Development of the method of multivariate spatial analysis and its application in spatial information science

当我们分析一个地区的多组空间数据时，我们使用的是包括统计方法在内的多元分析方法。在这种情况下，空间维度被等同于其他属性维度，这导致了分析中的概念和技术问题。例如，在回归分析中，邻域的属性通常被包括为自变量。这使得误差项的概率分布非常复杂，因此不可能通过分析获得最大似然。跨空间单元的空间聚合会导致分析结果依赖于用于聚合的空间单元定义的“可修改面积单元问题”，为了解决这一问题，需要从空间分析的角度在变量间关系分析--多元分析中明确引入空间的概念。将空间上定义的属性看作是一组位置函数，用空间多元分析方法对它们进行分析，从而发展了一种新的多元空间分析方法。该方法应1）明确纳入空间的概念，2）适用于探索性空间分析，3）在GIS中有广泛的应用。第一个要求是解决前面提到的问题。第二个需求是为了满足探索性空间数据分析的需求，这种需求随着海量空间数据的传播而迅速出现。第三个要求保证了该方法不仅适用于空间分析，而且适用于一般的多元分析，即把空间维作为定义变量的空间的一部分。分布在空间上的时间序列变量和在空间上测量的误差分布也是位置的函数。它们可以像本研究中讨论的属性变量一样处理。

When we analyze mare than one set of spatial data in a region, we use multivariate analytical methods including statistical methods. In this case, spatial dimension is treated equivalently as other attribute dimensions, which causes both conceptual and technical problems in analysis. In regression analysis, for instance, attributes of neighborhoods are often included as independent variables. This makes the probability distribution of error terms quite complicated so that it is impossible to obtain the maximum likelihood analytically. Spatial aggregation across spatial units causes the Modifiable Areal Unit Problem, which refers to the dependency of the results of analysis on the definition of spatial units used for aggregation.To resolve the problems, it is necessary to introduce the concept of space explicitly in analysis of the relationship among variables-multivariate analysis with a view of spatial analysis. Regarding the attributes defined over a space as a set of functions of location, we analyze them by a spatial multivariate analysis method.To this end, we develop a new method of multivariate spatial analysis. The method should 1)explicitly incorporate the concept of space, 2)be applicable to exploratory spatial analysis, and 3)have wide applications in GIS. The first requirement is recognized to resolve the problems mentioned earlier. The second requirement is put to answer the demand for exploratory spatial data analysis that has emerged rapidly with the spread of massive spatial data. The third reqirement assures us to apply the method not only to spatial analysis but also mare general multivariate analysis that contains spatial dimensions as a part of space where variables are defined. Time series variables distributed over a space and error distribution measured over a space are also functions of location. They can be treated in the same way as the attribute variables discussed in this research.