Collaborative filtering with hashing

Systems, methods, and machine readable and executable instructions are provided for collaborative filtering. Collaborative filtering includes representing users and objects by rows and columns in an ordinal ratings matrix having a particular dimensional space. Values in the ordinal ratings matrix are weighted with a weight matrix having the particular dimensional space. The weight matrix is hashed into a lower dimensional space by one of row and column by multiplying a projection matrix by the weight matrix. The ordinal ratings matrix is hashed into a lower dimensional space by multiplying the projection matrix by an element-wise product of the weight matrix and the ordinal ratings matrix to form a reduced ratings matrix, and element-wise dividing the reduced ratings matrix by the hashed weight matrix. The hashed ordinal ratings matrix and the hashed weight matrix are low-rank approximated by alternating least squares. A result of the low-rank approximation for the one of row and column is updated using the ordinal ratings matrix and the weight matrix. A recommendation of one of the objects can be generated for one of the users based on the updated result.