# I Which reduced vector should be used in cosine similarity?

1. Oct 27, 2016

In Latent semantic analysis, the truncated singular value decomposition (SVD) of a term-document matrix $A_{mn}$ is
$$A=U_rS_rV^T_r$$
In many references including wikipedia, the new reduced document column vector in r-space is scaled by the singular value $S$ before comparing it with other vectors by cosine similarity. This yields $q^T_r S$ where $q^T_r$ is just the component of a column vector of the $V^T_r$ matrix. and $S$ is the corresponding singular value.
But in other references, only $q^T_r$ is used for cosine similarity. which one of them is more appropriate and why?

2. Nov 1, 2016