  In this work, we contribute a new multi-layer neural network architecture
named ONCF to perform collaborative filtering. The idea is to use an outer
product to explicitly model the pairwise correlations between the dimensions of
the embedding space. In contrast to existing neural recommender models that
combine user embedding and item embedding via a simple concatenation or
element-wise product, our proposal of using outer product above the embedding
layer results in a two-dimensional interaction map that is more expressive and
semantically plausible. Above the interaction map obtained by outer product, we
propose to employ a convolutional neural network to learn high-order
correlations among embedding dimensions. Extensive experiments on two public
implicit feedback data demonstrate the effectiveness of our proposed ONCF
framework, in particular, the positive effect of using outer product to model
the correlations between embedding dimensions in the low level of multi-layer
neural recommender model. The experiment codes are available at:
https://github.com/duxy-me/ConvNCF
