Pattern classification based on conformal geometric algebra and optimization techniques

Benjamín Cruz; Ricardo Barrón; Humberto Sossa

doi:10.1007/978-3-540-88636-526

Pattern classification based on conformal geometric algebra and optimization techniques

Benjamín Cruz, Ricardo Barrón, Humberto Sossa

Centro de Investigación en Computación (CIC)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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 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.

Original language	English
Title of host publication	MICAI 2008
Subtitle of host publication	Advances in Artificial Intelligence - 7th Mexican International Conference on Artificial Intelligence, Proceedings
Pages	273-283
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-540-88636-526
State	Published - 2008
Event	7th Mexican International Conference on Artificial Intelligence, MICAI 2008 - Atizapan de Zaragoza, Mexico Duration: 27 Oct 2008 → 31 Oct 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5317 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th Mexican International Conference on Artificial Intelligence, MICAI 2008
Country/Territory	Mexico
City	Atizapan de Zaragoza
Period	27/10/08 → 31/10/08

Keywords

Conformal Geometric Algebra
Optimization
Pattern Classification

Access to Document

10.1007/978-3-540-88636-526

Cite this

Cruz, B., Barrón, R., & Sossa, H. (2008). Pattern classification based on conformal geometric algebra and optimization techniques. In MICAI 2008: Advances in Artificial Intelligence - 7th Mexican International Conference on Artificial Intelligence, Proceedings (pp. 273-283). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5317 LNAI). https://doi.org/10.1007/978-3-540-88636-526

Cruz, Benjamín ; Barrón, Ricardo ; Sossa, Humberto. / Pattern classification based on conformal geometric algebra and optimization techniques. MICAI 2008: Advances in Artificial Intelligence - 7th Mexican International Conference on Artificial Intelligence, Proceedings. 2008. pp. 273-283 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 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.",

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Cruz, B, Barrón, R & Sossa, H 2008, Pattern classification based on conformal geometric algebra and optimization techniques. in MICAI 2008: Advances in Artificial Intelligence - 7th Mexican International Conference on Artificial Intelligence, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5317 LNAI, pp. 273-283, 7th Mexican International Conference on Artificial Intelligence, MICAI 2008, Atizapan de Zaragoza, Mexico, 27/10/08. https://doi.org/10.1007/978-3-540-88636-526

Pattern classification based on conformal geometric algebra and optimization techniques. / Cruz, Benjamín; Barrón, Ricardo; Sossa, Humberto.
MICAI 2008: Advances in Artificial Intelligence - 7th Mexican International Conference on Artificial Intelligence, Proceedings. 2008. p. 273-283 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5317 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Cruz, Benjamín

AU - Barrón, Ricardo

AU - Sossa, Humberto

PY - 2008

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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

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KW - Pattern Classification

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DO - 10.1007/978-3-540-88636-526

M3 - Contribución a la conferencia

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SN - 9783540886358

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Cruz B, Barrón R, Sossa H. Pattern classification based on conformal geometric algebra and optimization techniques. In MICAI 2008: Advances in Artificial Intelligence - 7th Mexican International Conference on Artificial Intelligence, Proceedings. 2008. p. 273-283. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-88636-526

Pattern classification based on conformal geometric algebra and optimization techniques

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