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@InCollection{Schmidt:2009:GPTP, 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 http://www.genetic-programming.org/combined.php part of \cite{Riolo:2009:GPTP}", }

Genetic Programming entries for Michael D Schmidt Hod Lipson