In particular, given the wordpair (w, w ), and their provided contexts (c, c ) we define: Following the notation used in 3.2, K is the number of topics returned by the trained LDA model, x j is the word embedding trained on the subcorpus corresponding to the j-th topic after being projected to the unified vector space, p(j|w, c) denotes the posterior probability of topic j returned by LDA given as input the context c of word w, d denotes the cosine similarity between the two input representations and finallyx (w) = u argmax 1≤j≤K p(j|w,c) (w) is the vector representation of word w that corresponds to the topic with the maximum posterior for c. Intuitively, a higher score in MaxSimC indicates the existence of more robust multi-topic word representations.
the topic model splits the corpus into K (possibly overlapping) subcorpora.