I wonder if it is possible to represent NL phrases of a particular domain geometrically, for example, to compare their similarity. For example, if the phrase "Hey man, that chick is such a catch!" and more formal "..., this girl is pretty!" should be represented nearby because they are semantically similar.
This is an important question.
Recent research yields a positive answer to this question. The similarity between words (and phrases) from a geometric perspective, is the focus of the following paper:
Christina Boyce-Jacino, Simon DeDeo,
Opacity, Obscurity, and the Geometry of Question-Asking
https://arxiv.org/pdf/1809.08291.pdf
In this study, vector geometry is used to characterize words and phrases in terms of the coordinates of vectors in the Cartesian plane. Then the angle between pairs of vectors yields a similarity measure (see (1) on page 7).
More to the point, a geometry of natural language phrases can be introduced in terms of feature vectors. Here are the steps:
phrase features: Select features of interest for each phrase. Let P be a phrase, Phi(f) a real number assigned to a feature f of P such as frequency of occurrence.
phrase vector: Let f1, f2, ..., fi, ..., fk be features of a natural language phrase and let Phi(P) = ( Phi(f1),Phi(f2),...,Phi(fi),...,Phi(f1)) be a feature vector that describes a phrase P.
vector geometry similarity measure: Let Phi(P),Phi(Q) be descriptions of phrases P and Q. Then compute the angle theta between P and Q. See the paper by Christina Boyce-Jacino, Simon DeDeo to see how to do this. For a view of a phrase feataure on a Grassmann manifold, see the attached image from the paper by J. Zhang et al.
For more about this, see
Jiayao Zhang, Guangxu Zhu, Robert W. Heath Jr., and Kaibin Huang,
Grassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learning
https://arxiv.org/pdf/1808.02229.pdf
Thanks, James. Do you know this paper? They also consider geometry https://www.researchgate.net/publication/263851398.
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