# Session-Based Recommendations for e-Commerce with Graph-Based Data Modeling
## 6 Conclusions  
We have presented two graph-based methods for session-based recommendations in a generic e-commerce environment without employing user history, i.e., suitable for anonymous browsing. The methods are called Hierarchical Sequence Probability (HSP) and Recurrent Item Co-occurrence (RIC). HSP is based on the statistics of the _Next_ relationship between items computing the probabilities of triplets, pairs and single items, which are then used--in that order--to determine the position of each item in the recommendation list. The RIC method is primarily based on the _InSameSession_ relationship, which determines the co-occurrence of pairs of items in the same session. We introduce memory to RIC by incorporating a simple recurrent formula to determine the weight of each item which is subsequently used to place the item in its proper position in the recommendation list. Setting the value of the forgetting factor of this recurrent formula allows us to balance the effect on our current decision of previously visited items in the session.  
Both proposed methods have been compared to state-of-the-art Graph Neural Network models. Our experiments, which involve four diverse datasets, show that RIC can outperform the GNN models in two cases and achieve a performance quite close to that of the winner model in the other two. The HSP approach is typically inferior to RIC, indicating that the _Next_ relationship is not so important compared to the _InSameSession_ relationship when building the recommendation list.  
Additionally, both HSP and RIC methods are very fast compared to the GNN models. This happens despite the fact that the execution time of the GNN models is reduced thanks to the presence of a GPU accelerator, whereas the times recorded for our models are measured on a simple CPU-based machine.  
In future work, we plan to investigate the improvement of the RIC method by automatically determining the optimal parameter \(\alpha\) and also to determine whether the current item should be first or last in the recommendation list. Another important aspect of the algorithm which is worth investigating is the graph update as new data are collected in such a way that the computational cost of updating the new confidence vectors, cold-start probabilities and weight vectors is minimized.  
Figure 4: The execution time in minutes for all methods and each dataset. Our proposed methods are between \(10\times\) and \(180\times\) times faster than GNN models.  
**Author Contributions:** Conceptualization, M.D. and K.D.; methodology, M.D. and K.D.; software, K.D.; validation, M.D. and K.D.; formal analysis, M.D. and K.D.; investigation, M.D. and K.D.; resources, D.T. and M.S.; data curation, D.T., M.D., K.D. and M.S.; writing--original draft preparation, M.D. and K.D.; writing--review and editing, K.D., M.D. and M.S.; visualization, K.D.; supervision, K.D.; project administration, K.D. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by RESEARCH-CREATE-INNOVATE call (project code: T1 EDK-01776).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data for this study are available on request from the corresponding authors.  
**Acknowledgments:** This research has been co-financed by the European Regional Development Fund of the European Union and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the call RESEARCH-CREATE-INNOVATE (project code:T1 EDK-01776).  
**Conflicts of Interest:** The authors declare no conflict of interest.