Abstract
Conformal Geometric Algebra (CGA) is a high level language commonly used in mathematical, physics and engineering problems. At a top level, CGA is a free coordinate tool for designing and modeling geometric problems; at a low level CGA provides a new coordinate framework for numeric processing in problem solving. In this paper we show how to use quadratic programming and CGA for, given two sets p and q of points in ℝn, construct an optimal separation sphere S such that, all points of p are contained inside of it, and all points of q are outside. To classify an unknown pattern x, an inner product must be applied between x and S. Some numerical and real examples to test the proposal are given.
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© 2008 Springer-Verlag Berlin Heidelberg
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Cruz, B., Barrón, R., Sossa, H. (2008). Pattern Classification Based on Conformal Geometric Algebra and Optimization Techniques. In: Gelbukh, A., Morales, E.F. (eds) MICAI 2008: Advances in Artificial Intelligence. MICAI 2008. Lecture Notes in Computer Science(), vol 5317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88636-5_26
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DOI: https://doi.org/10.1007/978-3-540-88636-5_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88635-8
Online ISBN: 978-3-540-88636-5
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