Complementary recommendation gains increasing attention in e-commerce since it expedites the process of finding frequently-bought-with products for users in their shopping journey. Therefore, learning the product representation that can reflect this complementary relationship plays a central role in modern recommender systems. In this work, we propose a logical reasoning network, LOGIREC, to effectively learn embeddings of products as well as various transformations (projection, intersection, negation) between them. LOGIREC is capable of capturing the asymmetric complementary relationship between products and seamlessly extending to high-order recommendations where more comprehensive and meaningful complementary relationship is learned for a query set of products. Finally, we further propose a hybrid network that is jointly optimized for learning a more generic product representation. We demonstrate the effectiveness of our LOGIREC on multiple public real-world datasets in terms of various ranking-based metrics under both low-order and highorder recommendation scenarios.

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Given a resource-rich source graph and a resourcescarce target graph, how can we effectively transfer knowledge across graphs and ensure a good generalization performance? In many high-impact domains (e.g., brain networks and molecular graphs), collecting and annotating data is prohibitively expensive and time-consuming, which makes domain adaptation an attractive option to alleviate the label scarcity issue. In light of this, the state-of-the-art methods focus on deriving domain-invariant graph representation that minimizes the domain discrepancy. However, it has recently been shown that a small domain discrepancy loss may not always guarantee a good generalization performance, especially in the presence of disparate graph structures and label distribution shifts. In this paper, we present TRANSNET, a generic learning framework for augmenting knowledge transfer across graphs. In particular, we introduce a novel notion named trinity signal that can naturally formulate various graph signals at different granularity (e.g., node attributes, edges, and subgraphs). With that, we further propose a domain unification module together with a trinity-signal mixup scheme to jointly minimize the domain discrepancy and augment the knowledge transfer across graphs. Finally, comprehensive empirical results show that TRANSNET outperforms all existing approaches on seven benchmark datasets by a significant margin.

With the widespread development of algorithmic fairness, there has been a surge of research interest that aims to generalize the fairness notions from the attributed data to the relational data (graphs). The vast majority of existing work considers the fairness measure in terms of the low-order connectivity patterns (e.g., edges), while overlooking the higher-order patterns (e.g., -cliques) and the dynamic nature of real-world graphs. For example, preserving triangles from graph cuts during clustering is the key to detecting compact communities; however, if the clustering algorithm only pays attention to triangle-based compactness, then the returned communities lose the fairness guarantee for each group in the graph. Furthermore, in practice, when the graph (e.g., social networks) topology constantly changes over time, one natural question is how can we ensure the compactness and demographic parity at each timestamp efciently. To address these problems, we start from the static setting and propose a spectral method that preserves clique connections and incorporates demographic fairness constraints in returned clusters at the same time. To make this static method ft for the dynamic setting, we propose two core techniques, Laplacian Update via Edge Filtering and Searching and Eigen-Pairs Update with Singularity Avoided. Finally, all proposed components are combined into an end-to-end clustering framework named F-SEGA, and we conduct extensive experiments to demonstrate the efectiveness, efciency, and robustness of F-SEGA.