Collaborative Filtering for Recommendation in Geometric Algebra

• Published in: Database Systems for Advanced Applications Vol. 13246; pp. 256 - 263
• Main Authors: Wu, Longcan, Wang, Daling, Feng, Shi, Song, Kaisong, Zhang, Yifei, Yu, Ge
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2022; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Collaborative filtering; Geometric algebra; Recommendation
• ISBN: 9783031001253; 3031001257
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-031-00126-0_17

At present, recommender system plays an important role in many practical applications. Many recommendation models are based on representation learning, in which users and items are embedded into a low-dimensional vector space, and then historical interactions are used to train the models. We find that almost all of these methods model users and items in real-valued embedding space, which neglect the potential value of other non-real spaces. In this paper, we propose a Geometric Algebra-based Collaborative Filtering (GACF) model for recommendation. Specifically, GACF firstly uses multivectors to represent users and items. Then GACF uses geometric product and inner product to model the historical interaction between users and items. By using geometric product, the model prediction can obtain inter-dependencies between components of multivectors, which enable complex interactions between users and items to be captured. Extensive experiments on two real datasets demonstrate the effectiveness of GACF.