A multi-objective memetic algorithm for low rank and sparse matrix decomposition
A multi-objective memetic algorithm for low rank and sparse matrix decomposition
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DOI：
10.1016/j.ins.2018.08.037
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发表时间：
2018-11
期刊：
影响因子：
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通讯作者：
Tao Wu;Jiao Shi;Xiangming Jiang;Deyun Zhou;Maoguo Gong
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文献类型：
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作者：
Tao Wu;Jiao Shi;Xiangming Jiang;Deyun Zhou;Maoguo Gong
低秩稀疏矩阵分解因其在探索局部分量和全局分量方面的独特性质，在许多研究领域受到越来越多的关注。该问题的目标由两个相互冲突的项组成，即低秩项和稀疏项，以往的方法大多将这两个项组合成一个带权参数的标量目标。然而，权重参数的预置是一个困难的任务，因为在优化之前，关于两个项的任何先验知识都是不可用的。本文建立了一种基于奇异值编码的多目标低秩稀疏矩阵分解模型。构造了两个相互冲突的目标来寻找给定数据矩阵的低排序和稀疏分量。为了同时最小化两个目标，提出了一种新的多目标模因算法，该算法对低秩矩阵的奇异值进行编码。该方法可以得到一系列不同的低阶和稀疏分量的折衷解，决策者可以直接从中选择满意的解。实验结果表明，该方法是有效的，在分解精度和解的多样性方面都优于现有的一些方法。
Low rank and sparse matrix decomposition is increasingly concerned in many research fields for its particular properties in exploring local and global components. The objective of this problem consists of two conflicting terms, the low rank term and the sparse term, most of the previous methods combine these two terms into a scalar objective with weight parameter. However, the preset of weight parameter is a difficult task because any priori knowledge about two terms is unavailable before optimization. In this paper, we establish a singular value encoding based multi-objective low rank and sparse matrix decomposition model. Two conflicting objectives are constructed to find the low rank and sparse components of the given data matrix. A novel multi-objective memetic algorithm, which encodes the singular value of the low rank matrix, is proposed to minimize two objectives simultaneously. The proposed method can obtain a series of different trade-off solutions between low rank and sparse components, and decision makers can choose satisfying solution from them directly. The experimental results demonstrate that the proposed method is effective and has better performance than some existing approaches in terms of the decomposition accuracy and the diversity of solutions.