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The relation completion for knowledge graph requires expanding and enriching a knowledge graph by predicting the missing relation in a given triple which has known head and tail entities. In this paper, we propose a unified embedding-based relation completion framework which mainly includes two contributions. Firstly, based on embedding of triples generated by any embedding model, we utilize deep neural networks to learn feature representations of relations from head and tail entities. This allows us to propose a multi-dimensional feature prediction model for missing relations of triples. Based on the predictive features of missing relations, we match the best relation within the candidate relation set for relation completion. Secondly, to reduce the impact of noisy features and further improve the effectiveness of relation completion, we consider the extraction of key features as a submodular optimization problem by establishing a normalized, non-decreasing submodular function. Finally, testing on multiple public knowledge graph datasets, the results demonstrate that our proposed relation completion framework can significantly improve existing relation completion approaches. [ABSTRACT FROM AUTHOR]