The Research On A Kind Of Rank-Constrained Approximation Problem And Solving Method

As a technology for obtaining low rank denotation of extremely large matrix, Low-Rank Approximation plays an important role in many fields such as pattern recognition, machine learning and data mining. It is frequently used by human to discover the essential principal message which is deeply hidden in complicated data. As we all know, the best Low-rank Approximation of matrix A is its truncated SVD decomposition. In this paper, a new Low-Rank Approximation problem is proposed from another different angle, which can be used in semi-supervised problem.In this paper, I will give a brief introduction about the background and the existing research work of Low-Rank Approximation at first, then I will review matrix completely orthogonal decomposition and some classical conclutions about the usual Low-Rank Approximation problem. After this, from the proposed problem with unconstrained, I will consider the proposed constrained problem step by step. At last, the algorithm and perturbation analysis of the proposed problem in this paper will be given.