TopoLines: Topological Smoothing for Line Charts
TopoLines: Topological Smoothing for Line Charts
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DOI：
10.2312/evs.20201053
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发表时间：
2019-06
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影响因子：
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通讯作者：
Ashley Suh;Christopher Salgado;Mustafa Hajij;P. Rosen
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文献类型：
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作者：
Ashley Suh;Christopher Salgado;Mustafa Hajij;P. Rosen
折线图通常用于可视化一系列数据样本。当数据有噪声时，应用平滑使信号更明显。然而，信号和噪声之间的区别是不明确的，因为它取决于数据的应用领域。用于平滑折线图的常用方法，如秩滤波器、卷积滤波器、频域滤波器和子采样，对数据的各种属性进行优化。然而，这些方法仅在某些有限的情况下是理想的。我们提出TopoLines，一种利用拓扑数据分析技术平滑折线图的方法。TopoLines的设计目标是平滑折线图，同时保持数据中由持久同源性定义的显著峰值。我们使用来自4个应用领域的数据将TopoLines与5种流行的线平滑方法进行比较。随着简化阈值的变化，我们根据残差的$l^2$-范数来评估TopoLines，并且我们执行用户研究来评估用户对TopoLines准确性的感知。
Line charts are commonly used to visualize a series of data samples. When the data are noisy, smoothing is applied to make the signal more apparent. However, the difference between signal and noise is ill-defined, as it depends upon the application domain of the data. Common methods used to smooth line charts, such as rank filters, convolutional filters, frequency domain filters, and subsampling, optimize on various properties of the data. However, these methods are only ideal in certain limited scenarios. We present TopoLines, a method for smoothing line charts by leveraging techniques from Topological Data Analysis. The design goal of TopoLines is to smooth line charts while maintaining prominent peaks, as defined by persistent homology, in the data. We compare TopoLines to 5 popular line smoothing methods using data from 4 application domains. We evaluate TopoLines in terms of $l^2$-norm of the residual as the simplification threshold is varied, and we perform a user study to evaluate users' perception of the accuracy of TopoLines.