Visualization and Outlier Detection for Multivariate Elastic Curve Data.
Visualization and Outlier Detection for Multivariate Elastic Curve Data.
复制标题
可视化和多元弹性曲线数据的异常检测。
DOI：
10.1109/tvcg.2019.2921541
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发表时间：
2020-11
影响因子：
5.2
通讯作者：
Kurtek S
中科院分区：
文献类型：
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作者：
Xie W;Chkrebtii O;Kurtek S
我们提出了一种新的方法，用于弹性曲线数据的几何激励箱形图显示的建设和可视化。我们使用最近的形状分析框架，基于曲线的平方根速度函数表示，从弹性曲线，其中包括位置，规模，形状，方向和参数化提取不同的变异源。然后，我们专注于构建单独的显示这些不同的组件使用黎曼几何的表示空间。这涉及基于几何考虑的中位数、两个四分位数和两个极值的计算。弹性曲线的外向度也是基于五个分量中的每一个单独定义的。我们评估所提出的方法，使用多个模拟，然后把我们的注意力集中在真实的数据应用。特别是，我们研究（a）3D螺旋，（B）手写签名，（c）从扩散张量磁共振成像的3D纤维，和（d）洛伦兹系统的轨迹的变化。
We propose a new method for the construction and visualization of geometrically-motivated boxplot displays for elastic curve data. We use a recent shape analysis framework, based on the square-root velocity function representation of curves, to extract different sources of variability from elastic curves, which include location, scale, shape, orientation and parametrization. We then focus on constructing separate displays for these various components using the Riemannian geometry of their representation spaces. This involves computation of a median, two quartiles, and two extremes based on geometric considerations. The outlyingness of an elastic curve is also defined separately based on each of the five components. We evaluate the proposed methods using multiple simulations, and then focus our attention on real data applications. In particular, we study variability in (a) 3D spirals, (b) handwritten signatures, (c) 3D fibers from diffusion tensor magnetic resonance imaging, and (d) trajectories of the Lorenz system.