| Abstract: | An ordering of a two-dimensional matrix assigns consecutive integers to the cells in that matrix. This paper evaluates such orderings by concentrating on the differences between each cell's order key and the keys of its spatial neighbors. In all, ten systematically generated orderings and two hundred random trials from a newly defined class of orderings are compared. The row-by-row (raster) ordering often used in remote sensing and in matrix ordering within computer programs minimizes the mean absolute difference, the root-mean-squared difference (and hence the Geary statistic), and the mean maximum absolute difference for both 8-by-8 and 256-by-256 matrices; of the quadrant-recursive (“quadtree-compatible”) orderings examined, the Morton order had the lowest values for both mean absolute difference measures, whereas the Hilbert order had the lowest root-mean-squared neighbor difference. The Morton order has the overall minimum value for the Moran statistic. Heuristic search procedures applied to the 8-by-8 case found orderings which had considerably “better” values for these statistics (higher for Moran; lower for the others) than did any of the above, suggesting that it will be possible to define new systematic orderings with better scores than any ordering currently in the literature. |
