CAJ | 학술논문

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。
위료경호지해결고유수거구진저질희소분해문제，해문제출이Max-범수철화질함수적Max겁소화모형，병급출해모형적상응산법。재대신모형계산복잡성분석적기출상，해문진일보제출료Max약속모형，개진모형불부재분해문제중효과량호，차상응적투영제도산법구유경강적시효성。실험결과표명，해문제출적량조모형대우저질희소분해문제균행지유효。
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.