基于最大范数的低秩稀疏分解模型

摘要

为了更好地解决高维数据矩阵低秩稀疏分解问题，该文提出以Max-范数凸化秩函数的Max极小化模型，并给出该模型的相应算法。在对新模型计算复杂性分析的基础上，该文进一步提出了Max约束模型，改进模型不仅在分解问题中效果良好，且相应的投影梯度算法具有更强的时效性。实验结果表明，该文提出的两组模型对于低秩稀疏分解问题均行之有效。%In order to better solve the low-rank and sparse decomposition problem for high-dimensional data matrix, this paper puts forward a novel Max minimization model with Max-norm as the convex relaxation of the rank function, and provides the corresponding algorithm. Based on the complexity analysis on the novel model, an improved Max constraint model is further proposed, which not only has good performance in the decomposition problem but also can be solved with a fast projection gradient method. The experimental results show that the proposed two models are effective for low-rank sparse decomposition problem.