Vector space model: Difference between revisions

Revision as of 15:54, 20 October 2022

Revision as of 10:38, 25 November 2022

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:<math>\mathrm{cos}(d_j,q) = \frac{\mathbf{d_j} \cdot \mathbf{q}}{\left\| \mathbf{d_j} \right\| \left \| \mathbf{q} \right\|} = \frac{\sum _{i=1}^N w_{i,j}w_{i,q}}{\sqrt{\sum _{i=1}^N w_{i,j}^2}\sqrt{\sum _{i=1}^N w_{i,q}^2}}</math>

As all vectors under consideration by this model are element -wise nonnegative, a cosine value of zero means that the query and document vector are [[orthogonal]] and have no match (i.e. the query term does not exist in the document being considered). See [[cosine similarity]] for further information.

== Term frequency-inverse document frequency weights==