Classifications of dynamical systems and applications in vision geometry
Ying Liu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
In this paper, we study the families of dynamical systems which can be applied to learning. We first introduce three classifications of dynamical systems, based on attractor topology, space complexity of parameter space, and information capacity. Then, we demonstrate how each class of dynamical systems can be applied to learning. Thirdly, we show that there are three different types of geometry which are related to vision, the image geometry, the information geometry, and the dynamical system geometry. Finally, we discuss the relations between vision and all three geometries. This study helps in understanding the capabilities and limitations of a family of dynamical systems. Digital image geometry has been studied for a long time. Information geometry is proposed by Amari recently which study the manifold formed by free parameters of dynamical systems and its relation to vision. Dynamical system geometry abstractly studies the behavior of dynamical systems, and this study is independent of a detailed model, like neural networks or iterated function systems. A model, like neural network, usually occupies a subspace in the space of dynamical systems. In this paper, we also explore the relations among these three geometries.