Uncertainty-Aware Spectral Visualization

Area of Science:

• Data analysis and visualization
• Time series analysis
• Spectral analysis

Background:

• Visualizing spectra like Fourier and wavelet spectra is crucial for identifying dominant frequencies in time series data.
• Quantifying and visualizing data uncertainty in spectral analysis remains a challenge.

Purpose of the Study:

• To develop and visualize the propagation of data uncertainty to Fourier and continuous wavelet spectra.
• To create an interactive approach for exploring uncertain time series data in both temporal and spectral domains.

Main Methods:

• Modeling time series as Gaussian processes to derive uncertainty propagation in spectra.
• Utilizing percentile-based visualizations to encode non-normal uncertainty in 1D Fourier and 2D wavelet spectra.
• Incorporating correlation, sensitivity, and signal-to-noise analysis into visualizations.

Main Results:

• The propagation of uncertainty results in weighted non-central chi-squared distributions within the spectrum.
• Percentile-based visualizations effectively display non-normal uncertainty.
• An interactive visualization tool was developed for exploring uncertain time series data.

Conclusions:

• The proposed method provides a robust way to visualize data uncertainty in spectral analysis.
• The interactive approach enhances the investigation of time series data with uncertainty.
• The approach was validated through real-world data sets and expert interviews.