## 5 An Integrated Inductive-Deductive Framework for Data Mapping
### AMA Framework Details  
AMA utilises a blend of both inductive and deductive models to establish a successful mapping between the sensed data and the universal physical principles. For example, in WSNs forest fire application, factors such as the wind speed and direction, topography, and the type of forest have a big influence on the application. Some of these factors can not be sensed or the deployed hardware platform does not have suitable sensing equipment to gather this information. However, this information is very easy to acquire from external resources such as the GIS, geology databases, and weather stations, and can be integrated into the application to assure the consistency of the theory with the experimental data collected by the network. Therefore, it is desirable to combine the advantages of both methods.Deductive methods rely on a precise application environment and the explicit knowledge, called structural knowledge, of the underlying domain using first principles to create a model of the problem typically yielding governing equations [24]. On the other hand, inductive methods utilise experimental data as the only source of available knowledge [24]. Some applications can only be treated using experimental data knowledge due to the lack of other application domain knowledge. Nevertheless, the use of inductive information helps in the generation of data consistency checks based on the structural knowledge abstractions given in the domain model. However, applications have been observed to perform significantly better if they use a combination of the two methods [25]. Figure 3 shows how the inductive and deductive methods can be merged to capture the advantages of both methods. After the structural knowledge is fed into the system model (deductive process), the sensed data is used to refine and complement the basic structural model of the application domain. This refinement procedure can be done continuously throughout the network life to keep consistent mapping between the physical model and the sensed data.  
AMA performs mapping from related multiple types of sense data to overcome the limitations of generating a map from a single sense modality. A single sense modality map typically reveals only a small number of aspects of the monitored phenomena and is unable to infer the correct relations among other types in multi-modal sensing applications. In addition to this inherent data deficiency, high-throughput data sets also often contain errors and noise arising from imperfections of the sensing devices, which further obstructs mapping effectiveness. Maps generated from a combination of different types of data are likely to lead to a more coherent map by consolidating information on various aspects of the monitored phenomena. Additionally, the effects of data noise on generated maps will be dramatically reduced, assuming that sensing errors across different data sets are largely independent and the probability that an error is supported by more than one type of data is small. A natural approach to making use of the relation between the multiple types of sensed data to generate a map is to combine the maps generated from different types of data. We may combine the maps in different methods such as accepting a value at an observation point only when it is commensurate with all maps as defined in the given model. More interestingly, and perhaps with guarantees of delivering better maps, multiple types of data can be analysed concurrently under an integrated relational model. The latter method is novel in the sense that most existing \(n\)-dimensional interpolation schemes are defined by applying one-dimensional interpolation in each separate coordinate dimension without taking advantage of the known relations between diverse dimensions [26].