标题： 径向邻域平滑推荐系统 显示英文标题

标题： Radial Neighborhood Smoothing Recommender System

摘要： 推荐系统在潜在空间中固有地表现出低秩结构。 一个关键挑战是在潜在空间中定义有意义且可测量的距离，以有效捕捉用户-用户、物品-物品、用户-物品之间的关系。 在本工作中，我们证明可以系统地通过观察矩阵中的行方向和列方向距离来近似潜在空间中的距离，为距离估计提供了一个新的视角。 为了改进距离估计，我们引入基于经验方差估计器的修正，以考虑噪声引起的非中心性。 这种新颖的距离估计方法使得构建邻域更加结构化，从而提出了径向邻域估计器（RNE），该方法通过包括重叠和部分重叠的用户-物品对来构建邻域，并通过局部核回归进行邻域平滑以提高插补精度。 我们提供了所提出估计器的理论渐近分析。 我们在模拟和真实世界数据集上进行了评估，结果表明RNE相比现有的协同过滤和矩阵分解方法表现更优。 虽然我们的主要关注点是潜在空间中的距离估计，但我们发现RNE也能缓解“冷启动”问题。 显示英文摘要

摘要： 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.