We present a novel method to precisely impose tree-structured category information onto word-embeddings, resulting in ball embeddings in higher dimensional spaces (N-balls for short). Inclusion relations among N-balls implicitly encode subordinate relations among categories. The similarity measurement in terms of the cosine function is enriched by category information. Using a geometric construction method instead of back-propagation, we create large N-ball embeddings that satisfy two conditions: (1) category trees are precisely imposed onto word embeddings at zero energy cost; (2) pre-trained word embeddings are well preserved. A new benchmark data set is created for validating the category of unknown words. Experiments show that N-ball embeddings, carrying category information, significantly outperform word embeddings in the test of nearest neighborhoods, and demonstrate surprisingly good performance in validating categories of unknown words. Source codes and data-sets are free for public access \url{https://github.com/gnodisnait/nball4tree.git} and \url{https://github.com/gnodisnait/bp94nball.git}.
we show a geometric method to perfectly encode categroy tree information into pre-trained word-embeddings. The paper proposes N-ball embedding for taxonomic data where an N-ball is a pair of a centroid vector and the radius from the center. The paper presents a method for tweaking existing vector embeddings of categorical objects (such as words), to convert them to ball embeddings that follow hierarchies. Focuses on adjusting the pretrained word embeddings so that they respect the hypernymy/hyponymy relationship by appropriate n-ball encapsulation.