On the Complexity of Recognizing Iterated Differences of Polyhedra
| Type of publication: | Idiap-RR |
| Citation: | Mayo97a |
| Number: | Idiap-RR-10-1997 |
| Year: | 1997 |
| Institution: | IDIAP |
| Note: | Published in the Proceedings of ICANN'97 |
| Abstract: | The iterated difference of polyhedra $V = P_1 \backslash ( P_2 \backslash (... P_k ) ... )$ has been proposed independently in [Zwie-Aart-Wess92] and [Shon93] as a sufficient condition for $V$ to be exactly computable by a two-layered neural network. An algorithm checking whether $V$ included in $R^d$ is an iterated difference of polyhedra is proposed in [Zwie-Aart-Wess92]. However, this algorithm is not practically usable because it has a high computational complexity and it was only conjectured to stop with a negative answer when applied to a region which is not an iterated difference of polyhedra. This paper sheds some light on the nature of iterated difference of polyhedra. The outcomes are\,: (i) an algorithm which always stops after a small number of iterations, (ii) sufficient conditions for this algorithm to be polynomial and (iii) the proof that an iterated difference of polyhedra can be exactly computed by a two-layered neural network using only essential hyperplanes. |
| Userfields: | ipdmembership={learning}, |
| Keywords: | |
| Projects: |
Idiap |
| Authors: | |
| Crossref by |
Mayo97a1 |
| Added by: | [UNK] |
| Total mark: | 0 |
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