Singular Value Decomposition and Its Visualization
Singular Value Decomposition and Its Visualization
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DOI：
10.1198/106186007x256080
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发表时间：
2007-12
影响因子：
2.4
通讯作者：
Lingsong Zhang;J. Marron;Haipeng Shen;Zhengyuan Zhu-
中科院分区：
文献类型：
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作者：
Lingsong Zhang;J. Marron;Haipeng Shen;Zhengyuan Zhu-
奇异值分解 (SVD) 是函数数据分析 (FDA) 中的有用工具。与主成分分析 (PCA) 相比，SVD 更为基础，因为 SVD 同时提供行空间和列空间中的 PCA。我们从 FDA 的角度比较 SVD 和 PCA，并通过考虑不同的中心将通常的 SVD 扩展到变化。提出了广义碎石图以在实践中选择合适的中心。引入了 SVD 组件的几个有用的矩阵视图来探索数据中的不同特征，包括 SVD 曲面图、图像图、曲线影片和旋转影片。这些方法同时可视化双向矩阵的列和行信息，将矩阵与相关曲线联系起来，显示局部变化，并突出显示列和行之间的相互作用。设计了几个玩具示例来比较 SVD 的不同变体，并使用真实数据示例来说明可视化方法的有用性。
Singular value decomposition (SVD) is a useful tool in functional data analysis (FDA). Compared to principal component analysis (PCA), SVD is more fundamental, because SVD simultaneously provides the PCAs in both row and column spaces. We compare SVD and PCA from the FDA view point, and extend the usual SVD to variations by considering different centerings. A generalized scree plot is proposed to select an appropriate centering in practice. Several useful matrix views of the SVD components are introduced to explore different features in data, including SVD surface plots, image plots, curve movies, and rotation movies. These methods visualize both column and row information of a two-way matrix simultaneously, relate the matrix to relevant curves, show local variations, and highlight interactions between columns and rows. Several toy examples are designed to compare the different variations of SVD, and real data examples are used to illustrate the usefulness of the visualization methods.