Missing data imputation is a key issue in learning from incomplete data. Various techniques have been developed with great successes on dealing with missing values in data sets with homogeneous attributes (their independent attributes are all either continuous or discrete). This paper studies a new setting of missing data imputation, i.e., imputing missing data in data sets with heterogeneous attributes (their independent attributes are of different types), referred to as imputing mixed-attribute data sets. Although many real applications are in this setting, there is no estimator designed for imputing mixed-attribute data sets. This paper first proposes two consistent estimators for discrete and continuous missing target values, respectively. And then, a mixture-kernel-based iterative estimator is advocated to impute mixed-attribute data sets. The proposed method is evaluated with extensive experiments compared with some typical algorithms, and the result demonstrates that the proposed approach is better than these existing imputation methods in terms of classification accuracy and root mean square error (RMSE) at different missing ratios.

Knowledge graph-based recommendation methods are a hot research topic in the field of recommender systems in recent years. As a mainstream knowledge graph-based recommendation method, the propagation-based recommendation method captures users’ potential interests in items by integrating the representations of entities and relations in the knowledge graph and the high-order connection patterns between entities to provide personalized recommendations. For example, the collaborative knowledge-aware attentive network (CKAN) is a typical state-of-the-art propagation-based recommendation method that combines user-item interactions and knowledge associations in the knowledge graph, and performs heterogeneous propagation in the knowledge graph to generate multi-hop ripple sets, thereby capturing users’ potential interests. However, existing propagation-based recommendation methods, including CKAN, usually ignore the complex relations between entities in the multi-hop ripple sets and do not distinguish the importance of different ripple sets, resulting in inaccurate user potential interests being captured. Therefore, this paper proposes a top-N recommendation method named collaborative knowledge-aware graph attention network (CKGAT). Based on the heterogeneous propagation strategy, CKGAT uses the knowledge-aware graph attention network to extract the topological proximity structures of entities in the multi-hop ripple sets and then learn high-order entity representations, thereby generating refined ripple set embeddings. CKGAT further uses an attention aggregator to perform weighted aggregation on the ripple set embeddings, the user/item initial entity set embeddings, and the original representations of items to generate accurate user embeddings and item embeddings for the top-N recommendations. Experimental results show that CKGAT, overall, outperforms three baseline methods and six state-of-the-art propagation-based recommendation methods in terms of recommendation accuracy, and outperforms four representative propagation-based recommendation methods in terms of recommendation diversity.