Spatial interpolation vs neural network propagation as a method of extrapolating from field surveys

In a rapid changing society like South Africa, up to date and accurate information on the socioeconomic, service delivery, demographic, substance abuse, disease and other conditions of the nation is needed on a regular basis. The gathering of representative information in a vast country like South Africa can be a costly exercise. A well-designed sample, however, can lay the base for the collection of information and for further research and analysis. Utilising a good sample design together with a spatial extrapolation method provides an alternative to frequent and expensive surveys. In order to save on the cost of surveys the HSRC (Human Sciences Research Council) GIS Centre is using extrapolation methods via neural networks to assign values – based on existing socio-economic and demographic information to all entities not included in a sample survey. Another methodology that can be utilised in a GIS environment is spatial interpolation. This methodology estimate values for unsampled areas based on the values of surrounding sampled points. Both mentioned methods will save significant costs in terms of gathering of information. This paper aims to focus on the spatial interpolation method and compare results with neural network propagation outputs from a survey done on substance abuse behaviour linked to crime patterns in selected police stations throughout the country. This methodology provides comprehensive spatial information for decision makers in South Africa to make accurate and timely decisions about threatening social conditions like poverty, substance abuse, unemployment, crime and HIV/AIDS. INTRODUCTION Field surveys are costly exercises and the use of such data is often limited to a pre-defined geographic area. The spatial value of field survey results are regularly under utilised due to restricted application by users. The HSRC conducts several surveys a year and in the past couple of years artificial neural network propagation was used to extrapolate survey results to a more representative or national level. The aim of this paper is to examine the methodology of both models and to compare the results of spatial interpolation done on a recent substance abuse survey. BACKGROUND DATA The HSRC conducted a national survey on substance abuse patterns in 2000. A sample of 150 (out of 1089) police stations nationally were drawn using a stratified probability sample and arrestees at these stations were interviewed about their substance abuse and related crime behaviour. The results of these findings will be used by the two methodologies mentioned above. NEURAL NETWORKS Extrapolation refers to the estimation of values for unsampled points which lie outside the boundary of an existing sample set of data (AGI 1999). The extrapolation of sampled data is done to achieve a more complete analysis of a selected data set. In the past the HSRC GIS Centre used neural network propagation to obtain such results. The artificial neural networks are based on the structure and functioning of the human brain and consist of a large number of simple processing units known as neurons (Singh & Treleaven 1998: 2). Using the back propagation method the neural network software is able to use existing data to provide an output data set for non-sampled points (“Output” in Figure 1 below). In the past the result was extremely successful and verified by experts in the field of the particular application. The process of neural network propagation is often time consuming, especially if big data sets are being used. The process can be explained by the illustration below. Figure 1 The neural network software uses input data from a sample to create estimated values for non-sampled areas. In the case of substance abuse research INPUT Socio-economic & substance abuse “Relationship” OUTPUT Hidden Layer this input data set consisted of a substance abuse data set for a specific area (e.g. a sample) as well as a socio-economic data set matching the area for which the estimated substance abuse figures is needed (the “input” on Figure 1). The latter area is usually of provincial or national coverage. The software develops intricate relationships (“hidden layer” in Figure 1) between the two data sets in order to understand the factors determining the use and abuse of substances (the outcome). In other words it uses the familiar (socio-economic conditions for the whole as well as substance abuse results from the sample) to determine what the likelihood of substance abuse (the unfamilier) would be in non-sampled areas. Once this understanding is completed the software is able to provide an output data set for the desired area. The output data set consists of estimated substance abuse values for the ”non-sampled” area whether it is a province or at a national level. By using this method powerful data sets can be created using sampled data to extrapolate to a universe. The resulting data set provides an indication of what the expected outcome for specific variables will be. Extrapolated results based on this method are shown in Figure 2 below. Percentages of substance use were created in the original data set. This was used together with socio-economic data to determine what the possible substance use would be for areas not sampled. (In this case police station boundaries were identified as the primary spatial building block.) For the purpose of this analysis data from the Gauteng province only will be used, although the survey was done nationally.