Generalized measures of artificial neural network capabilities

Martha Alvey Carter; Mark E. Oxley

doi:10.1117/12.342875

22 March 1999 Generalized measures of artificial neural network capabilities

Martha Alvey Carter, Mark E. Oxley

Proceedings Volume 3722, Applications and Science of Computational Intelligence II; (1999) https://doi.org/10.1117/12.342875
Event: AeroSense '99, 1999, Orlando, FL, United States

Abstract

Current measures of an artificial neural networks (ANN) capability are the V-C dimension and its variations. These measures may be underestimating capabilities (in the primal sense) and hence overestimating the required number of examples for learning (in the dual sense). This is a result of relying on a single invariant description of the problem set, which is cardinality, and requiring worst case geometries and colorings. Generalization of a capability measure allows aligning the measure with desired characteristics of the problem sets. We present a mathematical framework in which to express other desired invariant descriptors of a capability measure, and guarantee proper application of the measure to ANNs. We define a collection of invariants defined on the problem space that yield new capability measures of ANNs. A specific example of an invariant is given which is based on geometric complexity of the problem set and yields a new measure of ANNs called the Ox-Cart dimension.

Citation Download Citation

Martha Alvey Carter and Mark E. Oxley "Generalized measures of artificial neural network capabilities", Proc. SPIE 3722, Applications and Science of Computational Intelligence II, (22 March 1999); https://doi.org/10.1117/12.342875

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