Learning Pretopological Spaces to Model Complex Propagation Phenomena: A Multiple Instance Learning Approach Based on a Logical Modeling
This work addresses the challenge of modeling complex propagation phenomena, such as forest fires, using pretopological theory, but it is incremental as it builds on existing Multiple Instance Learning frameworks to improve efficiency in a specific domain.
The paper tackles the problem of learning propagation models in pretopological spaces by defining a pseudo-closure operator as a logical combination of neighborhoods and framing it as a Multiple Instance Learning task. It proposes a method to handle exponential bag sizes and shows that this approach is significantly more efficient for propagation model recognition in simulated percolation processes like forest fires compared to existing methods.
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.