## 4 Experiments
### Experimental Results
#### 4.2.1 RQ1: Impacts on Convergence Speed and Recommendation Performance
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**MovieLens-100K**} & \multicolumn{3}{c}{**MovieLens-1M**} & \multicolumn{3}{c}{**Lastfm-2K**} & \multicolumn{3}{c}{**Foursquare**} \\ \cline{2-11}  & **Round** & **HR** & **NDCG** & **Round** & **HR** & **NDCG** & **Round** & **HR** & **NDCG** & **Round** & **HR** & **NDCG** \\ \hline PFedMF & 243 & **0.7243** & **0.4401** & 231 & **0.7339** & 0.4393 & 243 & 0.8196 & 0.7299 & 238 & 0.8609 & 0.7820 \\ PFedMF-I2 CG & **112** & 0.7211 & 0.4329 & **159** & 0.7305 & **0.4442** & **236** & **0.8540** & **0.7657** & **84** & **0.8613** & **0.7830** \\ \hline FedMF & 239 & 0.6522 & 0.3828 & 244 & **0.6816** & 0.4055 & 249 & **0.8181** & **0.6909** & 237 & 0.8261 & 0.6805 \\ FedMF-I2 CG & **136** & **0.6596** & **0.3959** & **151** & 0.6772 & **0.4072** & 93 & 0.8088 & **0.6861** & **190** & **0.8465** & **0.7269** \\ \hline PFedGMF & 198 & 0.6448 & 0.3573 & 225 & 0.6521 & 0.3741 & 112 & **0.7935** & 0.7155 & 237 & 0.8571 & 0.7783 \\ PGMF-I2 CG & **132** & **0.6670** & **0.4329** & **134** & **0.6647** & **0.3873** & **105** & 0.7893 & **0.7205** & **132** & **0.8587** & **0.7794** \\ \hline FedGMF & 245 & **0.6362** & **0.3595** & 236 & 0.6657 & 0.3963 & 249 & 0.7968 & 0.6290 & 238 & 0.8334 & 0.6896 \\ FedGMF-I2 CG & **115** & 0.6139 & 0.3578 & **143** & **0.6769** & **0.4037** & **217** & **0.7981** & **0.6715** & **103** & **0.8391** & **0.7034** \\ \hline PFedRECON & 247 & **0.7295** & 0.4355 & 297 & 0.7250 & 0.4366 & 198 & 0.8477 & 0.7524 & 166 & **0.8579** & **0.7719** \\ PFedRECON-I2 CG & **193** & 0.7158 & **0.4391** & **273** & **0.7360** & **0.4487** & **72** & **0.8477** & **0.7619** & **104** & 0.8492 & 0.7667 \\ \hline FedRECON & 247 & **0.6627** & **0.3892** & 282 & **0.6867** & 0.4097 & **104** & **0.8602** & **0.6997** & 202 & **0.8566** & **0.7662** \\ FedRECON-I2 CG & **242** & 0.6544 & 0.3867 & 202 & 0.6836 & **0.4128** & 110 & 0.8551 & 0.6932 & **129** & 0.8463 & 0.7517 \\ \hline PFedNCF & 246 & 0.6871 & 0.3977 & 299 & 0.6945 & 0.4008 & 239 & 0.8154 & 0.7422 & 247 & 0.8507 & 0.7700 \\ PFedNCF-I2 CG & **92** & **0.7190** & **0.4391** & **297** & **0.7275** & **0.4355** & **152** & **0.8446** & **0.7593** & **75** & **0.8575** & **0.7790** \\ \hline FedNCF & 243 & 0.6044 & 0.3430 & 287 & 0.6391 & 0.3689 & 227 & 0.7994 & 0.6499 & 242 & 0.8138 & 0.6704 \\ FedNCF-I2 CG & **200** & **0.6363** & **0.3755** & **267** & **0.6695** & **0.3963** & **110** & **0.8551** & **0.6932** & **187** & **0.8279** & **0.7204** \\ \hline PFedMLP & 249 & 0.6672 & 0.3849 & 249 & 0.6374 & 0.3622 & 233 & 0.6851 & **0.4806** & 234 & **0.7277** & 0.5130 \\ PFedMLP-I2 CG & **182** & **0.6713** & **0.4018** & **113** & **0.6401** & **0.3638** & **165** & **0.6866** & 0.4802 & **131** & 0.7260 & **0.5133** \\ \hline FedMLP & 234 & 0.6214 & 0.3697 & 189 & **0.6014** & 0.3471 & 245 & 0.6688 & 0.4787 & 196 & 0.7313 & 0.5142 \\ PFedMLP-I2 CG & **202** & **0.6214** & **0.3711** & **149** & 0.6011 & **0.3493** & **233** & **0.6799** & **0.4860** & **129** & **0.7325** & **0.5247** \\ \hline PFedMAvg & 177 & **0.7169** & **0.4258** & 289 & 0.7264 & 0.4438 & 197 & 0.8080 & 0.7165 & 199 & 0.8687 & **0.6891** \\ PFedMAvg-I2 CG & **47** & 0.7072 & 0.4210 & **245** & **0.7274** & **0.4451** & **98** & **0.8193** & **0.7235** & **101** & **0.8788** & 0.6750 \\ \hline FedMAvg & 150 & 0.6235 & **0.3790** & 238 & **0.6539** & 0.4039 & 173 & **0.7911** & **0.6994** & 249 & 0.8431 & 0.6761 \\ FedMAvg-I2 CG & **53** & **0.6373** & 0.3684 & **153** & 0.6523 & **0.4043** & **99** & 0.7900 & 0.6976 & **125** & **0.8473** & **0.6771** \\ \hline \hline \end{tabular}  
* We have highlighted the superior performance of the FRSs both before and after the implementation of the I2 CG strategy by applying bold formatting.  
\end{table} 
Table 4: Performance of FRSs with or without I2 CG. Evidently, as dataset sparsity increases, the impact of I2 CL in enhancing the model performance decreases.