| 基于谱正则化算法的大数据矩阵完备化研究 |
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| 引用本文： | 王金甲,闫利霄,洪文学. 基于谱正则化算法的大数据矩阵完备化研究[J]. 燕山大学学报, 2014, 0(5): 428-431 |
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| 作者姓名： | 王金甲 闫利霄 洪文学 |
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| 作者单位： | 燕山大学信息科学与工程学院;燕山大学电气工程学院; |
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| 基金项目： | 国家自然科学基金资助项目(61473339);中国博士后科学基金资助项目(2014M561202);河北省2014年度博士后专项资助项目(B2014010005);首批“河北省青年拔尖人才”资助项目 |
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| 摘 要： | 矩阵完备化是基于部分观测数据来完成全部矩阵预测的问题.随着互联网技术的发展,大数据时代的来临,大数据矩阵中大多数据依然是空白的,需要补充,即大数据存在矩阵完备化的问题.本文利用谱正则化模型和算法来解决大数据的矩阵完备化问题,该方法将矩阵完备化问题整理成核范数最小二乘问题,再通过截断奇异值分解、软输入算法和硬输入算法给出了一系列正则化低秩解.最后基于实际的Netflix 大数据的实验结果证明了本文的方法.
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| 关 键 词： | 大数据 矩阵完备化 谱正则化 核范数 截断奇异值分解 |
Big data matrix completion based on spectral regularization algorithm |
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| Affiliation: | WANG Jin-jia, YAN Li-xiao, HONG Wen-xue(1. College of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China;2. College of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China ) |
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| Abstract: | Matrix completion is based on the observed data to complete the forecast problem of the matrix. Now, with the developmentof Internet technology, the time of big data is coming, but the most data in the big data matrix is still blank, and need tosupplement. Namely, it is matrix completion problem of big data. The spectral regularization model is used to solve the matrixcompletion problemof big data. This model turns matrix completion probleminto nuclear regularized least squares problem. Andthe series of regularization low-rank solution are given by the truncated singular value decomposition using the convex relaxationtechnique. The experimental results of the Netflix big data proved the proposed method. |
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| Keywords: | big data matrix completion spectral regularization nuclear norm truncated singular value decomposition |
| 本文献已被 CNKI 维普 等数据库收录！ |
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