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摘要: 非负稀疏编码(Nonnegative sparse coding, NSC)已成功应用在很多领域的研究中. 目前使用的NSC算法通过梯度投影法和基于辅助函数的乘性更新法相结合来实现, 其性能受迭代步长的影响很大, 且效率较低. 为增强NSC的可应用性, 本文通过对一组凸超抛物面函数做交替最小化来实现NSC, 并依据凸超抛物面特性、点到非负数集合的投影规则以及点到原点处单位超球的投影规则构造了一个无用户定义优化参数的稳定高效的NSC算法---SENSC. 从数学角度, 文中推断了SENSC比现有算法高效且它的解优于当前算法的解, 证明了它的稳定性和收敛性. 实验验证了上述理论推断的正确, 说明了SENSC调节编码稀疏性的能力比已有算法更强.Abstract: 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.
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