finding the space spanned by user profiles of consumed items for making recommendations commences by first estimating a mean and covariance for a set of labeled items associated with a profile . thereafter , a vector is identified that belongs to a convex cone spanned by the user profiles based on the estimated mean and covariance , the labels and items . the labels are mirrored in a negative space defined by the identified vector . the weighted covariance matrix is computed based on the mirrored labels ; and eigenvalues and eigenvectors are computed of the weighted covariance matrix . a first set of eigenvalues share a value and wherein a remainder of the eigenvalues correspond to eigenvectors that span the profile .