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2022 | OriginalPaper | Chapter

4. Fisher-Shannon Analysis

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Abstract

This chapter discusses the Fisher-Shannon analysis, an effective and computationally efficient data exploration tool based on IT quantities. This method is highly versatile and can be used in various situations such as time series discrimination, complexity quantification, detection of non-linear relationships, generation of time series features, detection of dynamical changes and non-stationarity tracking of a signal.

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Footnotes
1
In this subsection, all physical interpretations were provided by Dr. Dasaraden Mauree and Dr. Luciano Telesca.
 
Literature
5.
go back to reference Cover TM, Thomas JA (2006) Elements of information theory (Wiley series in telecommunications and signal processing). Wiley- Interscience, New York, NY, USA, isbn: 0471241954 Cover TM, Thomas JA (2006) Elements of information theory (Wiley series in telecommunications and signal processing). Wiley- Interscience, New York, NY, USA, isbn: 0471241954
7.
go back to reference Esquivel RO, Angulo JC, Antolín J, Dehesa JS, López-Rosa S, Flores-Gallegos N (2010) Analysis of complexity measures and information planes of selected molecules in position and momentum spaces. Phys Chem Chem Phys 12(26):7108–7116. https://doi.org/10.1039/B927055H Esquivel RO, Angulo JC, Antolín J, Dehesa JS, López-Rosa S, Flores-Gallegos N (2010) Analysis of complexity measures and information planes of selected molecules in position and momentum spaces. Phys Chem Chem Phys 12(26):7108–7116. https://​doi.​org/​10.​1039/​B927055H
14.
go back to reference Telesca L, Chamoli A, Lovallo M, Stabile TA (2015) Investigating the tsunamigenic potential of earthquakes from analysis of the informational and multifractal properties of seismograms. Pure Appl Geophys 172(7):1933–1943, issn: 1420-9136. https://doi.org/10.1007/s00024-014-0862-3 Telesca L, Chamoli A, Lovallo M, Stabile TA (2015) Investigating the tsunamigenic potential of earthquakes from analysis of the informational and multifractal properties of seismograms. Pure Appl Geophys 172(7):1933–1943, issn: 1420-9136. https://​doi.​org/​10.​1007/​s00024-014-0862-3
17.
go back to reference Lovallo M, Shaban A, Darwich T, Telesca L (2013) Investigating the time dynamics of monthly rainfall time series observed in northern lebanon by means of the detrended fluctuation analysis and the Fisher-Shannon method. Acta Geophys 61(6):1538–1555, issn: 1895-7455. https://doi.org/10.2478/s11600-012-0094-9 Lovallo M, Shaban A, Darwich T, Telesca L (2013) Investigating the time dynamics of monthly rainfall time series observed in northern lebanon by means of the detrended fluctuation analysis and the Fisher-Shannon method. Acta Geophys 61(6):1538–1555, issn: 1895-7455. https://​doi.​org/​10.​2478/​s11600-012-0094-9
18.
go back to reference Pierini JO, Scian B, Lovallo M, Telesca L (2011) Discriminating climato- logical regimes in rainfall time series by using the Fisher-Shannon method. Int J Phys Sci 6(34):7799–7804 Pierini JO, Scian B, Lovallo M, Telesca L (2011) Discriminating climato- logical regimes in rainfall time series by using the Fisher-Shannon method. Int J Phys Sci 6(34):7799–7804
19.
22.
go back to reference Telesca L, Lovallo M (2013) Fisher-Shannon analysis of wind records. Int J Energy Stat vol 01(04):281–290 Telesca L, Lovallo M (2013) Fisher-Shannon analysis of wind records. Int J Energy Stat vol 01(04):281–290
23.
go back to reference Telesca L, Caggiano R, Lapenna V, Lovallo M, Trippetta S, Macchiato M (2009) Analysis of dynamics in Cd, Fe, and Pb in particulate matter by using the Fisher-Shannon method. Water, Air, Soil Pollut 201:33–41 Telesca L, Caggiano R, Lapenna V, Lovallo M, Trippetta S, Macchiato M (2009) Analysis of dynamics in Cd, Fe, and Pb in particulate matter by using the Fisher-Shannon method. Water, Air, Soil Pollut 201:33–41
24.
go back to reference Le ND, Zidek JV (2006) Statistical analysis of environmental space-time processes. Springer Science & Business Media Le ND, Zidek JV (2006) Statistical analysis of environmental space-time processes. Springer Science & Business Media
25.
go back to reference Lehmann E (1999) Elements of large-sample theory, Springer Texts in Statistics. Springer, New York, isbn: 978-0-387-98595-4 Lehmann E (1999) Elements of large-sample theory, Springer Texts in Statistics. Springer, New York, isbn: 978-0-387-98595-4
27.
go back to reference Zamir R (1998) A proof of the Fisher information inequality via a data processing argument. IEEE Trans Inf Theory 44:1246–1250MathSciNetCrossRef Zamir R (1998) A proof of the Fisher information inequality via a data processing argument. IEEE Trans Inf Theory 44:1246–1250MathSciNetCrossRef
30.
go back to reference P. K. Bhattacharya PK (1967) Estimation of a probability density function and its derivatives. Sankhyā: Indian J Stat, Ser A (1961–2002), 29(4):373–382 P. K. Bhattacharya PK (1967) Estimation of a probability density function and its derivatives. Sankhyā: Indian J Stat, Ser A (1961–2002), 29(4):373–382
32.
go back to reference Prakasa Rao B (1983) Nonparametric functional estimation, Probability and mathematical statistics: a series of monographs and textbooks. Academic Press Prakasa Rao B (1983) Nonparametric functional estimation, Probability and mathematical statistics: a series of monographs and textbooks. Academic Press
35.
go back to reference Wand M, Jones M (1994) Kernel smoothing. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Taylor & Francis, isbn: 9780412552700 Wand M, Jones M (1994) Kernel smoothing. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Taylor & Francis, isbn: 9780412552700
36.
go back to reference Sheather SJ, Jones MC (1991) A reliable data-based bandwidth selection method for kernel density estimation. J R Stat Soc Ser B (Methodological) 53(3):683–690, issn: 00359246 Sheather SJ, Jones MC (1991) A reliable data-based bandwidth selection method for kernel density estimation. J R Stat Soc Ser B (Methodological) 53(3):683–690, issn: 00359246
37.
go back to reference Kantz H, Schreiber T (2004) Nonlinear time series analysis. Cambridge university Press, vol 7 Kantz H, Schreiber T (2004) Nonlinear time series analysis. Cambridge university Press, vol 7
38.
go back to reference Marron JS, Wand MP (1992) Exact mean integrated squared error. Ann Stat 712–736 Marron JS, Wand MP (1992) Exact mean integrated squared error. Ann Stat 712–736
42.
go back to reference Oke TR, Mills G, Christen A, Voogt JA (2017) Urban climates. Cambridge University Press Oke TR, Mills G, Christen A, Voogt JA (2017) Urban climates. Cambridge University Press
44.
go back to reference Guignard F, Lovallo M, Laib M et al (2019) Investigating the time dynamics of wind speed in complex terrains by using the Fisher-Shannon method. Phys A 523:611–621CrossRef Guignard F, Lovallo M, Laib M et al (2019) Investigating the time dynamics of wind speed in complex terrains by using the Fisher-Shannon method. Phys A 523:611–621CrossRef
46.
47.
go back to reference Wikle CK, Zammit-Mangion A, Cressie N (2019) Spatio-temporal Statistics with R, Chapman & Hall/CRC the R series. CRC Press, Taylor & Francis Group Wikle CK, Zammit-Mangion A, Cressie N (2019) Spatio-temporal Statistics with R, Chapman & Hall/CRC the R series. CRC Press, Taylor & Francis Group
Metadata
Title
Fisher-Shannon Analysis
Author
Fabian Guignard
Copyright Year
2022
DOI
https://doi.org/10.1007/978-3-030-95231-0_4