@conference {
	title = {Convergence of a Neural Network Classifier},
	author = {Baras, John S., LaVigna, Anthony.},
	year = {1990},
	month = {12/1990},
	abstract = {In this paper, we show that the LVQ learning algorithm converges to locally asymptotic stable equilibria of an ordinary differential equation. We show that the learning algorithm performs stochastic approximation. Convergence of the Voronoi vectors is guaranteed under the appropriate conditions on the underlying statistics of the classification problem. We also present a modification to the learning algorithm which we argue results in convergence of the LVQ~for a larger set of initial conditions. Finally, we show that LVQ~is a general histogram classifier and that its risk converges to the Bayesian optimal risk as the appropriate parameters go to infinity with the number~of past observations.},
	address = {Honolulu, Hawaii},
	booktitle = {The 29th Conference on Decision and Control (CDC)},
	pages = {pp. 1735-1740}
}
@conference {
	title = {Convergence of the Vectors in Kohonen{\textquoteright}s Learning Vector Quantization},
	author = {Baras, John S., LaVigna, Anthony.},
	year = {1990},
	month = {07/1990},
	abstract = {Kohonen{\textquoteright}s Learning Vector Quantization is a nonparametric classification scheme which classifies observations by comparing them to k templates called Voronoi vectors. The locations of these vectors are determined from past labeled data through a learning algorithm. When learning is complete, the class of a new observation is the same as the class of the closest Voronoi vector. Hence LVQ is similar to nearest neighbors, except that instead of all of the past observations being searched only the k Voronoi vectors are searched.

In this paper, we show that the LVQ learning algorithm converges to asymptotically stable zeros of an ordinary differential eq{\"u}ation. It is shown that the learning algorithm performs stochastic approximation. Convergence of the vectors is guaranteed under the appropriate conditions on the underlying statistics of the classification problem. We also~present a modification to the learning algorithm which results in more robust convergence.},
	address = {Paris, France},
	booktitle = {The  1990 International Conference on Neural Networks},
	pages = {pp. 1028-1031}
}
