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Aldana-Bobadilla E.,National Autonomous University of Mexico | Kuri-Morales A.,Autonomus Institute of Technology of Mexico
Entropy | Year: 2015

Clustering is an unsupervised process to determine which unlabeled objects in a set share interesting properties. The objects are grouped into k subsets (clusters) whose elements optimize a proximity measure. Methods based on information theory have proven to be feasible alternatives. They are based on the assumption that a cluster is one subset with the minimal possible degree of "disorder". They attempt to minimize the entropy of each cluster. We propose a clustering method based on the maximum entropy principle. Such a method explores the space of all possible probability distributions of the data to find one that maximizes the entropy subject to extra conditions based on prior information about the clusters. The prior information is based on the assumption that the elements of a cluster are "similar" to each other in accordance with some statistical measure. As a consequence of such a principle, those distributions of high entropy that satisfy the conditions are favored over others. Searching the space to find the optimal distribution of object in the clusters represents a hard combinatorial problem, which disallows the use of traditional optimization techniques. Genetic algorithms are a good alternative to solve this problem. We benchmark our method relative to the best theoretical performance, which is given by the Bayes classifier when data are normally distributed, and a multilayer perceptron network, which offers the best practical performance when data are not normal. In general, a supervised classification method will outperform a non-supervised one, since, in the first case, the elements of the classes are known a priori. In what follows, we show that our method's effectiveness is comparable to a supervised one. This clearly exhibits the superiority of our method. © 2015 by the authors.

Acosta-Mejia C.A.,Autonomus Institute of Technology of Mexico
Computers and Industrial Engineering | Year: 2011

To improve the performance of control charts the conditional decision procedure (CDP) incorporates a number of previous observations into the chart's decision rule. It is expected that charts with this runs rule are more sensitive to shifts in the process parameter. To signal an out-of-control condition more quickly some charts use a headstart feature. They are referred as charts with fast initial response (FIR). The CDP chart can also be used with FIR. In this article we analyze and compare the performance of geometric CDP charts with and with no FIR. To do it we model the CDP charts with a Markov chain and find closed-form ARL expressions. We find the conditional decision procedure useful when the fraction p of nonconforming units deteriorates. However the CDP chart is not very effective for signaling decreases in p. © 2011 Elsevier Ltd. All rights reserved.

Palma-Mendoza J.A.,Autonomus Institute of Technology of Mexico
International Journal of Information Management | Year: 2014

A supply chain consists of different processes and when conducting supply chain re-design is necessary to identify the relevant processes and select a target for re-design. Through a literature review a solution is presented here to identify first the relevant processes using the Supply Chain Operations Reference (SCOR) model, then to use Analytical Hierarchy Process (AHP) analysis for target process selection. AHP can aid in deciding which supply chain processes are better candidates to re-design in light of predefined criteria. © 2014 Elsevier Ltd. All rights reserved.

Munoz D.F.,Autonomus Institute of Technology of Mexico
Operations Research Letters | Year: 2010

We discuss the asymptotic validity of confidence intervals for quantiles of performance variables when simulating a Markov chain. We show that a batch quantile methodology (similar to the batch means method) can be applied to obtain confidence intervals that are asymptotically valid under mild assumptions. © 2010 Elsevier B.V. All rights reserved.

Morales J.L.,Autonomus Institute of Technology of Mexico | Nocedal J.,Northwestern University
ACM Transactions on Mathematical Software | Year: 2011

This remark describes an improvement and a correction to Algorithm 778. It is shown that the performance of the algorithm can be improved significantly by making a relatively simple modification to the subspace minimization phase. The correction concerns an error caused by the use of routine dpmeps to estimate machine precision. © 2011 ACM 0098-3500/2011/11-ART7.

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