Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

Experimentation in the adaptation of the overhead projector utilizing 200 transparencies and 800 overlays in teaching engineering descriptive geometry curricula, June 1, 1959 to August 31, 1960. Final report, grant no. 741023.09, U. S. Office of Education, Dept. of Health, Education, and Welfare.

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Descriptive geometry, a pictorial approach

Mode of access: Internet.

Descriptive geometry, in six parts ...

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Elements of descriptive geometry : with their application to spherical trigonometry, spherical projections, and warped surfaces /

Mode of access: Internet.

Elements of descriptive geometry : with their application to spherical trigonometry, spherical projections, and warped surfaces /

Mode of access: Internet.

Elements of descriptive geometry ; with their application to spherical trigonometry, spherical projections, and warped surfaces /

Mode of access: Internet.

Experimentation in the adaptation of the overhead projector utilizing 200 transparencies and 800 overlays in teaching engineering descriptive geometry curricula

"Corrected graph iv" leaf inserted.

Elements of descriptive geometry: with its applications to shades, shadows, and perspective, and to topography /

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A manual of descriptive geometry, with numerous problems,

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Text-book on practical, solid or descriptive geometry.

Vol. 2: 3d ed.

Textbook on practical solid or descriptive geometry,

Mode of access: Internet.

The essentials of descriptive geometry,

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Elementary descriptive geometry,

Mode of access: Internet.