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Discovery of Structures and Processes in Temporal Data

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Knowledge Discovery in Spatial Data

Part of the book series: Advances in Spatial Science ((ADVSPATIAL))

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Abstract

Beyond any doubt, natural and man-made phenomena change over time and space. In our natural environment, temperature, rainfall, cloud cover, ice cover, water level of a lake, river channel morphology, surface temperature of the ocean, to name but a few examples, all exhibit dynamic changes over time. In terms of human activities, we have witnessed the change of birth rate, death rate, migration rate, population concentration, unemployment, and economic productivity throughout our history. In our interacting with the environment, we have experienced the time varying concentration of various pollutants, usage of natural resource, and global warming. For natural disasters, the occurrence of typhoon, flood, drought, earthquake, and sand storm are all dynamic in time. All of these changes might be seasonal, cyclical, randomly fluctuating, or trend oriented in a local or global scale.

To have a better understanding of and to improve our knowledge about these dynamic phenomena occurring in natural and human systems, we generally make a sequence of observations ordered by a time parameter within certain temporal domain. Time series are a special kind of realization of such variations. They measure changes of variables at points in time. The objectives of time series analysis are essentially the description, explanation, prediction, and perhaps control of the time varying processes. With respect to data mining and knowledge discovery, we are primarily interested in the unraveling of the generating structures or processes of time series data. Our aim is to discover and characterize the underlying dynamics, deterministic or stochastic, that generate the time varying phenomena manifested in chronologically recorded data.

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References

  • Andreo B, Jiménez P, Durán JJ, Carrasco I, Vadillo I, Mangin A (2006) Climatic and hydrological variations during the last 117–166 years in the south of the Iberian Penninsula, for spectral and correlation analyses and continuous wavelet analyses. J Hydrol 324:24–39

    Article  Google Scholar 

  • Angulo JM, Ruiz-Medina MD, Anh VV, Grecksch W (2000) Fractional diffusion and fractional heat equation. Appl Prob 32:1077–1099

    Article  Google Scholar 

  • Anh VV, Leonenko NN (2000) Scaling laws for the fractional diffusion-wave equation with random data. Stat Prob Lett 48:239–252

    Article  Google Scholar 

  • Anh VV, Leonenko NN (2001) Spectral analysis of fractional kinetic equations with random data. J Stat Phys 104(516):1349–1387

    Article  Google Scholar 

  • Anh VV, Duc H, Azzi M (1997a) Modelling anthropogenic trends in air quality data. J Air Waste Manag Assoc 47(1):66–71

    Google Scholar 

  • Anh VV, Gras F, Tsui HT (1996) Multifractal description of natural scenes. Fractals 4(1):35–43

    Article  Google Scholar 

  • Anh VV, Heyde CC, Tieng Q (1999a) Stochastic models for fractal processes. J Stat Plann Infer 80(1/2):123–135

    Article  Google Scholar 

  • Anh VV, Leung Y, Chen D, Yu ZG (2005b) Spatial variability of daily rainfall using multifractal analysis (unpublished paper)

    Google Scholar 

  • Anh VV, Leung Y, Lam KC, Yu ZG (2005b) Multifractal characterization of Hong Kong air quality data. Environmetrics 16:1–12

    Article  Google Scholar 

  • Bacry E, Muzy J, Arneodo A (1993) Singularity spectrum of fractal signals from wavelet analysis: exact results. J Stat Phys 70(314):635–647

    Article  Google Scholar 

  • Bennett RJ (1979) Spatial time series: analysis-forecasting-control. Pion, London

    Google Scholar 

  • Beran J (1992) Statistical methods for data with long-range dependence. Stat Sci 7:404–416

    Article  Google Scholar 

  • Beran J (1994) Statistics for long-memory processes. Chapman and Hall, New York

    Google Scholar 

  • Borgas MS (1992) A comparison of intermittency models in turbulence. Phys Fluid A 4(9):2055–2061

    Article  Google Scholar 

  • Box GEP, Jenkins GM (1976) Time series analysis: forecasting and control. Holden-Day, San Francisco, CA

    Google Scholar 

  • Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis: forecasting and control. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Chen Z, Ivanov PC, Hu K, Stanley HE (2002) Effect of nonstationarities on detrended fluctuation analysis. Phys Rev E 65(4):041107

    Article  Google Scholar 

  • Cihlar J (2000) Land cover mapping of large areas from satellites: status and research priorities. Int J Remote Sens 21(6):1093–1114

    Article  Google Scholar 

  • Daubechies I (1992) Ten lectures on wavelets. Society for industrial and applied mathematics, Philadelphia, Pennsylvania, pp. 357

    Google Scholar 

  • Davis A, Marshak A, Wiscombe W, Cahalan R (1996) Scale in invariance of liquid water distributions in marine stratocumulus. J Atmos Sci 53:1538–1558

    Article  Google Scholar 

  • Djamdji J-P, Bijaoui A, Maniere R (1993) Geometrical registration of images: the multiresolution approach. Photogr Eng Rem Sens 59:645

    Google Scholar 

  • Falco T, Francis F, Lovejoy S, Schertzer D, Kerman B, Drinkwater M (1996) Scale invariance and universal multifractals in sea ice synthetic aperature radar reflectivity fields. IEEE Trans Geosci Rem Sens 34:906–914

    Article  Google Scholar 

  • Falconer KJ (1985) The geometry of fractal sets. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Feder J (1988) Fractals. Plenum Press, New York

    Google Scholar 

  • Fisher Y (ed) (1995) Fractal image compression, theory and application. Springer, New York

    Google Scholar 

  • Frisch U (1995a) Turbulence. Cambridge University Press, Cambridge

    Google Scholar 

  • Frisch U (1995b) Turbulence. The legacy of A. Kolmogorov. Cambridge University Press, Cambridge

    Google Scholar 

  • Fung T, Leung Y, Anh VV, Marafa LM (2001) A multifractal approach for modeling, visualization and prediction of land cover changes with remote sensing data (proposal of a research project)

    Google Scholar 

  • Gaucherel C (2002) Use of wavelet transform for temporal characterization of remote watersheds. J Hydrol 269:101–121

    Article  Google Scholar 

  • Granger CW (1980) Long memory relationships and the aggregation of dynamic models. Econometrics 14:227–238

    Article  Google Scholar 

  • Grassberger P, Procaccia I (1983a) Measuring the strangeness of strange attractors. Phys D 9:189–208

    Article  Google Scholar 

  • Hentschel HGE, Procaccia I (1983) The infinite number of generalized dimensions of fractals and strange attractors. Phys D 8:435–444

    Article  Google Scholar 

  • Hilfer R (2000) Fractional time evolution. In: Hilfer R (ed) Fractional calculus in physics. World Scientific, Singapore, pp 87–130

    Chapter  Google Scholar 

  • Holden M, Øksendal B, Ubøe J, Zhang TS (1996) Stochastic partial differential equations. A modelling, white noise functional approach. Birkhäuser, Boston

    Google Scholar 

  • Hu K, Ivanov PC, Chen Z, Carpena P, Eugene Stanley H (2001) Effect of trends on detrended fluctuation analysis. Phys Rev E 64(1):011114

    Article  Google Scholar 

  • Jevrejeva S, Moore JC, Grinsted A (2003) Influence of the arctic oscillation and El Niño-Southern Oscillation (ENSO) on ice conditions in the baltic sea: the wavelet approach. J Geophys Res 108(D21):4677. doi:10.1029/2003JD003417

    Article  Google Scholar 

  • Jiang XH, Liu CM, Huang Q (2003) Multiple time scales analysis and cause of runoff changes of the upper and middle reaches of the Yellow River. Journal of Natural Resources 18(2):142–147 (in Chinese)

    Google Scholar 

  • Kahane J-P (1991) Produits de poids aléatoires indépendants et applications. In: Bélair J, Dubuc S (eds) Fractal geometry and analysis. Kluwer, Dordrecht, pp 277–324

    Google Scholar 

  • Kantelhardt JW, Zschiegner SA, Koscienlny-Bunde E, Halvin S, Bunde A, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Phys A: Stat Mech Appl 316(1–4):87–114

    Article  Google Scholar 

  • Kantz H, Schreider T (2004) Nonlinear time series analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Keller JM, Chen S, Crownover RM (1989) Texture description and segmentation through fractal geometry. Comput Graph Image Process 45:150–166

    Article  Google Scholar 

  • Labat D, Ababou R, Mangin A (2000) Rainfall-runoff relations for karstic springs. Part II: continuous wavelet and discrete orthogonal multi-resolution analyses. J Hydrol 238:149–178

    Article  Google Scholar 

  • Labat D, Ronchail J, Guyot JL (2005) Recent advances in wavelet analyses: Part 2–Amazon, Parana, Orinoco and Congo discharges time scale variability. J Hydrol 314:289–311

    Article  Google Scholar 

  • Laferrière A, Gaonac’h H (1999) Multifractal properties of visible reflectance fields from basaltic volcanoes. J Geophys Res 104:5115–5126

    Article  Google Scholar 

  • Li D, Shao J (1994) Wavelet theory and its application in image edge detection. Int J Photogr Rem Sens 49:4

    Google Scholar 

  • Lovejoy S, Schertzer D, Tessies Y, Gaonac’h H (2001) Multifractals and resolution-dependent remote sensing algorithm: the example of ocean colour. Int J Rem Sens 22:1191–1234

    Article  Google Scholar 

  • Mandelbrot BB (1985) Self-affine fractals and factal dimension. Phys Scripta 32:257–260

    Article  Google Scholar 

  • Mandelbrot BB (1999a) Multifractals and 1/f noise: wild self-affinity in physics. Springer, New York

    Google Scholar 

  • Monin AS, Yaglom AM (1975) Statistical fluid mechanism, vol 2. MIT, Cambridge, MA

    Google Scholar 

  • Novikov EA (1994) Infinitely divisible distributions in turbulence. Phys Rev E 50(5):3303–3305

    Article  Google Scholar 

  • Peleg S, Naor J, Hartley R, Avnir D (1984) Multiple resolution texture analysis and classification. IEEE PAMI 6:518–523

    Google Scholar 

  • Peng CK, Buldyrev SV, Havlin S, Simmons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49(2):1685

    Article  Google Scholar 

  • Pentland A (1984) Fractal based description of natural scenses. IEEE Trans PAMI 6:661–674

    Google Scholar 

  • Podlubny I (1999) Fractional differential equations. Academic, San Diego, MA

    Google Scholar 

  • Quattrochi DA, Goodchild MF (eds) (1997) Scale in remote sensing and GIS. CRC Lewis, Boca Raton, FL

    Google Scholar 

  • Ranchin T, Wald L (1993) The wavelet transform for the analysis of remotely sensed data. Int J Rem Sens 14:615

    Article  Google Scholar 

  • Rangarajan G, Ding M (eds) (2003) Processes with long-range correlations: theory and applications. Springer, Berlin

    Google Scholar 

  • Rees WG (1995) Characterization of imaging of fractal topography. In: Wilkinson G (Ed.) Fractals in geoscience and remote sensing. Luxembourg: Office for Official Publications of the European Communities, pp. 298–325

    Google Scholar 

  • Riedi RH, Crouse MS, Ribeiro VJ, Baraniuk RG (1999) A multifractal wavelet model with application to network traffic. IEEE Trans Inform Theor 45(3):992–1019

    Article  Google Scholar 

  • Tong H (1990) Non-linear time series: a dynamical system approach. Oxford University Press, New York

    Google Scholar 

  • Yu JG, Leung Y, Chen YQ, Zhang Q (2008) Multifractal analyses of daily rainfall in the Pearl River delta of China (unpublished paper)

    Google Scholar 

  • Zhang Q, Xu CY, Becker S, Jiang T (2006a) Sediment and runoff changes in the Yangtze past 50 years. J Hydrol 331:511–523

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Dept. of Geography & Resource Management Shatin, The Chinese University of Hong Kong, New Territories, Hong Kong SAR

    Prof. Yee Leung

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  1. Prof. Yee Leung
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Correspondence to Yee Leung .

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Leung, Y. (2010). Discovery of Structures and Processes in Temporal Data. In: Knowledge Discovery in Spatial Data. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02664-5_6

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