How to normalize results of Singular Value Decomposition (SVD) between 0 and 1?

Question

I'm building a recommender system and using SVD as one of the preprocessing techniques. However, I want to normalize all my preprocessed data between 0 and 1 because all of my similarity measures (cosine, pearson, euclidean) depend on that assumption.

After I take the SVD (A = USV^T), is there a standard way to normalize the matrix 'A' between 0 and 1? Thanks!

Edit: I want all of my similarity measurements to give results between 0 and 1 and my normalized euclidean distance in particular fails if the input matrix does not have values between 0 and 1.

Answer 1

Singular Value Decomposition is a linear algebraic technique as a result of which the notion of normalization is hard to define. In principle, you can do this normalization by dividing each element A(i,j) of the matrix by the sum (or max) of the elements in that particular (ith) row, i.e. A(i,j) = A(i, j) / \sum_{k=1}^{n} A(i,k)

However, a more elegant way to achieve this would be to apply a probabilistic dimensionality reduction technique such as PLSA or LDA. These dimensionality reduction techniques ensure that you always end up with probability values strictly between 0 and 1.