VC-dimension is an index of the capacity of a learning machine. It has been computed in several cases, but always in a Euclidean context. This paper extends the notion to classifiers acting in the more general environment of a manifold. General properties are proved, and some examples of simple classifiers on elementary manifolds are given. A large part of the research is directed towards a still open problem on product manifolds.
VC-dimension on manifolds: A first approach / Ferri M.; Frosini P.. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - 31:(2008), pp. 589-605. [10.1002/mma.927]
VC-dimension on manifolds: A first approach
FERRI, MASSIMO;FROSINI, PATRIZIO
2008
Abstract
VC-dimension is an index of the capacity of a learning machine. It has been computed in several cases, but always in a Euclidean context. This paper extends the notion to classifiers acting in the more general environment of a manifold. General properties are proved, and some examples of simple classifiers on elementary manifolds are given. A large part of the research is directed towards a still open problem on product manifolds.File in questo prodotto:
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