Joint Domain Adaptation and Unknown Class Recognition on Heterophilic Graphs

Graph domain adaptation becomes challenging when heterophily coexists with target classes absent from the labeled source graph. This setting requires learning transferable representations while avoiding the alignment of unknown target nodes with known source classes. Existing methods for heterophily or open-set adaptation focus on their respective challenges, leaving their joint treatment insufficiently explored. We propose HODA, a unified framework for $\mathbf{H}$eterophilic $\mathbf{O}$pen-set $\mathbf{D}$omain $\mathbf{A}$daptation. HODA uses multiscale spectral encoding to preserve complementary low-pass and high-pass information across propagation orders. Using the resulting representations, we adapt source class prototypes to the target distribution and introduce an unknown prototype for target private classes. Agreement between classifier predictions and prototype-based clustering selects target pseudo labels and excludes nodes jointly predicted as unknown from domain alignment. We also identify and correct inconsistent label encodings across the processed WebKB graphs, enabling semantically consistent cross domain evaluation. Experiments across multiple datasets and transfer directions demonstrate competitive performance in known-class classification and unknown-class recognition.