SENSC: a Stable and Efficient Algorithm for Nonnegative Sparse Coding
SENSC: 一个稳定高效的非负稀疏编码算法

Nonnegative sparse coding (NSC) has been successfully applied to many research fields. The applied algorithm for NSC is designed by the combination of gradient projection and auxiliary function-based multiplicative update, so its performance is significantly related to the choice of the iterative step size in gradient projection. Besides, its efficiency can not be very high due to the properties of optimization methods which it uses. To improve the applicability of NSC, we consider the implementation of NSC as alternately minimizing a group of convex hyperparaboloid functions, and propose a stable and efficient NSC algorithm (SENSC) without any user-defined optimization parameter by using the properties of convex hyperparaboloid and the projection formulas from a point to the set of all nonnegative numbers and to the unit super sphere at origin. It is mathematically deduced that SENSC is more efficient than and has solutions superior to the existing algorithm. Its stability and convergence are proven. Experiments have validated theoretical deduction and demonstrated that SENSC is more effective in the control on sparseness of coding results than the existing algorithm.