5 April 2002 Convexity of learning vectors and their N-dimension boundary
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Most neural networks consisting of discrete (or sign- function) neurons can be studied by discrete mathematics and N-dimension geometry. Particularly, the supervised learning of a feed-forward neural system is crucially related to the geometry of N-dimension convex cones in the N-space. It is shown in this paper that to learn a set of pattern sample vectors forming a convex cone in the N-space, it is only necessary to learn the boundary vectors (or the extreme edges) of this cone, which then makes the learning much more efficient. This paper provides a novel approach to test the convexity of a set of N-vectors (given numerically in an Euclidean N-space) and to find the boundary vectors of this set if it is convex.
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Chia-Lun John Hu, Chia-Lun John Hu, } "Convexity of learning vectors and their N-dimension boundary", Proc. SPIE 4668, Applications of Artificial Neural Networks in Image Processing VII, (5 April 2002); doi: 10.1117/12.461678; https://doi.org/10.1117/12.461678

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