Learning Pretopological Spaces to Model Complex Propagation Phenomena: A Multiple Instance Learning Approach Based on a Logical Modeling

This paper addresses the problem of learning the concept of "propagation" in the pretopology theoretical formalism. Our proposal is first to define the pseudo-closure operator (modeling the propagation concept) as a logical combination of neighborhoods. We show that learning such an operator lapses into the Multiple Instance (MI) framework, where the learning process is performed on bags of instances instead of individual instances. Though this framework is well suited for this task, its use for learning a pretopological space leads to a set of bags exponential in size. To overcome this issue we thus propose a learning method based on a low estimation of the bags covered by a concept under construction. As an experiment, percolation processes (forest fires typically) are simulated and the corresponding propagation models are learned based on a subset of observations. It reveals that the proposed MI approach is significantly more efficient on the task of propagation model recognition than existing methods.