A constrained non-negative matrix factorization in information retrieval

A novel method, which is called constrained non-negative matrix factorization, is presented to capture the latent semantic relations. An objective function is defined to impose three additional constraints, in addition to the non-negativity constraint in the standard non-negative matrix factorization. The update rules to solve the objective function with these constraints are presented, and its convergence is proved. In contrast to the standard non-negative matrix factorization, the constrained non-negative matrix factorization can capture the semantic relations as orthogonal as possible. The experiments indicate that the constrained non-negative matrix factorization has better precision than the standard non-negative matrix factorization in information retrieval.