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[ai-geostats] Network optimization: Thiessen/Voronoi polygons and nearest neighbours

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  • Gregoire Dubois
    Hello Michel, Thanks for the information! Regarding the use of Voronoi polygons, recommended by many, my problem with it is that you can have in a monitoring
    Message 1 of 2 , Jan 16, 2006
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      Hello Michel,

      Thanks for the information!

      Regarding the use of Voronoi polygons, recommended by many, my problem
      with it is that you can have in a monitoring networks clustered data
      that still have very large polygons compared to the average. The borders
      (also the case when using a convex hull for delineating boundaries) have
      thus a very strong impact on the weights attributed to the polygons. A
      border effect is also encountered with the fractal approach as well as
      with the Morisita index! This is a serious problem if you have a
      monitored area that has a complex geometry.

      I tried in the past to combine both the information provided by the
      distance to the nearest neighbour and the surface of the polygon of
      Thiessen/Voronoi. If you use as a reference system a grid with points
      located in the center of each cell of the grid, the surface of each
      Voronoi/Thiessen polygon is equal to the square of the nearest
      neighbours. This simple concept might be use to describe the level of
      clustering of a point in a network as well for declustering. The method
      proposed gave good results but further testing did not show any
      improvement over the cell-declustering approach and I believe the
      explanation of the lack of performance of my approach lies in
      mathematical morphology...and somewhere in the replies I received to my
      question.

      Thanks to all for the stimulating discussions!

      Gregoire


      (*) see Dubois G. and Saisana M., (2002). Optimizing spatial
      declustering weights – Comparison of methods. In: Terra Nostra, Heft Nr.
      03/2002, Proceedings of the 8th Annual conference of the International
      Association for Mathematical Geology, September 2002, Berlin, Germany.U.
      Bayer, H. Burger and W. Skala (Eds), Vol. 1, pp. 473-478
      __________________________________________
      Gregoire Dubois (Ph.D.)

      European Commission (EC)
      Joint Research Centre (JRC)
      WWW: http://www.ai-geostats.org

      "The views expressed are purely those of the writer and may not in any
      circumstances be regarded as stating an official position of the
      European Commission."



      -----Original Message-----
      From: Michel.Maignan@... [mailto:Michel.Maignan@...]
      Sent: 16 January 2006 16:55
      To: ai-geostats@...
      Subject: [ai-geostats] gregfoire network optimization


      hello gregoire

      Happy new year

      For network characterization and optimization, you have at disposal,
      dealing with the localization of samples, and not with measurements:

      - voronoi polygons, with statistics of area of polygons, distances
      between points
      - delaunay triangulation
      - Morishita diagram
      - entropy diagram
      - fractal dimension of monitoring network
      - declustering.

      Tehy are described, with their programs, in Chapter 2 "monitoring
      networks" of our book, "Analysis and Modelling of sptaial environmental
      and pollution data" (M. Kanevski, M. Maignan) and the software for it.
      This contributes to the analysis and optimal locations of measuring
      locations, wihtout considerations of the variable measured.


      In case your problem would be a classification problem, for instance the
      optimal locations of samples for separating two classes, then the SVM
      approach seems more adequate. Refer to our IAMG 2006 (in Toronto)
      publication, where the SVM Support Vector Machine shows the area for
      optimal additional sampling, based on conditional standard deviation of
      SISIM models (Re Chapter 9 Support Vector Machines for environmental
      spatial data). The SD at the border between the 2 regions separated by
      Support vectors is used for identification of the next optimal sampling
      locations, and this is different from the usual kriging estimation
      variance.



      best regards, Michel

      ************************************************************************
      ********************************




      De: "Gregoire Dubois" <gregoire.dubois@...>
      >>A: <ai-geostats@...>
      >>Date: Thu, 12 Jan 2006 16:00:33 +0100
      >>Sujet: [ai-geostats] Optimization of monitoring networks
      >>
      >>Dear list,
      >>
      >>I am looking for references (and possibly software) on network
      >>optimization. The variable monitored has no importance and I am
      >>looking for references and topological algorithms. A question I have
      >>is the following: given an area A with a particular shape (e.g.
      >>defined by country borders) and a number of stations N (e.g. for
      >>mobile phone emitters), how do I define the optimal locations for
      >>these stations?
      >>

      Michel Maignan
      Prof. Uni. Lausanne
      Dir. Gestion des Risques, BC Genève
      00 41 79 679 80 13
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