Topology-based classification error calculation for symbolic indoor positioning

The topology-based classification error calculation for symbolic indoor positioning is presented in this paper. Symbolic indoor positioning can be considered as a classification problem, where each category is a symbolic position. The evaluation of classifiers usually follows the CRISP approach, which treats each misclassification equally wrong. However, previous experimental results revealed the demand to distinguish the misclassification errors based on the topology of the building. There are three criteria against the topology-based classification error calculation. Firstly, the method has to take into count the size of the Zones. Secondly, the layout of the Zones has to be considered. Finally, the error values should be proportional to the size of the Zone so the function should be asymmetric. The new approach is based on the gravitational force used in physics, which can be treated as the similarity of two objects, Thus, the gravitational force is inversely proportional with the distance of the Zones and proportional with the product of its capacities. Dissimilarity can be expressed as the reciprocal of the gravitational force. The classification error has to be defined to increase with the dissimilarity of the Zones. Hence the selection of capacity function, and distance function with its reference points has a high impact on the error values. In this paper the method to determine the classification error matrix based on the topology of building is presented.