A statistical neural network for high-dimensional vector classification (1995) [3 citations — 0 self]
Abstract:
verleysen�dice.ucl.ac.be The minimum number of misclassi�cations in a multi�class classi�er is reached when the borders between classes are set according to the Bayes criterion. Unfortunately � this criterion necessitates the knowledge of the probability density function of each class of data � which is unknown in practical problems. The theory of kernel estimators �Parzen windows � provides a way to estimate these probability densities � given a set of data in each class. The computational complexity of these estimators is however much too large in most practical applications � we propose here a neural network aimed to estimate the probability density function underlying a set of data � in a sub�optimal way �while performances are quite similar to those in the optimal case� � but with a strongly reduced complexity which makes the method useful in practical situations. The algorithm is based on a �competitive learning � vector quantization of the data� and on the choice of optimal widths for the kernels. We study the in�uence of this factor on the classi�cation error rate � and provide examples of the use of the algorithm on real�world data. 1.
Citations
| 805 | An algorithm for vector quantizer design – Linde, Buzo, et al. - 1980 |
| 5 | Supervised design of optimal receivers – Comon, Bienvenu, et al. - 1992 |
| 1 | Cacoullos� �Estimation of a multivariate density – unknown authors - 1966 |
| 1 | Comon� �Supervised classi�cation� a proba� bilistic approach – unknown authors - 1995 |
| 1 | Estima� tion of performance bounds in supervised clas� si�cation – Voz�, Verleysen� - 1994 |
| 1 | Handwritten digit recognition by suboptimal bayesian classi�er – Thissen�, Legat� - 1994 |
| 1 | A practical view of suboptimal bayesian clas� si�cation – Thissen�, Legat� - 1995 |
| 1 | Suboptimal bayesian classi�cation by vector quantization with small clusters – Thissen�, Legat� - 1995 |
