Visual Analytics for Correlation-Based Comparison of Time Series Ensembles
An established approach to studying interrelations between two non‐stationary time series is to compute the ‘windowed’ cross‐correlation (WCC). The time series are divided into intervals and the cross‐correlation between corresponding intervals is calculated. The outcome is a matrix that describes t...
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| Published in | Computer graphics forum Vol. 34; no. 3; pp. 411 - 420 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Blackwell Publishing Ltd
01.06.2015
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| Subjects | |
| Online Access | Get full text |
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| Abstract | An established approach to studying interrelations between two non‐stationary time series is to compute the ‘windowed’ cross‐correlation (WCC). The time series are divided into intervals and the cross‐correlation between corresponding intervals is calculated. The outcome is a matrix that describes the correlation between two time series for different intervals and varying time lags. This important technique can only be used to compare two single time series. However, many applications require the comparison of ensembles of time series. Therefore, we propose a visual analytics approach that extends the WCC to support a correlation‐based comparison of two ensembles of time series. We compute the pairwise WCC between all time series from the two ensembles, which results in hundreds of thousands of WCC matrices. Statistical measures are used to derive a concise description of the time‐varying correlations between the ensembles as well as the uncertainty of the correlation values. We further introduce a visually scalable overview visualization of the computed correlation and uncertainty information. These components are combined with multiple linked views into a visual analytics system to support configuration of the WCC as well as detailed analysis of correlation patterns between two ensembles. Two use cases from very different domains, cognitive science and paleoclimatology, demonstrate the utility of our approach. |
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| AbstractList | An established approach to studying interrelations between two non-stationary time series is to compute the 'windowed' cross-correlation (WCC). The time series are divided into intervals and the cross-correlation between corresponding intervals is calculated. The outcome is a matrix that describes the correlation between two time series for different intervals and varying time lags. This important technique can only be used to compare two single time series. However, many applications require the comparison of ensembles of time series. Therefore, we propose a visual analytics approach that extends the WCC to support a correlation-based comparison of two ensembles of time series. We compute the pairwise WCC between all time series from the two ensembles, which results in hundreds of thousands of WCC matrices. Statistical measures are used to derive a concise description of the time-varying correlations between the ensembles as well as the uncertainty of the correlation values. We further introduce a visually scalable overview visualization of the computed correlation and uncertainty information. These components are combined with multiple linked views into a visual analytics system to support configuration of the WCC as well as detailed analysis of correlation patterns between two ensembles. Two use cases from very different domains, cognitive science and paleoclimatology, demonstrate the utility of our approach. |
| Author | Sips, M. Schinkel, S. Marwan, N. Witt, C. Dransch, D. Köthur, P. |
| Author_xml | – sequence: 1 givenname: P. surname: Köthur fullname: Köthur, P. organization: GFZ German Research Center for Geosciences, Potsdam, Germany – sequence: 2 givenname: C. surname: Witt fullname: Witt, C. organization: GFZ German Research Center for Geosciences, Potsdam, Germany – sequence: 3 givenname: M. surname: Sips fullname: Sips, M. organization: GFZ German Research Center for Geosciences, Potsdam, Germany – sequence: 4 givenname: N. surname: Marwan fullname: Marwan, N. organization: Potsdam Institute for Climate Impact Research, Potsdam, Germany – sequence: 5 givenname: S. surname: Schinkel fullname: Schinkel, S. organization: Potsdam Institute for Climate Impact Research, Potsdam, Germany – sequence: 6 givenname: D. surname: Dransch fullname: Dransch, D. organization: GFZ German Research Center for Geosciences, Potsdam, Germany |
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| CitedBy_id | crossref_primary_10_1080_17538947_2017_1327618 crossref_primary_10_1016_j_visinf_2023_09_001 crossref_primary_10_1016_j_jbi_2021_103941 crossref_primary_10_1016_j_visinf_2018_04_002 crossref_primary_10_3724_SP_J_1089_2022_19501 crossref_primary_10_1016_j_compag_2017_09_035 crossref_primary_10_1111_cgf_13397 crossref_primary_10_1016_j_visinf_2022_10_002 crossref_primary_10_1145_3265748 crossref_primary_10_1109_TVCG_2017_2779501 crossref_primary_10_1111_cgf_13697 crossref_primary_10_1109_TVCG_2018_2853721 crossref_primary_10_1016_j_visinf_2020_04_004 crossref_primary_10_1007_s00371_024_03670_2 crossref_primary_10_1109_TVCG_2019_2934289 crossref_primary_10_1007_s41060_017_0072_z crossref_primary_10_1007_s11704_020_0088_8 crossref_primary_10_1109_TVCG_2018_2865049 crossref_primary_10_1109_TVCG_2017_2744199 |
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| Copyright | 2015 The Author(s) Computer Graphics Forum © 2015 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2015 The Eurographics Association and John Wiley & Sons Ltd. |
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| References_xml | – reference: MacEachren A.M.: Visualizing uncertain information. Cartographic Perspectives 13 (1992), 10-19. 2 – reference: Kehrer J., Ladstädter F., Muigg P., Doleisch H., Steiner A., Hauser H.: Hypothesis Generation in Climate Research with Interactive Visual Data Exploration. IEEE T. Vis. Comput. Gr. 14, 6 (Nov 2008), 1579-1586. 2, 7 – reference: Shakhnovich E.I., Gutin A.M.: Engineering of stable and fast-folding sequences of model proteins. Proc. NAS 90, 15 (1993), 7195-7199. 1 – reference: Aigner W., Miksch S., Schumann H., Tominski C.: Visualization of time-oriented data. Springer, 2011. 2 – reference: Elmqvist N., Fekete J.-D.: Hierarchical aggregation for information visualization: Overview, techniques, and design guidelines. IEEE T. Vis. Comput. Gr. 16, 3 (May 2010), 439-454. 2, 5 – reference: Lachniet M.S.: Climatic and environmental controls on speleothem oxygen-isotope values. Quaternary Sci. Rev. 28 (2009), 412-432. 8 – reference: Rehfeld K., Marwan N., Heitzig J., Kurths J.: Comparison of correlation analysis techniques for irregularly sampled time series. Nonlinear Proc. Geoph. 18, 3 (2011), 389-404. 4 – reference: Marwan N., Kurths J.: Nonlinear analysis of bivariate data with cross recurrence plots. Phys. Lett. A 302, 5-6 (2002), 299-307. 9 – reference: Hashizume M., Terao T., Minakawa N.: The Indian Ocean Dipole and malaria risk in the highlands of western Kenya. Proc. NAS USA 106, 6 (2009), 1857-62. 1 – reference: Luck S.J.: An introduction to the event-related potential technique. MIT Press, Cambridge, 2005. 7 – reference: Dransch D., Köthur P., Schulte S., Klemann V., Dobslaw H.: Assessing the quality of geoscientific simulation models with visual analytics methods - a design study. Int. J. Geogr. Inf. Sci. 24, 10 (2010), 1459-1479. 2 – reference: MacEachren A.M., Robinson A., Hopper S., Gardner S., Murray R., Gahegan M., Hetzler E.: Visualizing Geospatial Information Uncertainty: What We Know and What We Need to Know. Cartogr. Geogr. Inf. Sci. 32, 3 (2005), 139-160. 2 – reference: Madsen H.: Time Series Analysis. Chapman & Hall/CRC texts in statistical science. Chapman & Hall/CRC, Boca Raton, 2008. 1 – reference: Pang A.T., Wittenbrink C.M., Lodha S.K.: Approaches to uncertainty visualization. Visual Comput. 13, 8 (1997), 370-390. 2 – reference: Novotný M., Hauser H.: Outlier-preserving focus+context visualization in parallel coordinates. IEEE T. Vis. Comput. Gr. 12, 5 (Sept 2006), 893-900. 2, 7 – reference: Boker S.M., Rotondo J.L., Xu M., King K.: Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychol. Methods 7, 3 (2002), 338-355. 1, 4 – reference: De Grandis L.: Theory and use of color. Abrams, 1986. 5 – reference: Höllt T., Magdy A., Zhan P., Chen G., Gopalakrishnan G., Hoteit I., Hansen C.D., Hadwiger M.: Ovis: A framework for visual analysisof ocean forecast ensembles. IEEE T. Vis. Comput. Gr. 20, 8 (2014), 1114-1126. 2 – reference: Zuk T.D.: Visualizing Uncertainty. PhD thesis, University of Calgary, Canada, 2008. AAINR38246. 2 – reference: Schinkel S., Ivanova G., Kurths J., Sommer W.: Modulation of the N170 adaptation profile by higher level factors. Biol. Psychol. 97 (2014), 27-34. 7 – reference: Piringer H., Pajer S., Berger W., Teichmann H.: Comparative visual analysis of 2d function ensembles. Comput. Graph. Forum 31, 3pt3 (2012), 1195-1204. 2 – reference: Sanyal J., Zhang S., Dyer J., Mercer A., Amburn P., Moorhead R.J.: Noodles: A Tool for Visualization of Numerical Weather Model Ensemble Uncertainty. IEEE T. Vis. Comput. Gr. 16, 6 (2010), 1421-1430. 2 – reference: Goswami B., Marwan N., Feulner G., Kurths J.: How do global temperature drivers influence each other? - A network perspective using recurrences. Eur. Phys. J. - Special Topics 222 (2013), 861-873. 1, 9 – reference: Kehrer J., Hauser H.: Visualization and visual analysis of multifaceted scientific data: A survey. IEEE T. Vis. Comput. Gr. 19, 3 (March 2013), 495-513. 2 – reference: Zubair L., Galappaththy G.N., Yang H., Chandimala J., Yahiya Z., Amerasinghe P., Ward N., Connor S.J.: Epochal changes in the association between malaria epidemics and el niño in sri lanka. Malaria J. 7, 1 (2008), 140. 1 – reference: Matković K., Gračanin D., Jelović M., Ammer A., Lež A., Hauser H.: Interactive visual analysis of multiple simulation runs using the simulation model view: Understanding and tuning of an electronic unit injector. IEEE T. Vis. Comput. 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| Snippet | An established approach to studying interrelations between two non‐stationary time series is to compute the ‘windowed’ cross‐correlation (WCC). The time series... An established approach to studying interrelations between two non-stationary time series is to compute the 'windowed' cross-correlation (WCC). The time series... |
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| SubjectTerms | Analysis Analytics Categories and Subject Descriptors (according to ACM CCS) Computer graphics Correlation Correlation analysis I.3.8 [Computer Graphics]: Applications Intervals Mathematical analysis Studies Time series Uncertainty Visual Visualization |
| Title | Visual Analytics for Correlation-Based Comparison of Time Series Ensembles |
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