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Discovery of Structures and Processes in Temporal Data

  • Yee LeungEmail author
Chapter
Part of the Advances in Spatial Science book series (ADVSPATIAL)

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.

Keywords

Fractional Brownian Motion Yangtze River Basin Detrended Fluctuation Analysis Runoff Change Queen Mary Hospital 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 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 324:24–39CrossRefGoogle Scholar
  2. Angulo JM, Ruiz-Medina MD, Anh VV, Grecksch W (2000) Fractional diffusion and fractional heat equation. Appl Prob 32:1077–1099CrossRefGoogle Scholar
  3. Anh VV, Leonenko NN (2000) Scaling laws for the fractional diffusion-wave equation with random data. Stat Prob Lett 48:239–252CrossRefGoogle Scholar
  4. Anh VV, Leonenko NN (2001) Spectral analysis of fractional kinetic equations with random data. J Stat Phys 104(516):1349–1387CrossRefGoogle Scholar
  5. Anh VV, Duc H, Azzi M (1997a) Modelling anthropogenic trends in air quality data. J Air Waste Manag Assoc 47(1):66–71Google Scholar
  6. Anh VV, Gras F, Tsui HT (1996) Multifractal description of natural scenes. Fractals 4(1):35–43CrossRefGoogle Scholar
  7. Anh VV, Heyde CC, Tieng Q (1999a) Stochastic models for fractal processes. J Stat Plann Infer 80(1/2):123–135CrossRefGoogle Scholar
  8. Anh VV, Leung Y, Chen D, Yu ZG (2005b) Spatial variability of daily rainfall using multifractal analysis (unpublished paper)Google Scholar
  9. Anh VV, Leung Y, Lam KC, Yu ZG (2005b) Multifractal characterization of Hong Kong air quality data. Environmetrics 16:1–12CrossRefGoogle Scholar
  10. Bacry E, Muzy J, Arneodo A (1993) Singularity spectrum of fractal signals from wavelet analysis: exact results. J Stat Phys 70(314):635–647CrossRefGoogle Scholar
  11. Bennett RJ (1979) Spatial time series: analysis-forecasting-control. Pion, LondonGoogle Scholar
  12. Beran J (1992) Statistical methods for data with long-range dependence. Stat Sci 7:404–416CrossRefGoogle Scholar
  13. Beran J (1994) Statistics for long-memory processes. Chapman and Hall, New YorkGoogle Scholar
  14. Borgas MS (1992) A comparison of intermittency models in turbulence. Phys Fluid A 4(9):2055–2061CrossRefGoogle Scholar
  15. Box GEP, Jenkins GM (1976) Time series analysis: forecasting and control. Holden-Day, San Francisco, CAGoogle Scholar
  16. Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis: forecasting and control. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  17. Chen Z, Ivanov PC, Hu K, Stanley HE (2002) Effect of nonstationarities on detrended fluctuation analysis. Phys Rev E 65(4):041107CrossRefGoogle Scholar
  18. Cihlar J (2000) Land cover mapping of large areas from satellites: status and research priorities. Int J Remote Sens 21(6):1093–1114CrossRefGoogle Scholar
  19. Daubechies I (1992) Ten lectures on wavelets. Society for industrial and applied mathematics, Philadelphia, Pennsylvania, pp. 357Google Scholar
  20. Davis A, Marshak A, Wiscombe W, Cahalan R (1996) Scale in invariance of liquid water distributions in marine stratocumulus. J Atmos Sci 53:1538–1558CrossRefGoogle Scholar
  21. Djamdji J-P, Bijaoui A, Maniere R (1993) Geometrical registration of images: the multiresolution approach. Photogr Eng Rem Sens 59:645Google Scholar
  22. 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 34:906–914CrossRefGoogle Scholar
  23. Falconer KJ (1985) The geometry of fractal sets. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. Feder J (1988) Fractals. Plenum Press, New YorkGoogle Scholar
  25. Fisher Y (ed) (1995) Fractal image compression, theory and application. Springer, New YorkGoogle Scholar
  26. Frisch U (1995a) Turbulence. Cambridge University Press, CambridgeGoogle Scholar
  27. Frisch U (1995b) Turbulence. The legacy of A. Kolmogorov. Cambridge University Press, CambridgeGoogle Scholar
  28. 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
  29. Gaucherel C (2002) Use of wavelet transform for temporal characterization of remote watersheds. J Hydrol 269:101–121CrossRefGoogle Scholar
  30. Granger CW (1980) Long memory relationships and the aggregation of dynamic models. Econometrics 14:227–238CrossRefGoogle Scholar
  31. Grassberger P, Procaccia I (1983a) Measuring the strangeness of strange attractors. Phys D 9:189–208CrossRefGoogle Scholar
  32. Hentschel HGE, Procaccia I (1983) The infinite number of generalized dimensions of fractals and strange attractors. Phys D 8:435–444CrossRefGoogle Scholar
  33. Hilfer R (2000) Fractional time evolution. In: Hilfer R (ed) Fractional calculus in physics. World Scientific, Singapore, pp 87–130CrossRefGoogle Scholar
  34. Holden M, Øksendal B, Ubøe J, Zhang TS (1996) Stochastic partial differential equations. A modelling, white noise functional approach. Birkhäuser, BostonGoogle Scholar
  35. Hu K, Ivanov PC, Chen Z, Carpena P, Eugene Stanley H (2001) Effect of trends on detrended fluctuation analysis. Phys Rev E 64(1):011114CrossRefGoogle Scholar
  36. 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:10.1029/2003JD003417CrossRefGoogle Scholar
  37. 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
  38. Kahane J-P (1991) Produits de poids aléatoires indépendants et applications. In: Bélair J, Dubuc S (eds) Fractal geometry and analysis. Kluwer, Dordrecht, pp 277–324Google Scholar
  39. 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):87–114CrossRefGoogle Scholar
  40. Kantz H, Schreider T (2004) Nonlinear time series analysis. Cambridge University Press, CambridgeGoogle Scholar
  41. Keller JM, Chen S, Crownover RM (1989) Texture description and segmentation through fractal geometry. Comput Graph Image Process 45:150–166CrossRefGoogle Scholar
  42. 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 238:149–178CrossRefGoogle Scholar
  43. 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 314:289–311CrossRefGoogle Scholar
  44. Laferrière A, Gaonac’h H (1999) Multifractal properties of visible reflectance fields from basaltic volcanoes. J Geophys Res 104:5115–5126CrossRefGoogle Scholar
  45. Li D, Shao J (1994) Wavelet theory and its application in image edge detection. Int J Photogr Rem Sens 49:4Google Scholar
  46. 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 22:1191–1234CrossRefGoogle Scholar
  47. Mandelbrot BB (1985) Self-affine fractals and factal dimension. Phys Scripta 32:257–260CrossRefGoogle Scholar
  48. Mandelbrot BB (1999a) Multifractals and 1/f noise: wild self-affinity in physics. Springer, New YorkGoogle Scholar
  49. Monin AS, Yaglom AM (1975) Statistical fluid mechanism, vol 2. MIT, Cambridge, MAGoogle Scholar
  50. Novikov EA (1994) Infinitely divisible distributions in turbulence. Phys Rev E 50(5):3303–3305CrossRefGoogle Scholar
  51. Peleg S, Naor J, Hartley R, Avnir D (1984) Multiple resolution texture analysis and classification. IEEE PAMI 6:518–523Google Scholar
  52. Peng CK, Buldyrev SV, Havlin S, Simmons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49(2):1685CrossRefGoogle Scholar
  53. Pentland A (1984) Fractal based description of natural scenses. IEEE Trans PAMI 6:661–674Google Scholar
  54. Podlubny I (1999) Fractional differential equations. Academic, San Diego, MAGoogle Scholar
  55. Quattrochi DA, Goodchild MF (eds) (1997) Scale in remote sensing and GIS. CRC Lewis, Boca Raton, FLGoogle Scholar
  56. Ranchin T, Wald L (1993) The wavelet transform for the analysis of remotely sensed data. Int J Rem Sens 14:615CrossRefGoogle Scholar
  57. Rangarajan G, Ding M (eds) (2003) Processes with long-range correlations: theory and applications. Springer, BerlinGoogle Scholar
  58. 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. 298–325Google Scholar
  59. Riedi RH, Crouse MS, Ribeiro VJ, Baraniuk RG (1999) A multifractal wavelet model with application to network traffic. IEEE Trans Inform Theor 45(3):992–1019CrossRefGoogle Scholar
  60. Tong H (1990) Non-linear time series: a dynamical system approach. Oxford University Press, New YorkGoogle Scholar
  61. 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
  62. Zhang Q, Xu CY, Becker S, Jiang T (2006a) Sediment and runoff changes in the Yangtze past 50 years. J Hydrol 331:511–523CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dept. of Geography & Resource Management ShatinThe Chinese University of Hong KongNew TerritoriesHong Kong SAR

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