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Alexander Kirillov edited bf_Abstract_The_goal_of__.tex
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the neural-networks language-modeling crowd, we had to struggle quite a bit to
figure out the rationale behind the equations.
We show how to consider similarity between
features for calculation of similarity of objects in the Vector Space Model (VSM) for machine
learning algorithms
and other classes of methods that involve similarity between objects. Unlike LSA, we assume
that similarity
between features is known (say, from a synonym dictionary) and does not need to be learned from the data.
We call the proposed similarity measure soft similarity.
Similarity between features is common, for example, in
natural language processing: words, n-grams, or syntactic n-grams can be somewhat different (which makes
them different features) but still have much in common:
for example, words “play” and “game” are different but
related. When there is no similarity between features
then our soft similarity measure is equal to the standard
similarity. For this, we generalize the well-known cosine
similarity measure in VSM by introducing what we call
“soft cosine measure”. We propose various formulas
for exact or approximate calculation of the soft cosine
measure. For example, in one of them we consider
for VSM a new feature space consisting of pairs of
the original features weighted by their similarity. Again,
for features that bear no similarity to each other, our
formulas reduce to the standard cosine measure.
\bf{Can we make this intuition more precise? We’d really like to see something
more formal. Goldberg, Levy. 2014. Литература № 4}