What size net gives valid generalization?
Neural Computation
Prediction-preserving reducibility
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
An introduction to computational learning theory
An introduction to computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
Randomized algorithms
Partial Classification: The Benefit of Deferred Decision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Are Multilayer Perceptrons Adequate for Pattern Recognition and Verification?
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Real classification problems involve structured data that can be essentially grouped into a relatively small number of clusters. It is shown that, under a local clustering condition, a set of points of a given class, embedded in binary space by a set of randomly parameterized surfaces, is linearly separable from other classes, with arbitrarily high probability. We call such a data set a local relative cluster. The size of the embedding set is shown to be inversely proportional to the squared local clustering degree. A simple parameterization by embedding hyperplanes, implementing a voting system, results in a random reduction of the nearest-neighbor method and leads to the separation of multicluster data by a network with two internal layers. This represents a considerable reduction of the learning problem with respect to known techniques, resolving a long-standing question on the complexity of random embedding. Numerical tests show that the proposed method performs as well as state-of the-art methods and in a small fraction of the time.