Finding the space spanned by user profiles from binary feedback

A method for finding the space spanned by user profiles, comprising:

• estimating a mean and covariance for a set of labeled items associated with a profile;
• identifying a vector that belongs to a convex cone spanned by the user profiles based on the estimated mean and covariance, the labels and items;
• mirroring the labels in a negative space defined by the identified vector;
• computing a weighted covariance matrix based on the mirrored labels;
• and
• computing eigenvalues and eigenvectors of the weighted covariance matrix, wherein a first set of eigenvalues share a value and wherein a remainder of the eigenvalues correspond to eigenvectors that span the profile.

A non-transitory computer readable storage medium comprising a computer readable program for finding the space spanned by user profiles, wherein the computer readable program when executed on a computer causes the computer to perform the steps of:

• estimating a mean and covariance for a set of labeled items associated with a profile;
• identifying a vector that belongs to a convex cone spanned by the user profiles based on the estimated mean and covariance, the labels and items;
• mirroring the labels in a negative space defined by the identified vector;
• computing a weighted covariance matrix based on the mirrored labels;
• and
• computing eigenvalues and eigenvectors of the weighted covariance matrix, wherein a first set of eigenvalues share a value and wherein a remainder of the eigenvalues correspond to eigenvectors that span the profile.