Gen-FW: Una generalización del problema de Fermat-Weber con aplicaciones al procesamiento de datos

This project proposes and justifies a generalization of the Fermat-Weber problem (or simply, the FW problem). The FW problem aims to find a vector that minimizes the sum of weighted distances to other given vectors in a vector space, where the vector to be minimized is represented by a linear transformation. The solution to the FW problem has various applications in engineering, for example, in the design of navigation algorithms and in mobile network connectivity with wireless sensors, among others.

The mathematical models we propose generalize the FW problem in two aspects: 1) They consider nonlinear transformations, unlike the FW problem, which only considers linear transformations. 2) They calculate the optimal transformations (linear or nonlinear) that belong to a set with a predetermined structure, unlike the FW problem, which does not optimize the associated linear transformation. The characteristics mentioned above will allow the numerical error obtained in the proposed models to be lower than the error obtained in the FW problem

Additionally, we will apply the generalization of the FW problem to data processing, particularly in applications in the field of forestry engineering, specifically in the analysis of hyperspectral signatures and tree bark. The proposed generalization of the FW problem will simplify the process of analyzing hyperspectral signatures in wood and leaves between 310 and 1100 nanometers, allowing us to determine the biotypic signature of each species. This would facilitate their identification in the field, either with terrestrial instrumentation or multiband satellite images. Furthermore, it will facilitate the process of identifying tree species bark by generating a biotypic photo of a species, which would simplify the process of identifying and studying tropical species bark

Desarrollar un modelo matemático que generalice el problema de Fermat-Weber, el cual mejore la estimación numérica del problema original y sea aplicado en procesamiento de datos.

Escuela de Matemáticas. Matemática aplicada: modelación, simulación, inteligencia artificial, análisis de datos, visualización de información, optimización y aplicaciones a la ingeniería y a las ciencias.
Escuela de Ingeniería Forestal: Manejo sostenible de bosques naturales