dorsal/arxiv
View SchemaThe Normalized Radial Basis Function Neural Network and its Relation to the Perceptron
| Authors | I. Grabec |
|---|---|
| Categories | |
| ArXiv ID | physics/0703229 |
| URL | https://arxiv.org/abs/physics/0703229 |
| Journal | Dynamics of Continuous, Discrete and Impulsive Systems, B, Special Volume: Advances in Neural Networks, 2007 (in print) |
Abstract
The normalized radial basis function neural network emerges in the statistical modeling of natural laws that relate components of multivariate data. The modeling is based on the kernel estimator of the joint probability density function pertaining to given data. From this function a governing law is extracted by the conditional average estimator. The corresponding nonparametric regression represents a normalized radial basis function neural network and can be related with the multi-layer perceptron equation. In this article an exact equivalence of both paradigms is demonstrated for a one-dimensional case with symmetric triangular basis functions. The transformation provides for a simple interpretation of perceptron parameters in terms of statistical samples of multivariate data.
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"abstract": "The normalized radial basis function neural network emerges in the\nstatistical modeling of natural laws that relate components of multivariate\ndata. The modeling is based on the kernel estimator of the joint probability\ndensity function pertaining to given data. From this function a governing law\nis extracted by the conditional average estimator. The corresponding\nnonparametric regression represents a normalized radial basis function neural\nnetwork and can be related with the multi-layer perceptron equation. In this\narticle an exact equivalence of both paradigms is demonstrated for a\none-dimensional case with symmetric triangular basis functions. The\ntransformation provides for a simple interpretation of perceptron parameters in\nterms of statistical samples of multivariate data.",
"arxiv_id": "physics/0703229",
"authors": [
"I. Grabec"
],
"categories": [
"physics.data-an",
"physics.comp-ph"
],
"journal_ref": "Dynamics of Continuous, Discrete and Impulsive Systems, B, Special\n Volume: Advances in Neural Networks, 2007 (in print)",
"title": "The Normalized Radial Basis Function Neural Network and its Relation to the Perceptron",
"url": "https://arxiv.org/abs/physics/0703229"
},
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