We develop some algorithms to determine viability kernels in large dimensions. Various strategies have been used, based on SVM (support vector machines, Deffuant et al. 2007), kd-Trees (Alvarez et al. 2013) or recursive simplex stars (Deffuant 2017). Our work consists in designing these algorithms, determining mathematically their convergence properties, and developing computer software that implement these algorithms. Approximated viability kernels can then be compared and manipulated with our ViNO platform.
Key contributed papers:
-Alvarez, I., De Aldama, R., Martin, S., & Reuillon, R. (2013, August). Assessing the Resilience of Socio-Ecosystems: Coupling Viability Theory and Active Learning with kd-Trees. Application to Bilingual Societies. In Proc. of the 23rd International Joint Conference on Artificial Intelligence (IJCAI’2013) (pp. 2776-2782).
-Deffuant, G. (2017). Recursive simplex stars. arXiv preprint arXiv:1707.08373.
-Alvarez, Reuillon, de Aldama. (2016). Viabilitree: A kd-tree Framework for Viability-based Decision. HAL preprint: hal-01319738.
-Deffuant, G., Chapel, L., & Martin, S. (2007). Approximating viability kernels with support vector machines. IEEE transactions on automatic control, 52(5), 933-937.