A Dynamical Systems Approach to Machine Learning

Abstract

Employing various mathematical tools in machine learning is crucial since it may enhance the learning problem's efficiency. Dynamic systems are among the most effective tools. In this study, an effort is made to examine a kind of machine learning from the perspective of a dynamic system, i.e., we apply it to learning problems whose input data is a time series. Using the discretization approach and radial basis functions, a new data set is created to adapt the data to a dynamic system framework. A discrete dynamic system is modeled as a matrix that, when multiplied by the data of each time, yields the data of the next time, or, in other words, can be used to predict the future value based on the present data, and the gradient descent technique was used to train this matrix. Eventually, using Python software, the efficacy of this approach relative to other machine learning techniques, such as neural networks, was analyzed.