Structured low rank approximation of non-negative matrices

In this paper we construct structured low rank matrix that is nearest to a given data matrix. The problem arises in various applications, ranging from linear system identification to language processing to computer algebra, where the data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected in the original system. The task to retrieve useful information while maintaining the underlying physical feasibility often necessitates search for a good structured lower rank approximation of the data matrix. This paper addresses some of the numerical issues involved in the problem. A new method to determine optimal non-negative low-rank approximations of non-negative matrices is presented, by SQP method which converge rapidly. This paper studies various methods for solving our problem that attempt to combine the best features of all these methods. Comparative numerical results are also reported.