Moreover, considering there are various relations among words, we use a lower dimension s for storage compression, with s < d. Thus, a transformation matrix X is introduced to transform u into the same vector space of c. As a result, the final embeddings v for head and tail of w under relation r are formulated as: (1) To train v r h,w and v r t,w for each w under r, we adopt the negative sampling strategy to conduct the learning process.
for each r, we use a relation tuple set T r , with each tuple t = (w h , r, w t ) ∈ T r , where w h is the head word and w t the tail word.