the hypernym-hyponym relationship between words can be approximated by a linear projection operator between word vectors Fu et al., 2014), we design a similar strategy to (Fu et al., 2014) between images and words so that the parent can be "predicted" given the image embedding of its child category and the projection matrix.
let (x n , x n ) be a parent-child pair in the training data, we learn a projection matrix Φ which minimizes the distance between Φv i n (i.e.