Recommender Systems: Does using Singular Value Decomposition rule out the possibility of using Euclidean Distance as way of measuring similarity?

Question

I'm learning about recommender systems and learning about different similarity algorithms. Euclidean distance would change as the scale of the objects being compared changes. In that case, would SVD (Singular Value Decomposition) and Euclidean Distance be incompatible?

Singular Value Decomposition is the multiplication of matrices U*S*V. U and V are orthonormal matrices (which do not alter the scale) but S is scaled diagonally by the eigenvalues.

Please correct me if I've misunderstood something here. Thanks!

Answer 1

SVD and Euclidean Distance are two different algorithms for recommendation systems. You would use one or the other - not both. The same goes for Cosine Similarity, Pearson Correlation, or any other similarity measure -- you would only use one of them (unless you happened to require another similarity measure).

After getting the SVD, you would multiply out the matrices USV and use the entries of the resultant matrix as the predicted values. So if you were trying to predict how many of a particular item a user would buy (based on a user x item matrix), you would simply look at the corresponding entry in the SVD of the matrix.