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Knowledge discovery from GIS in 'Natural Resources Targeting'
Multi-Criteria and Multi-objective Analysis
The problem of targeting natural resources requires predictive modelling using various procedures and tools for development of decision rules. A decision rule typically contains procedures for combining criteria into a single composite index and a statement of how alternatives are to be compared using this index, like assigning a threshold to a single criterion, which are structured in the context of a specific objective. An objective is thus a prospective that serves to guide the structuring of decision rules. To meet with a specific objective, several criteria are integrated and evaluated, called multi-criteria evaluation (Quilon, 1986).
Two common classes of GIS based multi-criteria evaluations are concordance and discordance analysis. The former handles all evidences with some assigned weights, while the latter analyzes degree to which, one evidence outranks the other on a specified criteria. Uncertainties involved with spatial data is handled with much of difficulties, when present, the decision rule need to incorporate modifications to the choice function or heuristic to accommodate the propagation of uncertainties through the rule and replace the hard decision (Lee et al., 1987). The uncertainties are handled by assigning probability to the evidences. Evaluation of relationships between evidences and belief/hypothesis is a forward chaining expert system, where propagation of favourability is through an inference-net which includes bayesian updating, fuzzy logic and dempster-shafer function. There is unidirectional propagation of evidences through a hierarchical network to an ultimate hypothesis.
Multi-Criteria Evaluations
A decision is a choice between alternatives and the basis for a decision is known as a criterion. Criteria may be of two types: factors and constraints. Factors may be a continuous, binary or a coded variable whereas, constraints are generally Boolean in character. Through a Multi-Criteria Evaluation, these criteria which represent suitability, are integrated to form a decision as a single suitability map, to a single objective. The method handles the tradeoff between factors, during integration of the knowledges. Factor weights, called tradeoff weights, is assigned by expert-knowledge or is data-driven.
In cases of Boolean criteria, the solution lies usually in the union (logical OR) or intersection (logical AND) of conditions. However for continuous factors, a weighted linear or log-linear combination is an usual practice. Order Weighted average technique considers factors, its weights and a rank assigned to the factor-weights. As criteria are measured at different scales, they are standardized before used for integration. Establishing factor weights is the most complicated aspect, for Boolean maps, a pair-wise comparison matrix is generally used. Analytical Hierarchy Process (Satty, 1992) provides a series of pair-wise comparisons of the relative importance of factors to the suitability of pixels for the activity being evaluated.
Multi-Objective Evaluations
Situation with conflicting multi-objectives, require integration of information gathered from a set of suitability maps, one for each objective. The relative weights assigned to each objective and the amount of area assigned to each are analyzed. This is basically a compromising programming analysis (Pereia and Duckstein, 1993), which attempts to allocate target potential areas for each objective, given the assigned weights. This technique uses a Min-Max rule, where in minimum of the maximum weighted deviation are sought for the composite layer and it provides a non-compensatory solution. Bayes theory and Dempster-Shafer theory are used to handle multi-objective evaluations.
Bayesian updating, Fuzzy theory and Belief function handle spatial uncertainties excellently. However there exists propagation of error in an inference net due to the reasons like adoption of subjective weighting and the procedure of scaling datasets, which again involves subjective judgments. Studies on interactions of evidences are not possible using above methods. Logistic regression analysis is a suitable technique of handling the above inadequacies. It handles varied data-types and the factor-weighting method is data-driven. Further the main effects and interactions of the evidences are studied nicely in this method. The case study given below describes the application of logistic regression analysis in targeting potential resources.
Theory
The logistic regression model has the form (Hosmer and Lemeshow, 1989)
Logit (r) = log(r/(1-r)) = bo + b'X
Where, X is the vector of explanatory variables
bo is the intercept parameter
b' is the vector of slope coefficients
As the equation is nonlinear, Newton-Raphson or iteratively reweighted least-squares are used to solve b'. Few statistics such as Wald's statistic, likelihood ratio test statistic, Akaiki Information Criterion (AIC), and Schartz Criterion (SC) are used to assess model fitting.
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