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Rivera M.,Center for Research in Mathematics | Dalmau O.,Center for Research in Mathematics
IEEE Transactions on Image Processing | Year: 2012

We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework. © 2011 IEEE.


Salinas-Gutierrez R.,Center for Research in Mathematics | Hernandez-Aguirre A.,Center for Research in Mathematics | Villa-Diharce E.R.,Center for Research in Mathematics
Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 | Year: 2010

A new Estimation of Distribution Algorithm is presented. The proposed algorithm, called D-vine EDA, uses a graphical model which is based on pair copula decomposition. By means of copula functions it is possible to model the dependence structure in a joint distribution with marginals of different type. Thus, this paper introduces the D-vine EDA and performs experiments and statistical tests to assess the best algorithm. The set of experiments shows the potential of the D-vine EDA. Copyright 2010 ACM.


Serrano Rubio J.P.,Center for Research in Mathematics | Hernandez Aguirre A.,Center for Research in Mathematics | Herrera Guzman R.,Center for Research in Mathematics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

This paper presents the implementation of a Multilayer Perceptron (MLP) using a new higher order neuron whose decision region is generated by a conic section (circle, ellipse, parabola, hyperbola). We call it the hyper-conic neuron. The conic neuron is defined for the conformal space where it can freely work and take advantage of all the rules of Geometric (Clifford) Algebra. The proposed neuron is a non-linear associator that estimates distances from vectors (points) to decision regions. The computational model of the conic neuron is based on the geometric product (an outer product plus an inner product) of geometric algebra in conformal space. The Particle Swarm Optimization (PSO) algorithm is used to find the values of the weights that properly define some MLP for a given classification problem. The performance is presented with a classical benchmark used in neural computing. © 2013 Springer-Verlag.


Segura C.,Center for Research in Mathematics | Coello Coello C.A.,National Polytechnic Institute of Mexico | Hernandez-Diaz A.G.,Pablo De Olavide University
Information Sciences | Year: 2015

Differential Evolution is an efficient metaheuristic for continuous optimization that suffers from the curse of dimensionality. A large amount of experimentation has allowed researchers to find several potential weaknesses in Differential Evolution. Some of these weaknesses do not significantly affect its performance when dealing with low-dimensional problems, so the research community has not paid much attention to them. The aim of this paper is to provide a better insight into the reasons of the curse of dimensionality and to propose techniques to alleviate this problem. Two different weaknesses are revisited and schemes for dealing with them are devised. The schemes increase the diversity of trial vectors and improve on the exploration capabilities of Differential Evolution. Some important mathematical properties induced by our proposals are studied and compared against those of related schemes. Experimentation with a set of problems with up to 1000 dimensions and with several variants of Differential Evolution shows that the weaknesses analyzed significantly affect the performance of Differential Evolution when used on high-dimensional optimization problems. The gains of the proposals appear when highly exploitative schemes are used. Our proposals allow for high-quality solutions with small populations, meaning that the most significant advantages emerge when dealing with large-scale optimization problems, where the benefits of using small populations have previously been shown. © 2015 Elsevier Inc.


Hasimoto-Beltran R.,Center for Research in Mathematics
Proceedings - 3rd International Conference on Multimedia Information Networking and Security, MINES 2011 | Year: 2011

We present a new LUT design consisting of a non-iterative plaintext transformation and a high dimensionally (K-map) populated dynamic Look-Up Table with random access that outperforms the security and speed of previous LUT based schemes. Experimental analysis of the proposed scheme reveals excellent statistical properties, sensitivity to plaintext/system-key changes, robustness to differential and chosen plaintext attack, and high performance for real-time multimedia communications. © 2011 IEEE.


Debruyne M.,University of Antwerp | Hubert M.,Catholic University of Leuven | Van Horebeek J.,Center for Research in Mathematics
Computational Statistics and Data Analysis | Year: 2010

Kernel Principal Component Analysis extends linear PCA from a Euclidean space to any reproducing kernel Hilbert space. Robustness issues for Kernel PCA are studied. The sensitivity of Kernel PCA to individual observations is characterized by calculating the influence function. A robust Kernel PCA method is proposed by incorporating kernels in the Spherical PCA algorithm. Using the scores from Spherical Kernel PCA, a graphical diagnostic is proposed to detect points that are influential for ordinary Kernel PCA. © 2009 Elsevier B.V. All rights reserved.


Salinas-Gutierrez R.,Center for Research in Mathematics | Hernandez-Aguirre A.,Center for Research in Mathematics | Villa-Diharce E.R.,Center for Research in Mathematics
Genetic and Evolutionary Computation Conference, GECCO'11 - Companion Publication | Year: 2011

The main objective of this doctoral research is to study Estimation of Distribution Algorithms (EDAs) based on copula functions. This new class of EDAs has shown that it is possible to incorporate successfully copula functions in EDAs. © 2011 ACM.


Segovia-Dominguez I.,Center for Research in Mathematics | Hernandez-Aguirre A.,Center for Research in Mathematics
GECCO 2015 - Proceedings of the 2015 Genetic and Evolutionary Computation Conference | Year: 2015

This paper introduces an Estimation of Distribution Algorithm (EDA), in which the parameters of the search distribution are updated by the natural gradient technique. The parameter updating is guided via the Kullback-Leibler divergence between the multivariate Normal and the Boltzmann densities. This approach makes sense because it is wellknown that the Boltzmann function yields a reliable model to simulate particles near to optimum locations. Three main contributions are presented here in order to build an effective EDA. The first one is a natural gradient formula which allows for an update of the parameters of a density function. These equations are related to an exponential parametrization of the search distribution. The second contribution involves the approximation of the developed gradient formula and its connection to the importance sampling method. The third contribution is a parameter update rule which is designed to control the exploration and exploitation phases of the algorithm. The proposed EDA is tested on a benchmark of 16 problems and compared versus the XNES and iAMaLGaM algorithms. The statistical results show that the performance of the proposed method is competitive and it is the winner in several problems. © 2015 ACM.


Almasalha F.,Applied Science Private University | Hasimoto-Beltran R.,Center for Research in Mathematics | Khokhar A.A.,Illinois Institute of Technology
Entropy | Year: 2014

Due to pervasive communication infrastructures, a plethora of enabling technologies is being developed over mobile and wired networks. Among these, video streaming services over IP are the most challenging in terms of quality, real-time requirements and security. In this paper, we propose a novel scheme to efficiently secure variable length coded (VLC) multimedia bit streams, such as H.264. It is based on code word error diffusion and variable size segment shuffling. The codeword diffusion and the shuffling mechanisms are based on random operations from a secure and computationally efficient chaos-based pseudo-random number generator. The proposed scheme is ubiquitous to the end users and can be deployed at any node in the network. It provides different levels of security, with encrypted data volume fluctuating between 5.5-17%. It works on the compressed bit stream without requiring any decoding. It provides excellent encryption speeds on different platforms, including mobile devices. It is 200% faster and 150% more power efficient when compared with AES software-based full encryption schemes. Regarding security, the scheme is robust to well-known attacks in the literature, such as brute force and known/chosen plain text attacks. © 2014 by the authors.


Hasimoto-Beltran R.,Center for Research in Mathematics
International Journal of Bifurcation and Chaos | Year: 2013

In this work, we present a new chaos-based cryptosystem scheme consisting of a noniterative plaintext transformation and a high dimensionally (K-map) populated dynamic Look-Up Table (LUT) with random access that outperforms the security and speed of previous LUT-based chaotic encryption schemes. Experimental analysis of the proposed scheme reveals excellent statistical properties, naturally extended permanent cycle, and high performance for real-time multimedia communications. Our scheme is one order of magnitude faster than the fastest LUT-based approach in the literature and robust to differential and chosen plaintext attacks. © 2013 World Scientific Publishing Company.

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