What does the "latent" mean in LSI?

Automatic Categorization: Latent Semantic Indexing(LSI) question: how to prove the formula for fitting new vector into LSI space?

• Here is the equation: I do not understand how this formula generated? right hand q is original vector, U is getting from svd, little k means we just need first k column E is also getting from svd, k means just need first k value, left hand q means q in the LSI space. more details yo can check http://nlp.stanford.edu/IR-book/html/htmledition/latent-semantic-indexing-1.html, search 244 I do not understand how this formula generated?

• Answer:

  I am not an expert in LSI but here are my thoughts. The SVD decomposition of CC C is C=UΣVTC=UΣVT C = U \Sigma V ^T . Thus, it is easy to show that V=UΣ−1CTV=UΣ−1CT V = U \Sigma ^{-1} C ^T , which is just a change of base (and just one step before your equation). The same holds for new input vectors.