1. Background and Objective of the Study
Temporal or dynamic analysis of spatial data is needed in various fields such as environmental systems analysis. One of the most fundamental problems which users are facing is the difficulties in generating spatio-temporal filed of quality data for analysis through an interpolation or integration of observational data. In several fields, to improve reliability of spatio-temporal interpolation/ extrapolation in generating quality data, models and/or equations describing an underlying mechanism and structure is integrated with observational data. By integrating observational data and models describing underlying mechanisms and structures of object-phenomenon with a GIS, we can provide a GIS-based environment, which allow dynamic update of spatio-temporal field of data whenever a new observational data and an improvement of models are given. If computational speed for integration is fast enough, we can store only observational data and can estimate data at any locations based on the requests.
Integration methods for data and models have been mainly developed for continuous variables in meteorology and oceanography such as temperature and precipitation. For categorized or class variables such as land use types, there are only very primitive interpolation methods such as nearest neighbor interpolation and so forth. This paper, propose a integration methods of models and class data from multi-sources under the framework of optimization of likelihood of spatio-temporal events. For optimizing the likelihood, genetic algorithm (GA) is modified by combining GA with classical "Hill climbing" method. .
2. Genetic Algorithm (GA) and Class Variable Interpolation
2.1 Introduction of Genetic Algorithm (GA)
John Holland and his colleagues develop genetic algorithms as an approach to optimization, which requires efficient and effective search in natural and artificial systems. They are search algorithms based on the mechanism of natural selection and evolution of natural genetics. They combine survival of the fittest among string structures with a structured but randomized gene exchange to form a search algorithm with some of innovative flair of human search.
Genetic algorithms are computationally simple and powerful in their search without restrictive assumptions about search spaces. In a simple genetic algorithm, five basic aspects should be considered: the representation or coding of problem, the initialization of population, the definition of evaluation function, the definition of genetic operators, and the determination of parameters.
2.2 Optimization Scheme for Class Variable Interpolation
Most natural properties may vary continuously. However, the observation that describe these, properties and which form the data bases of GISs are usually fragmentary. Ever where a complete cover of information exists, for instance from the satellite images, we still often need to resample because there are too many data to handle or analyze in any reasonable time. Because the properties are continuous that values in sites are close together in space are more likely to be similar than those further from one another, i.e., they depend on one another in a statistical sense. This important feature of spatial data provides the rationale for interpolation.
Spatial-temporal data can be divided into two types: continuous variables data and class variables data proposed a Kriging-based integrating/interpolation method for continuous variable data and an interpolation method for class variable data based on the estimation of time of changes according to "class boundary distance". But for the class variable data, the method of the time-of-change estimation seems not to work well, because complex temporal and spatial relations among classes around a pixel greatly affect class variation at this pixel and make it difficult to estimate the time of change at the pixel. In fact, interpolation problem of class variable data is a hardest combinatorial optimization problem in spatial and temporal dimensions .
In this research, we go to integrate observational class data with behavioral/structural models/rules to make robust and reliable spatio-temporal interpolation of class variables. Since searching for the most likely spatio-temporal field of class data is typical combinatorial optimization problem, we introduce the genetic algorithm as a optimization scheme for class variable data to get optimized interpolated time-slice data. To estimate the most likely spatio-temporal field of class data, we maximize the likelihood of estimated spatio-temporal field. The likelihood is computed based on both the fitness to observational data and that to behavioral/structural models/rules. The fitness to observational data is determined from the accuracy and resolution of observational data, while the fitness to behavioral/structural models/rules is computed as the combined likelihood (probability) of transitional events under the assumption that all transitions follow probabilistically the behavioral/structural models/rules.