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Agregacja danych punktowych i pól odniesienia a informacyjne własności map gęstości

Krzywicka-Blum E.

Polski Przegląd Kartograficzny

2003

T. 35, nr 3

175-184

W pracy przeprowadzona została analiza wpływu wielkości pól odniesienia i sposobu konstrukcji skali tematycznej na zmianę informacyjnych własności map przedstawiających zróżnicowanie gęstości danych punktowych. Na podstawie 44 różnych rozmieszczeń 300 punktów w 100-, a następnie 400-polowym podziale obszaru, dokonano analizy sposobu agregacji gęstości w klasy oraz wielkości pola odniesienia na zmianę poziomu i zakresu gęstości. Zastosowano metody statystyczne, wyrównanie metodą najmniejszych kwadratów i ocenę różnorodności za pomocą entropii. Ustalono korelację pewnych charakterystyk i wskazano możliwości ich wykorzystania we wstępnych etapach projektowania map.

The process of transformation of dot elements into specific thematic maps, which present the distribution of a particular feature using a choropleth or isopleth method depends on a proper size of reference space units and the criteria of aggregation of data into clases. In the paper 44 spatial distribution of 300 points have been analyzed according to the division of P area into 100 squares, which were later subdivided into 400. Two methods of grouping into density classes (the number of dots in reference area) have been applied. The first follows the natural breaks and the second bases on the classes of equal range. All 88 density patterns (before and after subdivision) have been aggregated into classes. 7 groups have been established according to the number of classes: "3-3", "4-4", "5-5", "4-3", "3-4", "5-4", and "5-3". statistic characteristics have been determined within each group. Relative entropy has been used as an especially important measure of diversity (of density in a group). Comparison of indicator levels before and after the subdivision of each area has been used to analyze the relation of area size and the reduction of the density range. Through the application of the method of the least squares for the two most numerous groups of aggregation (to 3 and, separately, to 4 classes of density) it was possible to establish a type of linear dependence between the density range and the level diversity. In the case of aggregation into three classes it has been proved, that the condition ot the same level of diversity is: xmax{100}=3 razy xmax{400} For onstance, when before the division of reference areas the diversity range of density was 0-18 and after the division 0-6, then (see fig. 6): h1(18)=h1'(6)=0,60 Finally, some interesting correlation indicators between average characteristics have been determined. Interdependence between the vakue of the indicator of relative change of density range and the compensation of the range of dot elements due to the subdivision of reference areas is a significant result of the analysis. Although presented conclusions can only be treated as empirically obtained results, the number and variety of examples allows to accept their usefulness for generalization procedures necessary in initial preparation of important types of thematic maps.