Blind Source Separation for Spatial Compositional Data

详细信息    查看全文

• 作者：Klaus Nordhausen ; Hannu Oja ; Peter Filzmoser ; Clemens Reimann
• 关键词：Principal component analysis ; Independent component analysis ; Clr transformation ; Ilr transformation ; 62M10 ; 60G35 ; 92C55
• 刊名：Mathematical Geosciences
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：47
• 期：7
• 页码：753-770
• 全文大小：2,244 KB
• 参考文献：Aitchison J (1983) Principal component analysis of compositional data. Biometrika 70:57鈥?5CrossRef
  Aitchison J (2003) The statistical analysis of compositional data. Blackburn, Caldwell
  Bailey TC, Krzanowski WJ (2012) An overview of approaches to the analysis and modelling of multivariate geostatistical data. Math Geosci 44:381鈥?93CrossRef
  Belouchrani A, Abed-Meraim K, Cardoso J-F, Moulines E (1997) A blind source separation technique using second-order statistics. IEEE Trans Signal Proces 45:434鈥?44CrossRef
  Cardoso J-F (1989) Source separation using higher order moments. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, vol 4, pp 2109鈥?112
  Comon P, Jutten C (2010) Handbook of blind source sepparation: independent component analysis and applications. Academic, Oxford
  Egozcue JJ, Pawlowsky-Glahn V, Mateu-Figueras G, Barcel贸-Vidal C (2003) Isometric logratio transformations for compositional data analysis. Math Geol 35:279鈥?00CrossRef
  Filzmoser P (2012) StatDA: statistical analysis for environmental data. R package version 1.6.3. http://鈥婥RAN.鈥婻-project.鈥媜rg/鈥媝ackage=鈥婼tatDA
  Filzmoser P, Hron K, Reimann C (2009a) Principal component analysis for compositional data with outliers. Environmetrics 20:621鈥?32CrossRef
  Filzmoser P, Hron K, Reimann C, Garrett RG (2009b) Robust factor analysis for compositional data. Comput Geosci 35:1854鈥?861CrossRef
  Legendre P, Legendre L (2012) Numerical ecology. Third English edition, Elsevier Science, The Netherlands
  Mart铆n-Fern谩ndez JA, Olea-Meneses RA, Pawlowsky-Glahn V (2001) Criteria to compare estimation methods of regionalized compositions. Math Geol 33(8):889鈥?09CrossRef
  Miettinen J, Nordhausen K, Oja H, Taskinen S (2012) Statistical properties of a blind source separation estimator for stationary time series. Stat Probabil Lett 82:1865鈥?873CrossRef
  Miettinen J, Nordhausen K, Oja H, Taskinen S (2014a) Deflation-based separation of uncorrelated stationary time series. J Multivariate Anal 123:214鈥?27CrossRef
  Miettinen J, Nordhausen K, Oja H, Taskinen S (2014b) Separation of uncorrelated stationary time series using autocovariance matrices. Preprint available as arXiv:鈥?405.鈥?388
  Pawlowsky-Glahn V, Olea RA (2004) Geostatistical analysis of compositional data. Oxford University Press, Oxford
  Reimann C, Filzmoser P, Garrett R, Dutter R (2008) Statistical data analysis explained: applied environmental statistics with R. Wiley, CichesterCrossRef
  Reimann C, 脛yr盲s M, Chekushin V, Bogatyrev I, Boyd R, De Caritat P, Dutter R, Finne TE, Halleraker JH, J忙ger 脴, Kashulina G, Lehto O, Niskavaara H, Pavlov V, R盲is盲nen ML, Strand TT, Volden T (1998) Environmental geochemical atlas of the central Barents region. NGU-GTK-CKE Special Publication, Geological Survey of Norway, Trondheim
  Reimann C, Niskavaara H (2006) Regional distribution of Pd, Pt and Au emissions from the nickel industry on the Kola Peninsula, NW-Russia, as seen in moss and humus samples. In: Zereini F, Alt F (eds) Palladium emissions in the environment. Analytical methods, environmental assessment and health effects. Springer, Heidelberg, pp 53鈥?0CrossRef
  Reimann C, Banks D, Kashulina G (2000) Processes influencing the chemical composition of the O-horizon of podzols along a 500 km north-south profile from the coast of the Barents Sea to the Arctic Circle. Geoderma 95:113鈥?39CrossRef
  Reimann C, Kashulina G, De Caritat P, Niskavaara H (2001) Multi-element, multi-medium regional geochemistry in the European arctic: element concentration, variation and correlation. Appl Geochem 16:759鈥?80CrossRef
  von Storch H, Zwiers FW (1999) Statistical analysis in climate research. Cambridge University Press, Cambridge
  Theis FJ, Meyer-B盲se A, Lang EW (2004) Second-order blind source separation based on multi-dimensional autocovariances. In: Puntonet CG, Prieto A (eds) Independent component analysis and blind signal separation. Springer, Berlin, pp 726鈥?33CrossRef
  Tolosana-Delgado R, Pawlowsky-Glahn V, Egozcue JJ (2008a) Indicator kriging without order relation violations. Math Geosci 40(3):327鈥?47CrossRef
  Tolosana-Delgado R, Pawlowsky-Glahn V, Egozcue JJ (2008b) Simplicial indicator kriging. J China Univ Geosci 19(1):65鈥?1CrossRef
  Tolosana-Delgado R, Egozcue JJ, S谩nchez-Arcilla A, G贸mez J (2011a) Wave height data assimilation using non-stationary kriging. Comput Geosci 37:363鈥?70CrossRef
  Tolosana-Delgado R, Egozcue JJ, S谩nchez-Arcilla A, G贸mez J (2011b) Classifying wave forecasts with model-based geostatistics and the Aitchison distribution. Stoch Env Res Risk A 25:1091鈥?100CrossRef
  Tong L, Soon VC, Huang YF, Liu R (1990) AMUSE: A new blind identification algorithm. In: Proceedings of IEEE International Symposium on Circuits and Systems, vol 1990, pp 1784鈥?787
  Tyler D, Critchley F, D眉mbgen L, Oja H (2009) Invariant coordinate selection. J Roy Stat Soc B 71:549鈥?92CrossRef
  
• 作者单位：Klaus Nordhausen (1)
  Hannu Oja (1)
  Peter Filzmoser (2)
  Clemens Reimann (3)
  
  1. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland
  2. Department of Statistics and Probability Theory, Vienna University of Technology, 1040, Vienna, Austria
  3. Geological Survey of Norway, PO Box 6315, Sluppen, 7491, Trondheim, Norway
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Mathematical Applications in Geosciences
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Geotechnical Engineering
  Hydrogeology
  
• 出版者：Springer Berlin Heidelberg
• ISSN：1874-8953

文摘

In regional geochemistry rock, sediment, soil, plant or water samples, collected in a certain region, are analyzed for concentrations of chemical elements. The observations are thus usually high dimensional, spatially dependent and of compositional nature. In this paper, a novel blind source separation approach for spatially dependent data is suggested. For the analysis, it is assumed that the multivariate observations are linear combinations or mixtures of latent components and that the spatial processes for these latent components are second order stationary and uncorrelated. In the present approach, the latent components are then recovered by simultaneously diagonalizing the covariance matrix and a local covariance (correlation) matrix. This method can be easily applied also in the context of compositional data after appropriate data transformations. The components obtained in this way are uncorrelated and easily interpretable, and can be used for dimension reduction and for visual presentation of different features of the data. To demonstrate the usefulness of the new method, the KOLA data are reanalyzed using the new procedure and the results are compared to the results coming from marginal principal component analysis and independent component analysis that ignore spatial dependence. Keywords Principal component analysis Independent component analysis Clr transformation Ilr transformation