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Cross-domain recommendation can alleviate the data sparsity problem inrecommender systems. To transfer the knowledge from one domain to another, onecan either utilize the neighborhood information or learn a direct mappingfunction. However, all existing methods ignore the high-order connectivityinformation in cross-domain recommendation area and suffer from thedomain-incompatibility problem. In this paper, we propose a \textbf{J}oint\textbf{S}pectral \textbf{C}onvolutional \textbf{N}etwork (JSCN) forcross-domain recommendation. JSCN will simultaneously operate multi-layerspectral convolutions on different graphs, and jointly learn a domain-invariantuser representation with a domain adaptive user mapping module. As a result,the high-order comprehensive connectivity information can be extracted by thespectral convolutions and the information can be transferred across domainswith the domain-invariant user mapping. The domain adaptive user mapping modulecan help the incompatible domains to transfer the knowledge across each other.Extensive experiments on $24$ Amazon rating datasets show the effectiveness ofJSCN in the cross-domain recommendation, with $9.2\%$ improvement on recall and$36.4\%$ improvement on MAP compared with state-of-the-art methods. Our code isavailable online ~\footnote{https://github.com/JimLiu96/JSCN}.

JSCN: Joint Spectral Convolutional Network for Cross Domain Recommendation