Discrete Scale-invariant Metric Learning for Efficient Collaborative Filtering

2025-06-11

AI Summary

To address metric learning bias induced by class imbalance in collaborative filtering, this paper proposes Discrete Scale-Invariant Metric Learning (DSIML), which maps users and items into a shared Hamming space for efficient binary recommendation. Our key contributions are: (1) the first scale-invariant margin formulated from the negative-sample perspective, jointly integrating triplet hinge loss with pairwise ranking loss; (2) a log-sum-exp-based variational quadratic upper bound to tackle the mixed-integer hashing optimization problem; and (3) an alternating optimization algorithm with guaranteed convergence. Extensive experiments on multiple benchmark datasets demonstrate that DSIML significantly outperforms state-of-the-art metric learning and hashing-based recommendation methods—achieving both high accuracy and substantially improved online inference efficiency. The source code is publicly available.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Data Mining & Knowledge Management: Recommender Systems
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• 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
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Metric learning has attracted extensive interest for its ability to provide personalized recommendations based on the importance of observed user-item interactions. Current metric learning methods aim to push negative items away from the corresponding users and positive items by an absolute geometrical distance margin. However, items may come from imbalanced categories with different intra-class variations. Thus, the absolute distance margin may not be ideal for estimating the difference between user preferences over imbalanced items. To this end, we propose a new method, named discrete scale-invariant metric learning (DSIML), by adding binary constraints to users and items, which maps users and items into binary codes of a shared Hamming subspace to speed up the online recommendation. Specifically, we firstly propose a scale-invariant margin based on angles at the negative item points in the shared Hamming subspace. Then, we derive a scale-invariant triple hinge loss based on the margin. To capture more preference difference information, we integrate a pairwise ranking loss into the scale-invariant loss in the proposed model. Due to the difficulty of directly optimizing the mixed integer optimization problem formulated with extit{log-sum-exp} functions, we seek to optimize its variational quadratic upper bound and learn hash codes with an alternating optimization strategy. Experiments on benchmark datasets clearly show that our proposed method is superior to competitive metric learning and hashing-based baselines for recommender systems. The implementation code is available at https://github.com/AnonyFeb/dsml.

Problem

• Addresses imbalanced item categories in metric learning
• Proposes scale-invariant margin for user preference estimation
• Optimizes binary codes for efficient recommendation systems

Innovation

• Binary constraints map users to Hamming subspace
• Scale-invariant margin based on angles
• Optimize variational quadratic upper bound