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

TL;DR

This work tackles knowledge-graph enhanced recommendation under KG noise, sparsity, and Euclidean geometric limitations by introducing SPARK, a multi-stage framework. SPARK denoises KGs with Tucker decomposition, then learns dual-space representations via an SVD-initialized hybrid GNN operating in Euclidean and Hyperbolic (Lorentz) spaces, and finally fuses signals adaptively based on item popularity while aligning views through contrastive learning. Empirical results on three real-world datasets show SPARK achieving state-of-the-art performance, with pronounced gains for long-tail items, validated through extensive ablations and hyperparameter analyses. The proposed approach offers a principled, scalable, geometry-aware path for knowledge-enhanced recommendation, with potential extensions to cold-start and temporal dynamics.

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.

Figures (4)

• Figure 1: Degree distribution across different datasets: (a) Yelp2018, (b) Amazon-Book, and (c) Alibaba-Fashion. All datasets exhibit the characteristic long-tail distribution.
• Figure 2: The overall architecture of SPARK. The framework integrates (1) Knowledge Graph (KG) representation learning with Tucker-based scoring for KG triples; (2) SVD-initialized Hybrid Geometric GNNs operating in parallel Euclidean and Hyperbolic (Lorentz model) spaces on the user-item interaction graph; (3) Contrastive alignment of SVD-derived collaborative views and KG-enhanced semantic views; and (4) Popularity-aware adaptive fusion to dynamically combine signals for final recommendation.
• Figure 3: Hyperparameter sensitivity on Amazon-Book for (left) SVD dimension $d_e$, (center) Tucker core dimension $d_c$, and (right) GNN layers $L$. R@k and N@k denote Recall@k and NDCG@k.
• Figure 4: t-SNE visualization of learned item embeddings on Yelp2018. Head items (top 10%, blue) and tail items (bottom 10%, red) are shown. SPARK (c) learns a more balanced embedding space where tail items are better integrated with head items, compared to baselines KGCL (a) and HCMKR (b).