Random projection RBF nets for multidimensional density estimation

Ewa Skubalska-Rafajłowicz

International Journal of Applied Mathematics and Computer Science (2008)

  • Volume: 18, Issue: 4, page 455-464
  • ISSN: 1641-876X

Abstract

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The dimensionality and the amount of data that need to be processed when intensive data streams are observed grow rapidly together with the development of sensors arrays, CCD and CMOS cameras and other devices. The aim of this paper is to propose an approach to dimensionality reduction as a first stage of training RBF nets. As a vehicle for presenting the ideas, the problem of estimating multivariate probability densities is chosen. The linear projection method is briefly surveyed. Using random projections as the first (additional) layer, we are able to reduce the dimensionality of input data. Bounds on the accuracy of RBF nets equipped with a random projection layer in comparison to RBF nets without dimensionality reduction are established. Finally, the results of simulations concerning multidimensional density estimation are briefly reported.

How to cite

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Ewa Skubalska-Rafajłowicz. "Random projection RBF nets for multidimensional density estimation." International Journal of Applied Mathematics and Computer Science 18.4 (2008): 455-464. <http://eudml.org/doc/207899>.

@article{EwaSkubalska2008,
abstract = {The dimensionality and the amount of data that need to be processed when intensive data streams are observed grow rapidly together with the development of sensors arrays, CCD and CMOS cameras and other devices. The aim of this paper is to propose an approach to dimensionality reduction as a first stage of training RBF nets. As a vehicle for presenting the ideas, the problem of estimating multivariate probability densities is chosen. The linear projection method is briefly surveyed. Using random projections as the first (additional) layer, we are able to reduce the dimensionality of input data. Bounds on the accuracy of RBF nets equipped with a random projection layer in comparison to RBF nets without dimensionality reduction are established. Finally, the results of simulations concerning multidimensional density estimation are briefly reported.},
author = {Ewa Skubalska-Rafajłowicz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {radial basis functions; multivariate density estimation; dimension reduction; normal random projection; novelty detection},
language = {eng},
number = {4},
pages = {455-464},
title = {Random projection RBF nets for multidimensional density estimation},
url = {http://eudml.org/doc/207899},
volume = {18},
year = {2008},
}

TY - JOUR
AU - Ewa Skubalska-Rafajłowicz
TI - Random projection RBF nets for multidimensional density estimation
JO - International Journal of Applied Mathematics and Computer Science
PY - 2008
VL - 18
IS - 4
SP - 455
EP - 464
AB - The dimensionality and the amount of data that need to be processed when intensive data streams are observed grow rapidly together with the development of sensors arrays, CCD and CMOS cameras and other devices. The aim of this paper is to propose an approach to dimensionality reduction as a first stage of training RBF nets. As a vehicle for presenting the ideas, the problem of estimating multivariate probability densities is chosen. The linear projection method is briefly surveyed. Using random projections as the first (additional) layer, we are able to reduce the dimensionality of input data. Bounds on the accuracy of RBF nets equipped with a random projection layer in comparison to RBF nets without dimensionality reduction are established. Finally, the results of simulations concerning multidimensional density estimation are briefly reported.
LA - eng
KW - radial basis functions; multivariate density estimation; dimension reduction; normal random projection; novelty detection
UR - http://eudml.org/doc/207899
ER -

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