How can we use knowledge graph in computing? A knowledge graph is a symbolic and logical system while applications often involve numerical computing in continuous spaces. Formal logic is neither tractable nor robust when dealing with knowledge graph. Hence the idea of Knowledge graph embeddings.
A knowledge graph is embedded into a low-dimensional continuous vector space while certain properties of it are preserved ([Bordes et al., 2013](http://papers.nips.cc/paper/5071-translating-embeddings-for-modeling-multi-rela), Socher et al., 2013; Chang et al., 2013; Wang et
al., 2014). Generally, each entity is represented
as a point in that space while each relation is interpreted as an operation over entity embeddings ((eg. in Bordes et al., a translation). The embedding representations are usually learnt by minimizing a global loss function involving all entities and relations so that each entity
embedding encodes both local and global connectivity patterns of the original graph. Thus, we can reason new facts from learnt embeddings
Traversing Knowledge Graphs in Vector Space (2015)(About) Knowledge graphs often have missing facts (edges) which disrupts path queries. Recent models for knowledge base completion impute missing facts by embedding knowledge graphs in vector spaces. We show that these models can be recursively applied to answer path queries, but that they suffer from cascading errors. This motivates a new "compositional" training objective, which dramatically improves all models' ability to answer path queries, in some cases more than doubling accuracy.