Linear, or non-linear, that is the question!

Taeyong Kong, Taeri Kim, Jinsung Jeon, Jeongwhan Choi, Yeon Chang Lee, Noseong Park, Sang Wook Kim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)


There were fierce debates on whether the non-linear embedding propagation of GCNs is appropriate to GCN-based recommender systems. It was recently found that the linear embedding propagation shows better accuracy than the non-linear embedding propagation. Since this phenomenon was discovered especially in recommender systems, it is required that we carefully analyze the linearity and non-linearity issue. In this work, therefore, we revisit the issues of i) which of the linear or non-linear propagation is better and ii) which factors of users/items decide the linearity/non-linearity of the embedding propagation. We propose a novel Hybrid method of linear and non-linear collaborative filtering method (HMLET, pronounced as Hamlet). In our design, there exist both linear and non-linear propagation steps, when processing each user or item node, and our gating module chooses one of them, which results in a hybrid model of the linear and non-linear GCN-based collaborative filtering (CF). The proposed model yields the best accuracy in three public benchmark datasets. Moreover, we classify users/items into the following three classes depending on our gating modules' selections: Full-Non-Linearity (FNL), Partial-Non-Linearity (PNL), and Full-Linearity (FL). We found that there exist strong correlations between nodes' centrality and their class membership, i.e., important user/item nodes exhibit more preferences towards the non-linearity during the propagation steps. To our knowledge, we are the first who design a hybrid method and report the correlation between the graph centrality and the linearity/non-linearity of nodes. All HMLET codes and datasets are available at:

Original languageEnglish
Title of host publicationWSDM 2022 - Proceedings of the 15th ACM International Conference on Web Search and Data Mining
PublisherAssociation for Computing Machinery, Inc
Number of pages9
ISBN (Electronic)9781450391320
Publication statusPublished - 2022 Feb 11
Event15th ACM International Conference on Web Search and Data Mining, WSDM 2022 - Virtual, Online, United States
Duration: 2022 Feb 212022 Feb 25

Publication series

NameWSDM 2022 - Proceedings of the 15th ACM International Conference on Web Search and Data Mining


Conference15th ACM International Conference on Web Search and Data Mining, WSDM 2022
Country/TerritoryUnited States
CityVirtual, Online

Bibliographical note

Funding Information:
The work of Sang-Wook Kim was supported by Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-IT1901-03. The work of Noseong Park was supported by the Yonsei University Research Fund of 2021 and the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (No. 2020-0-01361, Artificial Intelligence Graduate School Program (Yonsei University)).

Publisher Copyright:
© 2022 ACM.

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Software


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