Uncertainty-aware Spectral Visualization

Keywords

Uncertainty, Data visualization, Time series analysis, Visualization, Continuous wavelet transforms, Correlation, Wavelet analysis, Gaussian processes, Spectral analysis, Wavelet domain

Abstract

One common task in time series analysis is the visual investigation of spectra such as Fourier spectra or wavelet spectra to identify dominating frequencies. In this article, we present the propagation of data uncertainty to the spectra and its visualization. We consider the Fourier and continuous wavelet transformations, which are two common spectral analysis methods. Deriving the propagation for time series that can be modeled as a Gaussian process leads to a combination of weighted non-central chi-squared distributions in the spectrum. Percentile-based visualizations explicitly encode the non-normal uncertainty in the 1D Fourier and 2D wavelet spectrum. We enrich the visualization by including correlations, sensitivity, and signal-to-noise analysis. For visual exploration, we combine the different visualizations into an interactive approach that allows for investigating the uncertain time series in the temporal and spectral domains. Finally, we show the usefulness of our approach by applying it to several real-world data sets and by a qualitative interview study with visualization experts.