VC‐dimension on manifolds: a first approach |
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Authors: | Massimo Ferri Patrizio Frosini |
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Affiliation: | ARCES and Department of Mathematics, Piazza di Porta S. Donato, 5, I‐40126 Bologna, Italy |
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Abstract: | 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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Keywords: | statistical learning covering projection Vapnik– Chervonenkis‐dimension Morse function |
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