# Radial Neighborhood Smoothing Recommender System

arXiv: https://arxiv.org/abs/2507.09952 · HTML: https://mlsanity.com/paper/2507.09952/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 7 of 7)

- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [FineCIR: Explicit Parsing of Fine-Grained Modification Semantics for Composed Image Retrieval](https://mlsanity.com/paper/2503.21309/) (2025)
- [Time Series Modeling for Heart Rate Prediction: From ARIMA to Transformers](https://mlsanity.com/paper/2406.12199/) (2024)
- [Enhancing User Intent for Recommendation Systems via Large Language Models](https://mlsanity.com/paper/2501.10871/) (2025)
- [Nonparametric Matrix Estimation with One-Sided Covariates](https://mlsanity.com/paper/2110.13969/) (2021)
- [A Narrative Review on Large AI Models in Lung Cancer Screening, Diagnosis, and Treatment Planning](https://mlsanity.com/paper/2506.07236/) (2025)
- [Efficient or Powerful? Trade-offs Between Machine Learning and Deep Learning for Mental Illness Detection on Social Media](https://mlsanity.com/paper/2503.01082/) (2025)

## Abstract (arXiv)

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.