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
FROSINI, PATRIZIO
2008-01-01
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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