Abstract: To address the key challenges faced by existing graph neural network (GNN) based multi‑criteria recommendation algorithms under data‑sparse conditions—namely the long‑tail effect, the difficulty in synergistically integrating graph attention networks (GAT) and graph convolutional networks (GCN) , and the ambiguous discrimination between positive and negative samples caused by the difficulty of contrastive learning anchor selection in multi‑criteria rating scenarios—this paper proposes a multi‑criteria recommendation algorithm that fuses noisy graph neural networks with contrastive learning, termed NGCLR. The research objective is to systematically mitigate node embedding degradation, enhance cross‑criteria representation consistency, and optimize contrastive learning effectiveness by introducing dynamic noise augmentation, a progressive fusion mechanism, and a neighbor‑similarity‑based anchor selection strategy, thereby significantly improving the rating prediction accuracy and generalization capability of multi‑criteria recommender systems in sparse interaction environments. On the technical implementation side, the model first constructs a user item bipartite graph for each evaluation criterion independently and normalizes the adjacency relationships using a layer wise trained bipartite graph neural network matrix, so as to preserve the independent rating distribution characteristics of each criterion. To tackle the degradation phenomenon where long tail items' embeddings converge towards head items due to sparse neighborhoods, a Gaussian noise enhanced LightGCN module is designed: during each layer of graph convolution propagation, dynamic Gaussian noise with an initial intensity of 0.2 and an exponential decay rate of 0.5 per training epoch is injected into the current layer's node embeddings. This perturbation does not alter the graph topology but acts solely on the feature space, thereby breaking feature homogenization and encouraging a more uniform embedding distribution for long tail items. To fuse the complementary advantages of graph attention networks in capturing fine grained local interactions and graph convolutional networks in perceiving global structural patterns, a progressive fusion mechanism is proposed. At each propagation layer, the multi head attention outputs from GAT and the neighborhood aggregation outputs from LightGCN are concatenated, and a learnable parameter adaptively controls the contribution of each layer, achieving hierarchical fusion from low level local details to high level global semantics. To overcome the difficulty of reliably selecting contrastive learning anchors caused by the inconsistency between rating criteria and samples in multi criteria data, an anchor selection strategy based on average neighbor cosine similarity is designed: within each criterion view, the average similarity between each node's embedding and those of all its neighbors is computed, and the node with the highest similarity is selected as the anchor for that view, serving as a stable contrastive benchmark. On this basis, a dual contrastive learning task is constructed—the local contrastive loss maximizes the consistency of positive sample embeddings of the same node across different criteria while pushing away negative samples, and the global contrastive loss enhances cross criterion alignment among global embeddings (node means) of each criterion. These two losses are jointly optimized, and the total loss function combines the local loss, global loss, and an L₂ regularization term, balancing node level discriminability and distribution level consistency. To validate the model's effectiveness, experiments are conducted on three publicly available real‑world datasets: Yahoo!Movies, BeerAdvocate, and TripAdvisor. Yahoo!Movies contains 6,078 users, 976 movies, and 758,405 four‑criterion ratings; BeerAdvocate comprises 8,831 users, 2,698 beers, and 3,880,359 four‑criterion ratings; TripAdvisor includes 15,000 users, 1,325 hotels, and 20,830 seven‑criterion ratings, with a high sparsity level. Using mean absolute error and root mean square error as evaluation metrics, the proposed NGCLR is compared against more than ten baseline methods, including BMF, MSVD, MLR, SVR, CIC, DMCF, CFM, DNN‑MF, MCAE‑FADNN, and the best‑performing baseline D‑MGAC. Experimental results show that NGCLR achieves MAE and RMSE of 0.6028 and 0.8211 on Yahoo!Movies, corresponding to relative reductions of 2.94% and 3.79% over D‑MGAC; on BeerAdvocate, the values are 0.3931 and 0.5380, with relative reductions of 4.93% and 2.73%; and on TripAdvisor, they are 0.7338 and 0.9724, with relative reductions of 2.04% and 1.96%. Ablation studies demonstrate that removing the noise augmentation module, the progressive fusion mechanism, or the contrastive learning module leads to varying degrees of increase in both MAE and RMSE. In particular, the variant adopting a random anchor selection strategy yields MAE values that are 2.86%, 2.21%, and 0.69% higher than the full model on the three datasets, respectively, confirming the independent contributions and synergistic gains of each core component. Hyperparameter analysis indicates that the optimal performance is achieved with an embedding dimension of 256, 8 attention heads, and equal weights of 0.5 for both local and global contrastive losses; the dynamic decay noise strategy outperforms fixed‑noise and standard‑adaptive‑noise strategies, and the neighbor‑similarity‑based anchor selection surpasses both global‑average‑similarity and PageRank‑based strategies. Head‑vs‑tail group experiments show that the model achieves significantly greater MAE improvements on tail item groups than on head groups, and noise enhancement visualization further confirms that the embedding distribution of long‑tail items shifts from clustering towards dispersion. In summary, NGCLR effectively addresses the three major challenges in multi‑criteria recommendation—long‑tail degradation, insufficient fusion of graph modules, and anchor bias in contrastive learning—achieving consistently superior prediction accuracy across multiple real datasets, and thus provides an efficient and robust solution for multi‑criteria recommender systems.

摘要： 针对现有基于图神经网络（GNN）的多标准推荐算法在数据稀疏环境下存在的长尾效应、图注意力网络（GAT）与图卷积网络（GCN）模块间难以协同融合，以及多标准评分场景中对比学习锚点选取困难导致正负样本区分模糊等关键问题，提出一种融合噪声图神经网络与对比学习的多标准推荐算法（NGCLR）。研究目的在于通过引入动态噪声增强、渐进融合机制和基于邻居相似性的锚点选择策略，系统性缓解节点嵌入退化、提升跨标准表征一致性并优化对比学习效果，从而显著提高多标准推荐系统在稀疏交互场景下的评分预测精度与泛化能力。 在技术实现层面，模型首先为每个评价标准分别构建用户-项目多边二分图，并采用逐层训练的二分图神经网络矩阵对邻接关系进行归一化，以保留各标准独立的评分分布特征。针对长尾项目因邻域稀疏导致嵌入向头部项目收敛的退化现象，设计基于高斯噪声增强的LightGCN模块：在每一层图卷积传播过程中，向当前层节点嵌入施加初始强度为0.2、随训练轮次以0.5衰减率指数衰减的动态高斯噪声，扰动不改变图拓扑结构，仅作用于特征空间，以此打破特征趋同，促使长尾项目嵌入分布更加均匀。为融合图注意力与图卷积在局部细粒度交互捕捉和全局结构模式感知上的互补优势，提出渐进融合机制，在每一传播层将GAT的多头注意力输出与LightGCN的邻域聚合输出进行拼接，并通过可学习参数自适应控制各层贡献，实现从低层局部细节到高层全局语义的分层融合。针对多标准数据中评价标准与样本间存在不一致性导致对比学习锚点难以可靠选取的难题，设计基于平均邻居余弦相似度的锚点选择策略：在每个标准视图内，计算各节点与其所有邻居节点嵌入的平均相似度，选取相似度最高的节点作为该视图的锚点，以此作为稳定的对比基准。在此基础上，构建双对比学习任务——局部对比损失最大化同一节点在不同标准下正样本嵌入间的一致性并推开负样本，全局对比损失增强各标准全局嵌入（节点均值）间的跨标准对齐，两者协同优化，总损失函数结合局部损失、全局损失和L2正则项，平衡节点级判别力与分布级一致性。 为验证模型有效性，在Yahoo!Movies、BeerAdvocate和TripAdvisor三个公开真实数据集上进行实验。Yahoo!Movies包含6078名用户、976部电影及758405条四标准评分；BeerAdvocate含8831名用户、2698种啤酒及3880359条四标准评分；TripAdvisor含15000名用户、1325家酒店及20830条七标准评分，稀疏度较高。以平均绝对误差和均方根误差为评价指标，将NGCLR与BMF、MSVD、MLR、SVR、CIC、DMCF、CFM、DNN-MF、MCAE-FADNN及最优基线D-MGAC等十余种方法对比。实验结果显示，NGCLR在Yahoo!Movies上MAE和RMSE分别达到0.6028和0.8211，相比D-MGAC相对降低2.94%和3.79%；在BeerAdvocate上分别为0.3931和0.5380，相对降低4.93%和2.73%；在TripAdvisor上分别为0.7338和0.9724，相对降低2.04%和1.96%。消融实验表明，去除噪声增强模块、渐进融合机制或对比学习模块后，MAE和RMSE均出现不同程度上升，其中采用随机锚点策略的变体在三个数据集上MAE分别比完整模型高2.86%、2.21%和0.69%，验证了各核心组件的独立贡献与协同增益。超参数分析显示嵌入维度256、注意力头数8、局部与全局对比损失权重均为0.5时性能最优；动态衰减噪声策略优于固定噪声和标准自适应噪声策略；基于邻居相似度的锚点选择优于全局平均相似度和PageRank策略。头尾分组实验表明，模型在尾部项目组上的MAE提升幅度显著大于头部组，噪声增强可视化进一步证实长尾项目嵌入分布从聚集趋于分散。综上，NGCLR有效解决了多标准推荐中的长尾退化、图模块融合不足和对比学习锚点偏差三大难题，在多个真实数据集上取得稳定优异的预测精度，为多标准推荐系统提供了一种高效且鲁棒的解决方案。