SPARK: Adaptive Low-Rank Knowledge Graph Modeling in Hybrid Geometric Spaces for Recommendation

2025-09-14

AI Summary

Knowledge graphs (KGs) in recommendation systems face three key challenges: noise contamination, data sparsity, and the inability of Euclidean space to effectively model complex hierarchical relationships—particularly for long-tail entities—while existing methods lack popularity-aware mechanisms for fusing multi-source signals. To address these, we propose SPARK: (1) a Tucker low-rank decomposition module for KG denoising; (2) a hybrid geometric graph neural network—initialized via singular value decomposition—that models hierarchical structures of long-tail entities in hyperbolic space while capturing global associations in Euclidean space; and (3) contrastive learning to align multi-source embeddings, coupled with a popularity-aware dynamic weighting mechanism for adaptive signal fusion. Extensive experiments on multiple benchmark datasets demonstrate that SPARK significantly improves both overall and long-tail item recommendation performance, validating its effectiveness and robustness.

Technology Category

• Data Mining & Knowledge Management: Recommender Systems
• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Knowledge Graphs (KGs) enhance recommender systems but face challenges from inherent noise, sparsity, and Euclidean geometry's inadequacy for complex relational structures, critically impairing representation learning, especially for long-tail entities. Existing methods also often lack adaptive multi-source signal fusion tailored to item popularity. This paper introduces SPARK, a novel multi-stage framework systematically tackling these issues. SPARK first employs Tucker low-rank decomposition to denoise KGs and generate robust entity representations. Subsequently, an SVD-initialized hybrid geometric GNN concurrently learns representations in Euclidean and Hyperbolic spaces; the latter is strategically leveraged for its aptitude in modeling hierarchical structures, effectively capturing semantic features of sparse, long-tail items. A core contribution is an item popularity-aware adaptive fusion strategy that dynamically weights signals from collaborative filtering, refined KG embeddings, and diverse geometric spaces for precise modeling of both mainstream and long-tail items. Finally, contrastive learning aligns these multi-source representations. Extensive experiments demonstrate SPARK's significant superiority over state-of-the-art methods, particularly in improving long-tail item recommendation, offering a robust, principled approach to knowledge-enhanced recommendation. Implementation code is available at https://github.com/Applied-Machine-Learning-Lab/SPARK.

Problem

• Denoise knowledge graphs for robust entity representations
• Model hierarchical structures in hybrid geometric spaces
• Adaptively fuse multi-source signals for item popularity

Innovation

• Tucker low-rank decomposition for KG denoising
• Hybrid geometric GNN in Euclidean and Hyperbolic spaces
• Popularity-aware adaptive fusion of multi-source signals