A Neural Network-Based Method for Solving "Nested Hierarchy" Areal Interpolation Problems

Article excerpt

Introduction

Spatially aggregated data have a number of drawbacks that hinder spatial analysis. One dilemma often encountered is the need to overlay multiple spatial datasets defined by varying scales (Openshaw and Taylor 1981). Because different organizations collect data for different areal units at different scales, the scale differences must be reconciled before comparisons can be made. If possible, large-scale data representing smaller areas will be aggregated to the level of the small-scale data representing larger areas. Often, even at the same scale, the boundaries of two datasets are misaligned with respect to one another (Flowerdew et al. 1991). In geographic information science (GISc), this problem is solved by first overlaying the two different polygon layers representing the areal units and then using areal interpolation to estimate the attribute values for the intersection zones before these units are re-aggregated to the desired areal unit.

Numerous areal interpolation procedures have been developed, and it is difficult to identify one single technique as being optimal in every case (Gregory 2000). The choice of which areal interpolation procedure to use often depends on such objectives as the statistical properties of the variable being estimated (Goodchild and Lam 1980), the assumptions regarding the source data used in the interpolation process (Flowerdew and Green 1992), the spatial orientation of the areal units (Park 1983), and whether or not the estimated values are volume (value) preserving (Tobler 1979).

This study proposes an alternative approach to solving areal interpolation problems by using artificial neural networks. For this method, the values to be estimated are total populations for census tracts and census block groups in Hartford County, Connecticut. Neural networks are defined as a set of computational models inspired by artificial intelligence. These models differ from other computational models because the results derived from neural networks are the product of learning of patterns presented as input, rather than the result of a specific algorithm (Openshaw and Openshaw 1997).

Neural networks have become widely used in spatial analysis, including applications within the sub-fields of remote sensing (Civco 1993; Filippi and Jensen 2006), spatial interaction modeling (Black 1995; Fischer and Reismann 2002), cognitive mapping (Lloyd 2000, and visualization of geo-spatial data (Takatsuka 2001; Skupin and Hagelman 2005). These models have also gained in popularity as a method of spatial interpolation for continuous data (Chen and Tim 1995; Snell et al. 2000; Byran and Adams 2002; Merwin et al. 2002) and as a modeling technique for other types of applications where continuous spatial data are present (Ermini et al. 2005; Pavel et al. 2008; Melchiorre et al. 2008).

One advantage of using neural networks for applications in spatial analysis is that there are no required underlying assumptions concerning the data used in the models (Filippi and Jensen 2006). Because areal interpolation problems often require assumptions to be made regarding the attribute data--with a particular emphasis on the spatial distribution of attributes within areal units--neural network modeling is a suitable approach to solving such problems. Another area of concern regarding some areal interpolation techniques is the assumption of linearity between possible explanative variables and the variable to be predicted. Neural networks also have the ability to account for nonlinear relationships between input variables and the predicted output variable. Finally, these models have proven to be an effective data mining technique, where underlying patterns are more easily seen in the input data presented to the neural networks (Cravin and Shavlik 1997).

Areal Interpolation Methods

GIS users are now able to analyze large databases of geographic entities measured and classified at various scales. …