The algorithm for text topic discovery is based on the SVD. One of the factors of the SVD gives a numTerm by K(number of topics) matrix of weights or loadings. That matrix is rotated to increase the separation between large and small term weights in each of those vectors. Terms with a larger weight in each of the K vectors "define" the topic and these vectors can be multiplied with any given document vector to produce document scores for its membership in each topic.
