- author = "Michael Schmidt and Hod Lipson",
- title = "Symbolic Regression of Implicit Equations",
- booktitle = "Genetic Programming Theory and Practice {VII}",
- year = "2009",
- editor = "Rick L. Riolo and Una-May O'Reilly and Trent McConaghy",
- series = "Genetic and Evolutionary Computation",
- address = "Ann Arbor",
- month = "14-16 " # may,
- publisher = "Springer",
- chapter = "5",
- pages = "73--85",
- keywords = "genetic algorithms, genetic programming, Symbolic Regression, Implicit Equations, Unsupervised Learning",
- isbn13 = "978-1-4419-1653-2",
-
DOI = "
doi:10.1007/978-1-4419-1626-6_5",
- abstract = "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 difficult to define. We studied several direct and indirect techniques, and present a successful method based on implicit derivatives. Our experiments identified implicit relationships found in a variety of datasets, such as equations of circles, elliptic curves, spheres, equations of motion, and energy manifolds.",
-
notes = "Entered 2010 HUMIES GECCO 2010
part of \cite{Riolo:2009:GPTP}",
