## 5 Discussion and Conclusions  
In this paper, we proposed an improvement to the ACF algorithm [1] to better deal with the sparsity problem by introducing an initial clustering phase on the users according to their preferences represented by pheromones, of which there are far fewer compared to the number of users. The experiments on several larger datasets, including Movielens 10M, Douban book, and NetEase music datasets, demonstrate its excellence over the ACF algorithm in both scenarios, i.e., the rating-based recommendation and the ranking-based recommendation.  
As mentioned earlier, K-means was used for clustering implementation because it is more appropriate for our dataset. However, a typical issue for K-means is the determination of the parameter K, i.e., the number of clusters. We empirically determined the number of \(K\) in our experiments. This could be studied further.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Algorithm** & **Precision** & **Recall** & **F1** & **Time (s)** & \(p\)**-Value** \\ \hline \multirow{6}{*}{Douban} & User-based & 0.45 & 0.67 & 0.538 & 289.3 \\  & Item-based & 0.33 & 0.73 & 0.455 & 2212.6 \\  & NBI & 0.09 & 0.84 & 0.163 & 5314.0 \\  & RSM & 0.29 & 0.78 & 0.423 & 2350 \\  & BM25-Item & 0.08 & 0.89 & 0.147 & 2010.0 \\ \cline{2-6}  & ACF & 0.57 & 0.61 & 0.589 & 913.1 \\  & IACF & 0.70 & 0.50 & 0.583 & 290.4 \\ \hline \multirow{6}{*}{NetEase} & User-based & 0.50 & 0.71 & 0.587 & 901.4 \\  & Item-based & 0.40 & 0.78 & 0.529 & 1024.3 \\ \cline{1-1}  & NBI & 0.03 & 0.90 & 0.058 & 3121.2 \\ \cline{1-1}  & RSM & 0.49 & 0.71 & 0.579 & 802.1 \\ \cline{1-1}  & BM25-Item & 0.28 & 0.81 & 0.416 & 3223.1 \\ \cline{1-1} \cline{2-6}  & ACF & 0.76 & 0.36 & 0.489 & 728.3 \\ \cline{1-1}  & IACF & 0.81 & 0.30 & 0.438 & 413.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Ranking results comparison.  
**Author Contributions:** Conceptualization, X.L. ([PERSON]); Formal analysis, X.L. ([PERSON]); Funding acquisition, X.L. ([PERSON]); Investigation, X.L. ([PERSON]); Methodology, X.L. ([PERSON]); Resources, Q.X.; Software, H.W.; Supervision, Y.W.; Validation, X.L. ([PERSON]); Writing--original draft, X.L. ([PERSON]); Writing--review and editing, X.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China grant number 61762062 and 61862042, Science and Technology Innovation Platform Project of Jiangxi Province under grant number 20181 BCD40005, Major Discipline Academic and Technical Leader Training Plan Project of Jiangxi Province under grant number 20172 BCB22030, Primary Research & Development Plan of Jiangxi Province under grant number 20192 BBE50075 and 20181 ACE50033, and Jiangxi Province Natural Science Foundation of China under grant number 20192 BAB207019.  
**Acknowledgments:** The authors thank the anonymous reviewers for their helpful comments.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.