计算机辅助设计与图形学学报
計算機輔助設計與圖形學學報
계산궤보조설계여도형학학보
Journal of Computer-Aided Design & Computer Graphics
2015年
11期
2065-2076
,共12页
广义低秩逼近%缺失成分%重构误差%迭代优化算法
廣義低秩逼近%缺失成分%重構誤差%迭代優化算法
엄의저질핍근%결실성분%중구오차%질대우화산법
generalized low-rank approximation%missing components%reconstruction error%iterative algorithm
针对在许多实际应用中数据以矩阵形式而非向量形式存在的问题, 重点讨论含缺失成分的矩阵低秩逼近问题的广义版本, 即如何对一组含缺失成分的矩阵进行低秩逼近. 首先构造一个最优化问题来表达原始的广义低秩逼近问题, 该最优化问题最小化输入矩阵组中已知成分的总重构误差; 然后提出了一种迭代优化算法来求解上述的最优化问题; 最后给出详细的算法分析. 大量的模拟实验与真实图像实验结果表明, 文中算法具有较好的性能.
針對在許多實際應用中數據以矩陣形式而非嚮量形式存在的問題, 重點討論含缺失成分的矩陣低秩逼近問題的廣義版本, 即如何對一組含缺失成分的矩陣進行低秩逼近. 首先構造一箇最優化問題來錶達原始的廣義低秩逼近問題, 該最優化問題最小化輸入矩陣組中已知成分的總重構誤差; 然後提齣瞭一種迭代優化算法來求解上述的最優化問題; 最後給齣詳細的算法分析. 大量的模擬實驗與真實圖像實驗結果錶明, 文中算法具有較好的性能.
침대재허다실제응용중수거이구진형식이비향량형식존재적문제, 중점토론함결실성분적구진저질핍근문제적엄의판본, 즉여하대일조함결실성분적구진진행저질핍근. 수선구조일개최우화문제래표체원시적엄의저질핍근문제, 해최우화문제최소화수입구진조중이지성분적총중구오차; 연후제출료일충질대우화산법래구해상술적최우화문제; 최후급출상세적산법분석. 대량적모의실험여진실도상실험결과표명, 문중산법구유교호적성능.
Considering that data used in many applications are intrinsically in matrix form rather than in vector form, this paper focuses on the generalized version of the problem of a low-rank approximation of a matrix with missing components, i.e. low-rank approximations of a set of matrices with missing components. This generalized problem is formulated as an optimization problem at first, which minimizes the total reconstruction error of the known components in these matrices. Then, an iterative algorithm is designed for calculating the generalized low-rank approximations of matrices with missing components, called GLRAMMC. Finally, detailed algorithmic analysis is given. Extensive experimental results on synthetic data as well as on real image data show the effectiveness of our proposed algorithm.