  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:
https://github.com/qbxlvnf11/HMLET.
