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 .
Line charts are commonly used to visualize a series of data values . When the data are noisy, smoothing is applied to make the signal more apparent. Conventional methods used to smooth line charts, e.g., using subsampling or filters, such as median, Gaussian, or low-pass, each optimize for different properties of the data. The properties generally do not include retaining peaks (i.e., local minima and maxima) in the data, which is an important feature for certain visual analytics tasks . We present TopoLines, a method for smoothing line charts using techniques from Topological Data Analysis. The design goal of TopoLines is to maintain prominent peaks in the data while minimizing any residual error. We evaluate TopoLines for 2 visual analytics tasks by comparing to 5 popular line smoothing methods with data from 4 application domains .
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samples
values
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However, the difference between signal and noise is ill-defined, as it depends upon the application domain of the data. Common
Conventional
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such as rank filters, convolutional filters, frequency domain filters, and subsampling, optimize on various
e.g., using subsampling or filters, such as median, Gaussian, or low-pass, each optimize for different
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However, these methods are only ideal in certain limited scenarios
The properties generally do not include retaining peaks (i.e., local minima and maxima) in the data, which is an important feature for certain visual analytics tasks
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by leveraging
using
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smooth line charts while maintaining prominent peaks , as defined by persistent homology,
maintain prominent peaks
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. We compare TopoLines
while minimizing any residual error. We evaluate TopoLines for 2 visual analytics tasks by comparing
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using
with
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. 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