A Method for Estimating the Proximity of Vector Representation Groups in Multidimensional Space. On the Example of the Paraphrase Task

The following paper presents a method of comparing two sets of vectors. The method can be applied in all tasks, where it is necessary to measure the closeness of two objects presented as sets of vectors. It may be applicable when we compare the meanings of two sentences as part of the problem of paraphrasing. This is the problem of measuring semantic similarity of two sentences (group of words). The existing methods are not sensible for the word order or syntactic connections in the considered sentences. The method appears to be advantageous because it neither presents a group of words as one scalar value, nor does it try to show the closeness through an aggregation vector, which is mean for the set of vectors. Instead of that we measure the cosine of the angle as the mean for the first group vectors projections (the context) on one side and each vector of the second group on the other side. The similarity of two sentences defined by these means does not lose any semantic characteristics and takes account of the words traits. The method was verified on the comparison of sentence pairs in Russian.