Of all the methods in isolation, the simple approach of Section 4.1 — to use the total cosine similarity between a potential answer and the other words in the sentence — has performed best.

For the LSA model, the linear combination has three inputs: the total word similarity, the cosine similarity between the sum of the answer word vectors and the sum of the rest of sentence’s word vectors, and the number of out—of—vocabulary terms in the answer.

An important property of SVD is that the rows of US — which represents the words — behave similarly to the original rows of W, in the sense that the cosine similarity between two rows in US approximates the cosine similarity between the corre—

sponding rows in W. Cosine similarity is defined as

Let m be the smallest cosine similarity between h and any word in the vocabulary V: m = minwev sim(h, w).

Cosine similarity with previous sentence.

Here we use the cosine similarity between sentences, where each sentence is represented as a vector of words, with term weight calculated using TD-IDF (term frequency times inverse document frequency).

* Cosine similarity with previous sentence.

The nearest neighbors of a word are computed by comparing the cosine similarity between the center word and all other words in the dictionary.

Table 1: Nearest neighbors of words based on cosine similarity .

Table 2: Nearest neighbors of word embeddings learned by our model using the multi-prototype approach based on cosine similarity .