Radial Neighborhood Smoothing Recommender System

TL;DR

This paper introduces the Radial Neighborhood Smoothing Recommender System, which improves distance estimation in latent space for better neighborhood construction, leading to enhanced recommendation accuracy and cold-start mitigation.

Contribution

It proposes a novel distance estimation method using observed matrix row and column distances, combined with variance correction, to improve neighborhood-based recommendations.

Findings

RNE outperforms existing collaborative filtering methods.

The approach effectively mitigates the cold-start problem.

Theoretical analysis supports the estimator's asymptotic properties.

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.