Matrix Completion with Ordering Relation Constraints and its Applications
Yizhen Huang, Yepeng Guan, Jiawen Wang · International Journal of Pattern Recognition and Artificial Intelligence · 2015
We relax the equality constraints in the very general and well-known affine Schatten p-norm minimization problem into complete loss function-based constraints. Owing to the imposed equality constraints, existing methods only have limited degree of model flexibility, via their optimization of the objective energy function. By our proposed transformation, the decision variables in the objective function can directly achieve L0 norm minimization via the process of enumerating the matrix rank (i.e. matrix ordering constraint). We show that, our new objective function is still reasonable, and its minimum can be obtained by a more general form of the Fixed-Point Continuation framework with almost the same computational cost at each matrix order enumeration. Experiments show that, our algorithm has good performance compared to its predecessor over some datasets and applications.