VC‐dimension on manifolds: a first approach | Zendy

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VC‐dimension on manifolds: a first approach

Author(s) -

Ferri Massimo,

Frosini Patrizio

Publication year - 2007

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.927

Subject(s) - mathematics , dimension (graph theory) , simple (philosophy) , manifold (fluid mechanics) , euclidean geometry , context (archaeology) , product (mathematics) , euclidean space , euclidean distance , pure mathematics , index (typography) , algebra over a field , computer science , geometry , epistemology , mechanical engineering , paleontology , philosophy , world wide web , engineering , biology

The Vapnik–Chervonenkis‐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 toward a still open problem on product manifolds. Copyright © 2007 John Wiley & Sons, Ltd.

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