Adaptive Scaling of Codebook Vectors

this paper we introduce a vector quantization algorithm in which the codebook vectors are extended with a scale parameter to let them represent Gaussian functions. The means of these functions are determined by a standard vector quantization algorithm; and for their scales we have derived a learning rule. Our algorithm estimates the probability densities efficiently. The main application is pattern classification. Pattern classification is trivial if a function is available which describes the probability distribution of the classes in the pattern space. In that case we can use the Bayesian classifier; classify a pattern according to the class with the largest probability at the respective sample position in the pattern space. The obvious problem is then to find a function which describes this probability distribution. A standard method is Parzen window estimation [1]. In this method each pattern is seen as a Gaussian distribution whose mean equals the pattern position and whose standard deviation (or scale) has some arbitrary value. The estimated probability function is the average of all Gaussians. The major advantage of this method is that any probability function will be estimated correctly if the number of samples reaches infinity. The main disadvantages are: (i) a large number of samples is necessary to obtain a reasonable estimate; (ii) the probability function is in terms of a large number of Gaussians and evaluation of the function is time and memory consuming, and (iii) the choice of the standard deviation is arbitrary. In this paper we propose a new method which reduces the mentioned disadvantages but keeps the nice properties of Parzen window estimation. 2 Related Wor

Proposal for a strategic planning for the replacement of products in stores based on sales forecast

This paper presents a proposal for strategic planning for the replacement of products in stores of a supermarket network. A quantitative method for forecasting time series is used for this, the Artificial Radial Basis Neural Networks (RBFs), and also a qualitative method to interpret the forecasting results and establish limits for each product stock for each store in the network. The purpose with this strategic planning is to reduce the levels of out-of-stock products (lack of products on the shelves), as well as not to produce overstocking, in addition to increase the level of logistics service to customers. The results were highly satisfactory reducing the Distribution Center (DC) to shop out-of-stock levels, in average, from 12% to about 0.7% in hypermarkets and from 15% to about 1.7% in supermarkets, thereby generating numerous competitive advantages for the company. The use of RBFs for forecasting proved to be efficient when used in conjunction with the replacement strategy proposed in this work, making effective the operational processes