A Simple yet Effective Negative Sampling Plugin for Constructing Positive Sample Pairs in Implicit Collaborative Filtering

Most implicit collaborative filtering (CF) models are trained with negative sampling, where existing work designs sophisticated strategies for high-quality negatives while largely overlooking the exploration of positive samples. Although some denoising recommendation methods can be applied to implicit CF for denoising positive samples, they often sparsify positive supervision. Moreover, these approaches generally overlook user activity bias during training, leading to insufficient learning for inactive users. To address these issues, we propose a simple yet effective negative sampling plugin, PSP-NS, from the perspective of enhancing positive supervision signals. It builds a user-item bipartite graph with edge weights indicating interaction confidence inferred from global and local patterns, generates positive sample pairs via replication-based reweighting to strengthen positive signals, and adopts an activity-aware weighting scheme to effectively learn inactive users’ preferences. We provide theoretical insights from a margin-improvement perspective, explaining why PSP-NS tends to improve ranking quality (e.g., Precision@k/Recall@k), and conduct extensive experiments on four real-world datasets to demonstrate its superiority. For instance, PSP-NS boosts Recall@30 and Precision@30 by 32.11% and 22.90% on Yelp over the strongest baselines. PSP-NS can be integrated with various implicit CF recommenders or negative sampling methods to enhance their performance.

💡 Research Summary

This paper tackles a largely overlooked aspect of implicit collaborative‑filtering (CF) systems that rely on negative sampling: the quality and coverage of positive training signals. While most prior work focuses on designing sophisticated negative‑sampling distributions (e.g., popularity‑based, score‑based, adversarial), they treat every observed interaction as a true positive and ignore the presence of false positives (e.g., clicks that do not reflect genuine interest) and user activity bias. Existing denoising methods attempt to filter noisy positives but suffer from two major drawbacks: (1) they sparsify the positive supervision by discarding many true interactions, and (2) they do not compensate for the long‑tail distribution of user activity, leaving inactive users under‑represented in the learning process.

The authors propose PSP‑NS (Positive Sample Pair – Negative Sampling), a simple yet effective plug‑in that enhances positive supervision while remaining compatible with any existing negative‑sampling scheme. PSP‑NS consists of three stages:

1. Weighted bipartite graph construction.

   • The raw binary interaction matrix (A) is first normalized by row and column degrees to mitigate popularity bias.
   • Randomized SVD is applied to the normalized matrix, retaining only the top‑(q) singular values. This captures global interaction patterns efficiently even for large sparse datasets.
   • For each user, the SVD‑derived preference vector is used to select the top‑(K) items as adaptive neighbors, where (K) equals the user’s historical interaction count. This adaptive neighbor selection avoids manual tuning and aligns the graph density with user activity.
   • The resulting graph (G_{\text{SVD}}) is merged with the original graph (G) to form a weighted graph (\hat G). Edge weight (\hat W(u,i)) is set to a high confidence value (s>1) if the edge appears in both graphs, otherwise to 1 (or 0 if absent from both).

2. Positive sample pair generation and activity‑aware user weighting.

   • Positive Sample Pairs (PSP) are built by replication‑based reweighting: an edge with weight (s) is replicated (s) times in the training set, while weight 1 edges are kept once. Each replica will be paired with a different negative item during training, providing multiple independent constraints for the same positive interaction.
   • User activity bias is mitigated by assigning each user a weight (t_u = 1 / \log(a \cdot |\hat P_u| + 1)), where (|\hat P_u|) is the number of items incident to user (u) in (\hat G) and (a) controls sensitivity. Inactive users thus receive larger weights, amplifying their contribution to the loss.

3. Model optimization.

   • The standard negative‑sampling loss (e.g., BPR) is modified to incorporate the replicated positives and user weights:
     \