Table 3 Performance assessment of recommendation approaches constructed with the Fed-FR-MVD framework in the absence of noise and under varying noise levels with and without FR.

	Precision@10	Recall@10	HR@10	NDCG@10	F1@10	MRR@10	Coverage@10	AUC
Normal	0.460	0.365	0.555	0.605	0.410	0.460	0.750	0.800
5%	0.450	0.355	0.545	0.595	0.400	0.450	0.740	0.790
10%	0.440	0.345	0.535	0.585	0.390	0.440	0.730	0.780
15%	0.430	0.335	0.525	0.575	0.380	0.430	0.720	0.770
RFR 5%	0.435	0.345	0.535	0.585	0.385	0.435	0.730	0.780
RFR 10%	0.420	0.330	0.520	0.570	0.370	0.420	0.715	0.765
RFR 15%	0.400	0.315	0.505	0.555	0.355	0.405	0.700	0.750

This table highlights the exceptional performance of the Fed-FR-MVD framework across a range of metrics, including Precision@10, Recall@10, HR@10, NDCG@10, F1-Score@10, MRR@10, Coverage@10, and AUC@10. The reported values—0.460, 0.365, 0.555, 0.605, 0.410, 0.460, 0.750, and 0.800—illustrate the model’s effectiveness in delivering high-quality recommendations. This assessment serves to establish a baseline for comparison with future evaluations under varying conditions, underscoring the framework’s reliability and robustness when noise is not a factor.

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