低秩矩阵分解揭示用户偏好潜空间，提升推荐系统可扩展性与准确性。
Latent Geometry of Taste: Scalable Low-Rank Matrix Factorization for Recommender Systems
- 基于交替最小二乘法构建可扩展的低秩模型，优化参数以平衡精度与泛化能力。
- 在MovieLens 32M数据集上，低秩模型比高维模型更优，RMSE显著降低。
- 无监督生成语义类型聚类，适用于冷启动场景和个性化推荐需求。
可扩展性和数据稀疏性仍是大规模交互数据上协同过滤的关键瓶颈。本研究利用MovieLens 32M数据集，探索用户偏好的潜在几何结构，实现高性能、并行化的交替最小二乘（ALS）框架。通过广泛的超参数优化，证明受限的低秩模型在泛化能力上显著优于高维模型，实现了均方根误差（RMSE）与排序精度之间的最佳平衡。我们可视化了学习到的嵌入空间，揭示了语义类型聚类的无监督涌现，证实模型仅从交互数据中捕捉深层结构关系。最后，在冷启动场景中验证了系统的实用性，引入可调评分参数，有效管理流行度偏差与个性化亲和力之间的权衡。研究代码库见：https://github.com/joshsalako/recommender.git。
原文摘要 · Abstract (English)
Scalability and data sparsity remain critical bottlenecks for collaborative filtering on massive interaction datasets. This work investigates the latent geometry of user preferences using the MovieLens 32M dataset, implementing a high-performance, parallelized Alternating Least Squares (ALS) framework. Through extensive hyperparameter optimization, we demonstrate that constrained low-rank models significantly outperform higher dimensional counterparts in generalization, achieving an optimal balance between Root Mean Square Error (RMSE) and ranking precision. We visualize the learned embedding space to reveal the unsupervised emergence of semantic genre clusters, confirming that the model captures deep structural relationships solely from interaction data. Finally, we validate the system's practical utility in a cold-start scenario, introducing a tunable scoring parameter to manage the trade-off between popularity bias and personalized affinity effectively. The codebase for this research can be found here: https://github.com/joshsalako/recommender.git
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