In wikipedia: https://en.wikipedia.org/wiki/Latent_semantic_analysis

it is mentioned in Derivation section "....You can now do the following: See how related documents j and q are in the low-dimensional space by comparing the vectors $\Sigma_{k} d^{'}_{j}$ and $\Sigma_{k} d^{'}_{q}$ (typically by cosine similarity).

My question is: as we already have the embedding vectors for both $d^{'}_{j}$ and $d^{'}_{q}$ so why do we need to multiply them by $\Sigma_{k}$ for comparing them, I think we can apply cosine similarity directly without multiplying by $\Sigma_{k}$ ?


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