Radial Neighborhood Smoothing Recommender System

2025-07-14

AI Summary

Inaccurate distance metrics in the latent space of recommender systems distort user–user, item–item, and user–item relationship modeling, exacerbating the cold-start problem. To address this, we propose Radial Neighborhood Smoothing (RNS): first, it constructs radial neighborhoods along the user (row) and item (column) dimensions using an empirically variance-calibrated distance estimator; second, it applies local kernel regression within these neighborhoods to smooth observed interactions, jointly leveraging matrix factorization and collaborative filtering for accurate latent-space distance modeling and rating imputation; third, it enhances structural robustness in sparse scenarios by explicitly incorporating overlapping or partially overlapping user–item pairs. Extensive experiments on synthetic and multiple real-world datasets demonstrate that RNS significantly outperforms state-of-the-art collaborative filtering and matrix factorization methods, particularly improving recommendation accuracy for cold-start users.

Technology Category

• Data Mining & Knowledge Management: Recommender Systems
• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Recommender systems inherently exhibit a low-rank structure in latent space. A key challenge is to define meaningful and measurable distances in the latent space to capture user-user, item-item, user-item relationships effectively. In this work, we establish that distances in the latent space can be systematically approximated using row-wise and column-wise distances in the observed matrix, providing a novel perspective on distance estimation. To refine the distance estimation, we introduce the correction based on empirical variance estimator to account for noise-induced non-centrality. The novel distance estimation enables a more structured approach to constructing neighborhoods, leading to the Radial Neighborhood Estimator (RNE), which constructs neighborhoods by including both overlapped and partially overlapped user-item pairs and employs neighborhood smoothing via localized kernel regression to improve imputation accuracy. We provide the theoretical asymptotic analysis for the proposed estimator. We perform evaluations on both simulated and real-world datasets, demonstrating that RNE achieves superior performance compared to existing collaborative filtering and matrix factorization methods. While our primary focus is on distance estimation in latent space, we find that RNE also mitigates the ``cold-start'' problem.

Problem

• Define measurable latent space distances for user-item relationships
• Improve distance estimation with noise correction and variance adjustment
• Enhance recommendation accuracy via Radial Neighborhood Estimator (RNE)

Innovation

• Systematic latent distance approximation via matrix distances
• Correction using empirical variance for noise reduction
• Radial Neighborhood Estimator with kernel regression smoothing