TY - GEN
T1 - Pattern classification based on conformal geometric algebra and optimization techniques
AU - Cruz, Benjamín
AU - Barrón, Ricardo
AU - Sossa, Humberto
PY - 2008
Y1 - 2008
N2 - 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 ℝ n , 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.
AB - 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 ℝ n , 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.
KW - Conformal Geometric Algebra
KW - Optimization
KW - Pattern Classification
UR - http://www.scopus.com/inward/record.url?scp=57049181809&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-88636-526
DO - 10.1007/978-3-540-88636-526
M3 - Contribución a la conferencia
SN - 3540886354
SN - 9783540886358
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 273
EP - 283
BT - MICAI 2008
T2 - 7th Mexican International Conference on Artificial Intelligence, MICAI 2008
Y2 - 27 October 2008 through 31 October 2008
ER -