rapidly with increasing support thresholds, as confirmed by the Kruskal-Wallis test.
* A strong positive correlation (r \(\approx\) 0.97) was observed between the output values of the two algorithms, with linear regression indicating that FP-Growth results can be estimated from the Apriori outputs under controlled conditions.  
These insights provide practitioners with a clear understanding of when to use each algorithm based on the dataset size, desired rule complexity, and computational constraints.  
Although this study provides valuable insights into the comparative behaviors of Apriori and FP-Growth, several directions remain open for further investigation:  
* Scalability in big data environments--future work could explore the performance on distributed systems using frameworks such as Apache Spark, where FP-Growth is natively supported and optimized.
* Hybrid approaches--combining Apriori's interpretability with FP-Growth's performance may yield hybrid methods that balance transparency and speed.
* Real-time mining--investigating the feasibility of applying FP-Growth to streaming data environments would be beneficial for dynamic recommendation systems in e-commerce.
* Extension to multi-level and temporal rules--enriching the rule-mining process by incorporating hierarchical product structures or temporal sequencing of transactions could lead to more meaningful insights.
* Cross-domain validation--applying these methods to domains beyond e-commerce (e.g., cybersecurity, healthcare, and finance) would help generalize the findings and refine best practices for association rule mining.  
Conceptualization, I.D.H. and N.C.; Methodology, O.-A.T.; Software, I.D.H.; Validation, N.C. and O.-A.T.; Formal analysis, N.C. and O.-A.T.; Resources, O.-A.T.; Data curation, N.C. and O.-A.T.; Writing--original draft, I.D.H.; Funding acquisition, I.D.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Lucian Blaga University of Sibiu through the research grant LBUS-IRG-2023.  
Not applicable.  
The data presented in this study are available in article.  
The authors declare no conflicts of interest.