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[ai-geostats] Spatial Neighborhood Weighting Matrix for Lattice data

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  • Dean Monroe
    Group: I have an idea for designing a flexible weighting matrix for my county level data. In many of the texts on lattice analysis, I have found or rather not
    Message 1 of 1 , Nov 23, 2004
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      Group:

       

                  I have an idea for designing a flexible weighting matrix for my county level data.  In many of the texts on lattice analysis, I have found or rather not found any standard techniques of defining a neighborhood for irregular lattices.  In regular lattices we have Rook, Queen, Bishop, etc. configurations.  My thought is: given a spatial weight matrix, for example

       

      0          1          0

       

      0.5        X          0.5

       

      0          1          0

      Where the weighting is different horizontally than vertically.  Can an adaptive weighting matrix be made that switches the direction of main weights (say 1) and minimum weights (say 0.5), based on a property of location X? 

       

      For instance, looking at counties for a given state.  Say each county has a main road traveling through it at some direction.  I would assume the county to county influence would be aligned with the road.  So take two counties A and B; A has a main road running north to south and B has a main road running east and west, can I build a weighting scheme that

       

      For A

        

      0          1          0

       

      0.5        X          0.5

       

      0          1          0

       

      For B

      0          0.5        0

       

      1          X          1

       

      0          0.5        0

       

      Where the weighting scheme is dependent on the direction of the main road?  Who you think this violates the idea of translation invariance?

       

       

      Dean Monroe

      OSU Environmental Sciences

       

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