# How can I interpret the results of LSA?

I implemented LSA (Latent Semantic Analysis) on MATLAB. I have a $$D\times N$$ term-document matrix, where $$D$$: # of words, $$N$$: # of docs. I did low-rank approximation using SVD, and got $$X_k = U_k \cdot S_k \cdot V_k' (D=1000, N=600, K=4)$$

Now I want to classify the documents into 4 classes, and I know I have to use the col-vectors of $$V_k'$$.

Each column of it has 4 values. I think each value indicates how much the document is related to the topic (in latent spaces). Am I right?

But when I see the column's value, it has both positive and negative values. How can I interpret it?

• Yes $V$ does indeed relate on how much each document is related to the topic but it does not have to be strictly positive. I think you just need to read into what $X = U S V^T$ actually means in terms of Linear Algebra; everything will immediately fall into place after that. The Wikipedia article on en.wikipedia.org/wiki/Singular_Value_Decomposition is quite good to start you off. – usεr11852 Apr 19 '14 at 12:54