TransINT: Embedding Implication Rules in Knowledge Graphs with\n Isomorphic Intersections of Linear Subspaces

Knowledge Graphs (KG), composed of entities and relations, provide a\nstructured representation of knowledge. For easy access to statistical\napproaches on relational data, multiple methods to embed a KG into f(KG) $\\in$\nR^d have been introduced. We propose TransINT, a novel and interpretable KG\nembedding method that isomorphically preserves the implication ordering among\nrelations in the embedding space. Given implication rules, TransINT maps set of\nentities (tied by a relation) to continuous sets of vectors that are\ninclusion-ordered isomorphically to relation implications. With a novel\nparameter sharing scheme, TransINT enables automatic training on missing but\nimplied facts without rule grounding. On a benchmark dataset, we outperform the\nbest existing state-of-the-art rule integration embedding methods with\nsignificant margins in link Prediction and triple Classification. The angles\nbetween the continuous sets embedded by TransINT provide an interpretable way\nto mine semantic relatedness and implication rules among relations.\n