Symbolic Regression of Implicit Equations
نویسندگان
چکیده
Traditional Symbolic Regression applications are a form of supervised learning, where a label y is provided for every ~x and an explicit symbolic relationship of the form y = f(~x) is sought. This chapter explores the use of symbolic regression to perform unsupervised learning by searching for implicit relationships of the form f(~x, y) = 0. Implicit relationships are more general and more expressive than explicit equations in that they can also represent closed surfaces, as well as continuous and discontinuous multi-dimensional manifolds. However, searching these types of equations is particularly challenging because an error metric is diff cult to def ne. We studied several direct and indirect techniques, and present a successful method based on implicit derivatives. Our experiments identif ed implicit relationships found in a variety of datasets, such as equations of circles, elliptic curves, spheres, equations of motion, and energy manifolds.
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