Algoritmos de ICA em alfabetos finitos: um estudo comparativo

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2019.Recentemente, algoritmos de Análise de Componentes Independentes (ICA) em alfabetos finitos foram propostos. Tendo em vista cenários não-testados e a replicação de resultados anteriores, desejamos comparar estes algoritmos, bem como verificar como os algoritmos mais generalistas desempenham em relação aos que assumem corpos finitos. Desta maneira, nesta dissertação avaliamos, através de simulações, o desempenho de algoritmos de ICA linear como aplicação ao problema de Separação Cega de Fontes (BSS) em corpos finitos. Duas métricas foram consideradas: tempo de execução e Separação Total das Fontes, uma métrica mais pessimista de separação. Apesar dos algoritmos AMERICA, SA4ICA e GLICA convergirem para 100% de Separação Total ao crescermos a quantidade de amostras observadas, o algoritmo SA4ICA apresenta comportamento que rompe este padrão, o que não foi reportado anteriormente. Adicionalmente, implementamos o algoritmo GLICA. Este último apresentou desempenho de separação praticamente igual em relação ao algoritmo AMERICA, apesar de seu tempo de execução se apresentar superior. Além disso, realizou-se um experimento tendo em vista a aplicação de ICA por si mesma, i.e, a minimização da informação mútua. Os algoritmos lineares previamente aplicados no caso de BSS estão, agora, inseridos em um contexto cuja geração das amostras observadas não se dá por uma mistura linear, o que a princípio não privilegiaria estes algoritmos em relação a um algoritmo não-linear. Porém, ao serem comparados ao algoritmo não-linear QICA, cuja premissa envolve lidar com esses modelos geradores mais genéricos, este mesmo algoritmo detém desempenho inferior na maioria dos cenários em relação aos lineares, que inclusive demonstraram resultados, entre eles mesmos, praticamente iguais em todos os cenários. Ademais, o algoritmo QICA toma muito tempo para ser executado em relação à todos os outros algoritmos. Desta forma, os resultados sugerem que os algoritmos lineares detiveram vantagem tanto temporal quanto em desempenho em relação a este novo algoritmo. Para isto, contamos com o uso de inferência estatística em ambos os experimentos para validação de nossos resultados.In recent years, Independent Component Analysis (ICA) algorithms over finite alphabets, as well as the particular case of these: finite fields, have been proposed. Given the untested scenarios and the replication of previous results, we want to compare these algorithms with each other, as well as verify how the more generalist algorithms perform compared to those that assume a finite field structure. Thus, in this dissertation we evaluated, through stochastic simulations, the performance of linear ICA algorithms as an application to the Blind Source Separation (BSS) problem over finite fields. Two metrics were considered: execution time and Total Source Separation, a more pessimistic separation metric. Although the AMERICA, SA4ICA and GLICA algorithms converge at 100% Total Separationas we grow the number of samples observed, the SA4ICA algorithm has anomalous behavior that breaks this pattern, which was not previously reported. Additionally, we implemented the GLICA algorithm. The latter presented a practically equal separation performance in relation to the AMERICA algorithm, although its execution time is superior to this more consolidated technique. In addition, we conducted an experiment to apply ICA by itself, that is, to minimize mutual information. The linear algorithms previously applied in the case of BSS are now inserted in a context whose generation of the observed samples is not by a linear mixture, which in principle would not privilege these algorithms over a nonlinear algorithm. However, when compared to the nonlinear QICA algorithm, whose premise involves dealing with these more generic generator models, this same algorithm has lower performance in most scenarios than the linear ones, which even showed results, among themselves, practically the same in all scenarios. Moreover, the QICA algorithm takes a long time to execute relative to all other linear algorithms. Thus, the results suggest that linear algorithms had both temporal and performance advantage over this new algorithm. For this, we rely on the use of statistical inference in both experiments to validate our results

Programming Languages and Systems

This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

A Michigan-like immune-inspired framework for performing independent component analysis over Galois fields of prime order

sem informaçãosem informaçãoIn this work, we present a novel bioinspired framework for performing ICA over finite (Galois) fields of prime order P. The proposal is based on a state-of-the-art immune-inspired algorithm, the cob-aiNet[C], which is employed to solve a combinatorial optimization problem associated with a minimal entropy configuration adopting a Michigan-like population structure. The simulation results reveal that the strategy is capable of reaching a performance similar to that of standard methods for lower-dimensional instances with the advantage of also handling scenarios with an elevated number of sources. (C) 2013 Elsevier B.V. All rights reserved.In this work, we present a novel bioinspired framework for performing ICA over finite (Galois) fields of prime order P. The proposal is based on a state-of-the-art immune-inspired algorithm, the cob-aiNet[C], which is employed to solve a combinatorial opt96B153163FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICOsem informaçãosem informaçãosem informaçãosem informaçã

A Michigan-like Immune-inspired Framework For Performing Independent Component Analysis Over Galois Fields Of Prime Order

In this work, we present a novel bioinspired framework for performing ICA over finite (Galois) fields of prime order P. The proposal is based on a state-of-the-art immune-inspired algorithm, the cob-aiNet[C], which is employed to solve a combinatorial optimization problem - associated with a minimal entropy configuration - adopting a Michigan-like population structure. The simulation results reveal that the strategy is capable of reaching a performance similar to that of standard methods for lower-dimensional instances with the advantage of also handling scenarios with an elevated number of sources. © 2013 Elsevier B.V.96PART B153163Comon, P., Jutten, C., (2010) Handbook of Blind Source Separation, , Academic PressHotelling, H., Analysis of a complex of statistical variables into principal components (1933) Journal of Educational Psychology, 24 (6), pp. 417-441Yeredor, A., ICA in boolean XOR mixtures (2007) ICA 2007 - Independent Component Analysis and Signal Separation, pp. 827-835. , SpringerGutch, H.W., Gruber, P., Theis, F.J., ICA over finite fields (2010) ICA 2010 - Latent Variable Analysis and Signal Separation, Springer, pp. 645-652Adleman, L.M., Molecular computation of solutions to combinatorial problems (1994) Science, 266 (5187), pp. 1021-1024Lidl, R., Niederreiter, H., (1997) Finite Fields, 20 VOL.. , Cambridge University PressWaterhouse, W.C., How often do determinants over finite fields vanish? (1987) Discrete Mathematics, 65 (1), pp. 103-104Coelho, G.P., De Franca, F.O., Von Zuben, F.J., A concentration-based artificial immune network for combinatorial optimization (2011) 2011 IEEE Congress on Evolutionary Computation (CEC), IEEE, pp. 1242-1249Back, T., Fogel, D.B., Michalewicz, Z., (1997) Handbook of Evolutionary Computation, , IOP Publishing LtdGutch, H.W., Gruber, P., Yeredor, A., Theis, F.J., ICA over finite fields - Separability and algorithms (2012) Signal Processing, 92 (2), pp. 1796-1808Silva, D.G., Attux, R., Nadalin, E.Z., Duarte, L.T., Suyama, R., An immune-inspired information-theoretic approach to the problem of ICA over a Galois field (2011) Information Theory Workshop (ITW), IEEE, pp. 618-622Shannon, C., A mathematical theory of communication (1948) The Bell System Technical Journal, 27 (3), pp. 379-423. , 623-656Yeredor, A., Independent component analysis over Galois fields of prime order (2011) IEEE Transactions on Information Theory, 57 (8), pp. 5342-5359Delfosse, N., Loubaton, P., Adaptive blind separation of independent sources a deflation approach (1995) Signal Processing, 45 (1), pp. 59-83Dietrich, F.A., (2008) Robust Signal Processing for Wireless Communications, 2 VOL.. , SpringerDe Castro, L.N., Von Zuben, F.J., Learning and optimization using the clonal selection principle (2002) IEEE Transactions on Evolutionary Computation, 6 (13), pp. 239-251Coelho, G.P., Von Zuben, F.J., A concentration-based artificial immune network for continuous optimization (2010) 2010 IEEE Congress on Evolutionary Computation (CEC), IEEE, pp. 1-8De Castro, L.N., (2006) Fundamentals of Natural Computing Basic Concepts, Algorithms, and Applications, , Chapman & Hall/CRCHolland, J.H., (1992) Adaptation in Natural and Artificial Systems, , MIT PressRudolph, G., Convergence analysis of canonical genetic algorithms (1994) IEEE Transactions on Neural Networks, 5 (1), pp. 96-101Rudolph, G., Convergence of evolutionary algorithms in general search spaces (1996) Proceedings of IEEE International Conference on Evolutionary Computation, IEEE, pp. 50-54Neumann, F., Witt, C., (2010) Bioinspired Computation in Combinatorial Optimization Algorithms and Their Computational Complexity, , SpringerDe França, F.O., Coelho, G.P., Von Zuben, F.J., On the diversity mechanisms of opt-ainet: Acomparative study with fitness sharing (2010) 2010 IEEE Congress on Evolutionary Computation (CEC), IEEE, pp. 1-8De Castro, L.N., Timmis, J., (2002) Artificial Immune Systems A New Computational Intelligence Approach, , SpringerBurnet, F.M., Clonal selection and after (1978) Theoretical Immunology, pp. 63-85. , G.I. Bell, A.S. Perelson, G.H. Pimbley, Marcel Dekker IncJerne, N.K., Towards a network theory of the immune system (1974) Annales d'Immunologie, 125 (12), pp. 373-389Bersini, H., Revisiting idiotypic immune networks (2003) Proceedings of the 7th European Conference on Advances in Artificial Life (ECAL), pp. 164-174Carlton, A.G., On the bias of information estimates (1969) Psychological Bulletin, 71 (2), pp. 108-109Schürmann, T., Bias analysis in entropy estimation (2004) Journal of Physics A Mathematical and General, 37 (27), p. 295Principe, J.C., (2010) Information Theoretic Learning Renyi's Entropy and Kernel Perspectives, , SpringerEiben, A.E., Smith, J.E., (2003) Introduction to Evolutionary Computing, , SpringerCover, T.M., Thomas, J.A., (2006) Elements of Information Theory, , 2nd ed. Wiley-InterscienceYeredor, A., (2011) MATLAB Code for ICA over GF(P), , http://www.eng.tau.ac.il/~arie/ICA4GFP.rar, AMERICA and MEXIC

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