Explicit continuous vector representation such as vector representation of words, phrases, etc. has been proven effective for various NLP tasks. This paper proposes a novel method of constructing such vector representation for both entity-pairs and relation expressions which link them in text. Based on the insight of the duality of relations, the representation is constructed by embedding of two separately constructed semantic spaces, one for entity-pairs and the other for relation expressions, into a common semantic space. By representing the two different types of objects (i.e. entity-pairs and relation expressions) in the same semantic space, we can treat the two tasks, relation mining and relation expression mining (a.k.a. pattern mining), systematically and in a unified manner. The approach is the first attempt to construct a continuous vector representation for expressions whose validity can be explicitly checked by their proximities to known sets of entity-pairs. We also experimentally validate the effectiveness of the common space for relation mining and relation expression mining.
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