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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Sent: 16 January 2006 16:55 To: ai-geostats@unil.ch 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" <[EMAIL PROTECTED]> >>A: <ai-geostats@unil.ch> >>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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