Effective representation of physiological dynamics by fuzzy rough set: a review
Keywords:
Fuzzy/rough sets, Physiological dynamics, Dimensionality reduction, Intrinsic representation, Feature extraction/selection
Abstract
The latest generation of biomedical systems record at short time intervals the physiological dynamic in large databases. The correct interpretation of the information is difficult to obtain by the expertise of a single physician, so the decision is based only on some selected variables. Effective representation of physiological variables by fuzzy Rough Set type 1 can be applied to characterize and extract relevant information from physiological dynamics, however the disadvantages of these techniques are the complexity of their algorithms and the high computational cost, therefore it is necessary to apply fuzzy rough set type 2 techniques , associated with axiomatic methods through low and high diffuse approximation operators as primitive concepts for generating a dimension reduction system with a tendency to lower computational cost in biomedical engineering applications. This article reviews the state of the art of effective representation of physiological dynamics using fuzzy rough set, in order to determine the ability of these techniques to be included in automatic decision making procedures that support the clinical opinion of a specialist.
Downloads
Download data is not yet available.
References
[1] A. López and C. Vázquez, “Algoritmo de compresión para la señal de pulso arterial periférico,” Universidad, Ciencia y Tecnología, vol. 9, no. 34, pp. 75-79, Junio 2005.
[2] D. Sánchez, “Procesado y transmisión de señales biomédicas para el diagnóstico de trastornos y enfermedades del sueño,” Universidad de Cádiz, Tesis Doctoral 2008.
[3] M. Imhoff, R. Fried, U. Gather, and V. Lanius, “Dimension Reduction for Physiological Variables Using Graphical Modeling,” in AMIA 2003 Symposium Proceedings, Germany, 2003, pp. 313-317.
[4] J. H. Rivera, G. Castellanos, and J. S. Mejía, “Selección efectiva de características para bioseñales utlizando el analisis de componentes principales,” Scientia et Technica, vol. 13, no. 34, pp. 127-131, May 2007.
[5] L. Xie and J. Li, “A Novel Feature Extraction Method Assembled with PCA and ICA for Network Intrusion Detection,” in International Forum on Computer ScienceTechnology and Applications, vol. 3, Chongqing, 2009, pp. 31-34, 25-27.
[6] K. Hongfa and C. Yongguang, “An Interpolation Technique Based on Grey Relational Theory,” The Journal of Grey System, vol. 18, no. 1, pp. 79-83, 2006.
[7] E. Delgado, G. Castellanos, and M. Vallverdú, Análisis de Relevancia en Espacios de Representación Orientado al Soporte de Diagnóstico: Aplicaciones en la Dinámica Cardíaca. Manizales: Ediciones Universidad Nacional de Colombia, 2009, vol. I.
[8] L. Zhang, Y. Zhong, B. Huang, J. Gong, and P. Li, “Dimensionality Reduction Based on Clonal Selection for Hyperspectral Imagery,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 12, pp. 4172- 4186, Dec 2007.
[9] L. A. Zadeh, “FuzzySets,” Information and Control, vol. 8, pp. 338-353, 1965.
[10] L. Zadeh, “Probability measures of fuzzy events,” J. Math. Anal. Appl., vol. 23, pp. 421–427, 1968.
[11] Z. Pawlak, Rough Sets, Theoretical Aspects of Reasoning About Data. Netherlands: Kluwer Academic Publishers, 1991.
[12] Y. Y. Yao, “A Comparative Study of Fuzzy Sets and Rough Sets,” Information Sciences, vol. 109, no. 1-4, pp. 227-242, 1998.
[13] D. Dubois and H. Prade, “Rough fuzzy sets and fuzzy rough sets,” International Journal of General Systems, vol. 17, no. 2 y 3, pp. 191–209, 1990.
[14] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Mathematics in Science and engineering. New York: ACADEMIC PRESS, INC, 1980, vol. 144.
[15] D. Chen and S. Zhao, “Local reduction of decision system with fuzzy rough sets,” Fuzzy Sets and Systems, vol. 161, no. 13, pp. 1871–1883, Jul. 2010.
[16] E. Delgado, F. A. Sepúlveda, S. Röthlisberger, and G. Castellanos, “The Rademacher Complexity Model over Acoustic Features for Improving Robustness in Hypernasal Speech Detection. Volume. Editors: Ni,” in Computers and Simulation in Modern Science. UK: WSEAS Press, University of Cambridge, 2011, pp. 130-135.
[17] T. Wagner, “Nonparametric estimates of probability densities,” Information Theory, IEEE Transactions on, vol. 21, no. 4, pp. 438- 440, Jul 1975.
[18] B. Xia, D. Hong, and K. Hongfa, “Study on Grey Parameter Estimation Approach of Small Samples,” in Grey Systems and Intelligent Services, 2009. GSIS 2009., Nov.2009, pp. 311-315.
[19] D. C. Caccia, D. Percival, M. J. Cannon, R. Gary, and J. B. Bassingthwaighte, “Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods,” Physica A: Statistical and Theoretical Physics, vol. 246, no. 3-4, pp. 609-632, December 1997.
[20] J. B. Bassingthwaighte and G. M. Raymond, “Evaluating rescaled range analysys for time series,” Annals of Biomedical Engineering, vol. 22, no. 4, pp. 432-444, July 1994.
[21] D. Peña and F. J. Prieto, “Multivariate Outlier Detection and Robust Covariance Matrix Estimation,” Technometrics, vol. 43, no. 3, pp. 286-310, Aug. 2001.
[22] A. C. Rencher, Methods of Multivariate Analysis. , 2nd ed. New York: Wiley Series in Probability and Statistics, 2002.
[23] D. Peña, Análisis de datos multivariantes.: Mc Graw Hill, 2002.
[24] Z. M. Bokal and R.B. Sinitsyn, “Nonparametric method for estimating spoken language sound multivariate probability density function,” in Microwaves, Radar and Remote Sensing Symposium, 2008. MRRS 2008, Kiev , Sept. 2008, pp. 170-171, 22-24.
[25] V. Babovic, M. Keijzer, and M. Stefansson, “Chaos theory, optimal embedding and evolutionary algorithms,” Tech. Rep. TR-9800463, Danish Technical Research Council (STVF), January 2001.
[26] M. L. Petrovich and M. I. Davidovich, Estimación Estadística y Prueba de Hipótesis en el Computador (Rus). Moscú: Finansy i Statistika, 1989.
[27] L. Baringhaus and N. Henze, “Limit Distributions for Measures of Multivariate Skewness and Kurtosis Based on Projections,” Journal of Multivariate Analysis, vol. 38, no. 1, pp. 51–69, July 1991.
[28] K. Umayahara and Y. Nakamori, “N-dimensional views in fuzzy data analysis,” in Intelligent Processing Systems1997. ICIPS ‘97. 1997 IEEE International Conference on, vol. 1, Oct. 1997., pp. 54-57.
[29] T. W. Anderson and Bahadur R. R., “Classification Into Two Multivariate Normal Distributions With Different Covariance Matrices,” The Annals of Mathematical Statistics, vol. 33, no. 2, pp. 420–431, 1962.
[30] E. Delgado, A. Perera, M. Vallverdú, P. Caminal, and G. Castellanos, “Dimensionality reduction oriented toward the feature visualization for ischemia detection,” IEEE Transactions on Information Technology in Biomedicine, vol. 13, no. 4, pp. 590-598, Mar. 2009.
[31] R. Jensen and Q. Shen, “Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches,” IEEE Transactions On Knowledge and Data Engineering, vol. 16, no. 12, pp. 1457-1471, Dec. 2004.
[32] F. S. Tsai and K. L. Chan, “Dimensionality Reduction Techniques for Data Exploration,” in Information, Communications & Signal Processing, 2007 6th International Conference on, Dec. 2007, pp. 1-5, 10-13.
[33] G. Hu and S. Yuemei, “An Attribute Reduction Method based on Fuzzy-Rough Sets Theories,” in First International Workshop on Education Technology and Computer Science, vol. 3, China, Mar. 2009., pp. 828-831.
[34] I.K Sethi, “Entropy nets: from decision trees to neural networks,” Proceedings of the IEEE, vol. 78, no. 10, pp. 1605-1613, Oct. 1990.
[35] I. Guyon, S. Gunn, M. Nikravesh, and L. A. Zadeh, Feature Extraction Foundations and Applications. Netherlands: Springer-Verlag, 2006.
[36] D. Gering. (2002., Apr. ) Linear and Nonlinear Data Dimensionality Reduction. [Online]. http://people.csail. mit.edu/gering/
[37] K. Pearson, “On lines and planes of closest fit to systems of points in space,” Philosophical Magazine, vol. 2, no. 6, pp. 559-572, 1901.
[38] T. Cox and M. Cox, Multidimensional Scaling, Second Edition ed. New York: Chapman & Hall, 2001.
[39] S. T. Roweis and Saul L. K., “Nonlinear Dimensionality Reduction by Locally Linear Embedding,” Science, vol. 290, pp. 2323-2326, Dec. 2000.
[40] J. Tenenbaum, V. de Silva, and J. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction,” Science, vol. 290, pp. 2319-2323, Dec. 2000.
[41] F. S. Tsai, “Dimensionality reduction techniques for blog visualization,” Expert Systems with Applications, vol. 38, no. 3, pp. 2766–2773, 2011.
[42] N. Kwak, C. Kim, and H. Kim, “Dimensionality reduction based on ICA for regression problems,” Neurocomputing, vol. 71, no. 13-15, pp. 2596-2603, August 2008.
[43] I. Joliffe, Principal Component Analysis, Second edition ed. New York: Springer-Verlag, 1986.
[44] A. Hyvarinen, J. Karhunen, and E. Oja, Independent component analysis. Canada: John Wiley & Sons, 2001.
[45] K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd ed.: Academic Press, 1990.
[46] A. H. Sahoolizadeh, B. Z. Heidari, and C. H. Dehghani, “A New Face Recognition Method using PCA, LDA and Neural Network,” International Journal of Electrical and Electronics Engineering, vol. 2, no. 8, pp. 507- 512, 2008.
[47] L. H. Chan, S. H. Salleh, and C. M. Ting, “PCA, LDA and neural network for face identification,” in Industrial Electronics and Applications, ICIEA 2009. 4th IEEE Conference on, xi’an, May. 2009., pp. 1256-1259, 25- 27.
[48] M. Soo Park, J. H. Na, and J. Y. Cho, “PCA-based Feature Extraction using Class Information,” in Systems, Man and Cybernetics, 2005 IEEE International Conference on, vol. 1, Oct. 2005., pp. 341- 345.
[49] W. Jiao and Y. Chang, “Fault diagnosis of rotor systems Using ICA Based Feature Extraction ,” in Proceedings of the 2009 IEEE International Conference on Robotics and Biomimetics, Dec. 2009. , pp. 1286-1291.
[50] W. Liao and J. Jiang, “Image Feature Extraction based on Kernel ICA,” in Image and Signal Processing, 2008. CISP ‘08. Congress on, vol. 2, Sanya, May. 2008., pp. 763-767.
[51] F.R. Bach and M.I. Jordan, “Kernel Independent Component Analysis,” Journal of Machine Learning Research, vol. 3, pp. 1-48., 2002.
[52] W. Yang, L. Zhang, and C. Sun, “Fuzzy 2DLDA for Face Recognition,” in Pattern Recognition, 2009. CCPR 2009, Chinese Conference on, Nov. 2009., pp. 1-4, 4-6.
[53] J.H. Friedman, “Regularized discriminant analysis,” Journal of the American Statistical Association, vol. 84, no. 405, pp. 165–175., Mar. 1989.
[54] J. Yang, D. Zhang, A. F. Frangi, and J. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 26, no. 1, pp. 131-137, Jan. 2004.
[55] H. Kong et al., “Generalized 2D principal component analysis,” in Neural Networks, 2005. IJCNN ‘05. Proceedings. 2005 IEEE International Joint Conference on, vol. 1, Jul. 2005., pp. 108- 113.
[56] L. Wang, X. Wang, X. Zhang, and J. Feng, “The equivalence of two-dimensional PCA to line-based PCA,” Pattern Recognition Letters, vol. 26, no. 1, pp. 57-60, January 2005.
[57] J. Yang and L. Chengjun, “Horizontal and Vertical 2DPCA-Based Discriminant Analysis for Face Verification on a Large-Scale Database,” Information Forensics and Security, IEEE Transactions on, vol. 2, no. 4, pp. 781-792, Dec. 2007.
[58] W.S. Zheng, J.H. Lai, and Z. Li Stan, “1D-LDA vs. 2DLDA: when is vector-based linear discriminant analysis better than matrix-based,” Pattern Recognition, vol. 41, no. 7, pp. 2156–2172, 2008.
[59] W. Yan, X. Yan, L. Zhang , and C. Sun, “Feature extraction based on fuzzy 2DLDA,” Neurocomputing, vol. 73, no. 10-12, pp. 1556–1561, Jun. 2010.
[60] C. Deisy, B. Subbulakshmi, S. Baskar, and N. Ramaraj, “Efficient Dimensionality Reduction Approaches for Feature Selection,” in International Conference on Computational Intelligence and Multimedia Applications, vol. 2, Sivakasi, Tamil Nadu, Dec. 2007, pp. 121-127.
[61] M. Dash and H. Liu, “Feature Selection for Classification,” Intelligent Data Analysis: An Internat. J., vol. 1, no. 1, pp. 131-156, 1997.
[62] M. Dash and H. Liu, “Consistency-based search in feature selection,” Artificial Intelligence, vol. 151, no. 1-2, pp. 155-176, Dec. 2003.
[63] K. Jaber, R. Abdullah, and N.A. Rashid, “A framework for decision tree-based method to index data from large protein sequence databases,” in Biomedical Engineering and Sciences (IECBES), 2010 IEEE EMBS Conference on, Kuala Lumpur, Nov.2011, pp. 120-125.
[64] I.K Sethi, “Entropy nets: from decision trees to neural networks,” Proceedings of the IEEE, vol. 78, no. 10, pp. 1605-1613, Oct. 1990.
[65] T. Kohonen, Self-Organizing Maps, Third Edition ed. Berlin: Springer, 1995.
[66] R. Kohav and G.H. John, “Wrappers for Feature Subset Selection,” Artificial Intelligence, vol. 97, pp. 273-324, May. 1997.
[67] M. Blachnik, W. Duch, A. Kachel, and J. Biesiada, “Feature Selection for Supervised Classification: A Kolmogorov-Smirnov Class Correlation-Based Filter,” in AIMeth Series 2009, Symposium On Method of Artificial Intelligence, Gliwice, Nov.2009, pp. 18-19.
[68] P. A. Devijver and J. Kittler, Pattern Recognition: A Statistical Aproach, Prmera edición ed.: Englrwood Cliffs: Pretince Hall, 1982.
[69] D. W. Aha and R. L. Bankert, “A Comparative Evaluation of Sequential Feature Selection Algorithms,” in Learning from data: artificial intelligence and statistics V. New York: Springer Verlag, 1996., ch. 19, pp. 199-206.
[70] P. Pudil, J. Novovicova, and J. Kittle, “Floating Search Methods in Feature Selection,” Pattern Recognition Letters, vol. 15, no. 11, pp. 1,119-1,125, Nov. 1994.
[71] M. Kudo and J. Sklansky, “Comparison of Algorithms that Selects Features for Pattern Classifiers,” Pattern Recognition, vol. 33, no. 1, pp. 25-41, Jan. 2000.
[72] S. K. Pal, R. K. De, and J. Basak, “Unsupervised Feature Evaluation: A Neuro-Fuzzy Approach,” IEEE Trans. Neural Network, vol. 11, no. 2, pp. 366-376, Mar. 2000.
[73] K. Kira and L. Rendell, “A practical Approach to Feature Selection,” in Proc. Ninth Int’l. Workshop Machine Learning, San Francisco, 1992., pp. 249-256.
[74] D. Koller and M. Sahami, “Towards Optimal Feature Selection,” in Proc. 13th Int’l. Conf. Machine Learning, 1996, pp. 284-292.
[75] P. Mitra, P. Murthy, and S. K. Pal, “Unsupervised feature selection using feature similarity,” IEEE Transactions On Pattern Analysis And Machine Intelligente, vol. 24, no. 6, pp. 301-312, Jun. 2002.
[76] L. A. Zadeh, “FuzzySets,” Information and Control, vol. 8, pp. 338-353, 1965.
[77] Z. Wang, Q. Wang, M Bai, Z. Chen, and Z. Sun, “Further exploration on relationship between crisp sets and fuzzy sets,” in Computer and Automation Engineering (ICCAE), 2010 The 2nd International Conference on, vol. 2, 2010, pp. 609-613.
[78] W. Pedricz, A. Skowron, and V. Kreinovich, Handbook of Granular Computing. England: A Jhon Wiley & Sons, 2008.
[79] L. Zehua, J. Hai, and Y. Pingpeng, “The Theory of Triangle Type-2 Fuzzy Sets,” in Computer and Information Technology, 2009. CIT ‘09. Ninth IEEE International Conference on, Oct. 2009, pp. 57-62, 11-14.
[80] J.M. Mendel and Wu Hongwei, “Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems,” Fuzzy Systems, IEEE Transactions on , vol. 14, no. 6, pp. 781-792, Dec. 2006.
[81] J.M. Mendel, “Type-2 fuzzy sets and systems: An overview.,” IEEE Comput. Intell. Mag., vol. 2, no. 1, pp. 20– 29., Feb. 2007.
[82] H. Hagras, “Type-2 FLCs: A New Generation of Fuzzy Controllers ,” Computational Intelligence Magazine, IEEE , vol. 2, no. 1, pp. 30-43, Feb. 2007.
[83] J.M. Mendel, R.I. John, and Liu Feilong, “On using type1 fuzzy set mathematics to derive interval type-2 fuzzy logic systems,” in Fuzzy Information Processing Society, 2005. NAFIPS 2005. Annual Meeting of the North American, 2005, pp. 528- 533.
[84] K. W. Reed, “Type-1 And Type-2 Fuzzy Systems For Detecting Visitors In An Uncertain Environment,” Dissertations, Academic, University of Missouri, Columbia , Computer engineering, Columbia, Tesis Maestria 2009.
[85] H. Wu, H. Wu, and J. Luo, “An Interval Type-2 Fuzzy Rough Set Model for Attribute Reduction,” IEEE Transactions on Fuzzy System, vol. 17, no. 2, pp. 301-315, 2009.
[86] E. C. Tsang, D. Chen, D. S. Yeung, X. Z. Wang, and J. W. Lee, “Attributes Reduction Using Fuzzy Rough Sets,” IEEE Transactions On Fuzzy Systems, vol. 16, no. 5, pp. 1130-1141, 2008.
[87] R. Jensen and Q. Shen, “Fuzzy-Rough Sets for descriptive Dimensionality Reduction,” in Fuzzy Systems, IEEE International Conference, Honolulu, HI , USA , 2002, pp. 29-34.
[88] R. B. Bhatt and M. Gopa, “On fuzzy-rough sets approach to feature selection,” Pattern Recognition Letters, vol. 26, no. 7, pp. 965-975, May 2005.
[89] G. C. Tsang, C. Degang, E. C. Tsang, J. W. Lee, and D. S. Yeung, “On attributes reduction with fuzzy rough sets,” in IEEE Conferences, vol. 3, 2005, pp. 2775-2780.
[90] P. Maji and S. K. Pal, “Feature Selection Using F-information Measures in Fuzzy Approximation Spaces,” IEEE Transaction on Knowledge and data Engineering, vol. 22, no. 6, pp. 854-867, Jun. 2010.
[2] D. Sánchez, “Procesado y transmisión de señales biomédicas para el diagnóstico de trastornos y enfermedades del sueño,” Universidad de Cádiz, Tesis Doctoral 2008.
[3] M. Imhoff, R. Fried, U. Gather, and V. Lanius, “Dimension Reduction for Physiological Variables Using Graphical Modeling,” in AMIA 2003 Symposium Proceedings, Germany, 2003, pp. 313-317.
[4] J. H. Rivera, G. Castellanos, and J. S. Mejía, “Selección efectiva de características para bioseñales utlizando el analisis de componentes principales,” Scientia et Technica, vol. 13, no. 34, pp. 127-131, May 2007.
[5] L. Xie and J. Li, “A Novel Feature Extraction Method Assembled with PCA and ICA for Network Intrusion Detection,” in International Forum on Computer ScienceTechnology and Applications, vol. 3, Chongqing, 2009, pp. 31-34, 25-27.
[6] K. Hongfa and C. Yongguang, “An Interpolation Technique Based on Grey Relational Theory,” The Journal of Grey System, vol. 18, no. 1, pp. 79-83, 2006.
[7] E. Delgado, G. Castellanos, and M. Vallverdú, Análisis de Relevancia en Espacios de Representación Orientado al Soporte de Diagnóstico: Aplicaciones en la Dinámica Cardíaca. Manizales: Ediciones Universidad Nacional de Colombia, 2009, vol. I.
[8] L. Zhang, Y. Zhong, B. Huang, J. Gong, and P. Li, “Dimensionality Reduction Based on Clonal Selection for Hyperspectral Imagery,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 12, pp. 4172- 4186, Dec 2007.
[9] L. A. Zadeh, “FuzzySets,” Information and Control, vol. 8, pp. 338-353, 1965.
[10] L. Zadeh, “Probability measures of fuzzy events,” J. Math. Anal. Appl., vol. 23, pp. 421–427, 1968.
[11] Z. Pawlak, Rough Sets, Theoretical Aspects of Reasoning About Data. Netherlands: Kluwer Academic Publishers, 1991.
[12] Y. Y. Yao, “A Comparative Study of Fuzzy Sets and Rough Sets,” Information Sciences, vol. 109, no. 1-4, pp. 227-242, 1998.
[13] D. Dubois and H. Prade, “Rough fuzzy sets and fuzzy rough sets,” International Journal of General Systems, vol. 17, no. 2 y 3, pp. 191–209, 1990.
[14] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Mathematics in Science and engineering. New York: ACADEMIC PRESS, INC, 1980, vol. 144.
[15] D. Chen and S. Zhao, “Local reduction of decision system with fuzzy rough sets,” Fuzzy Sets and Systems, vol. 161, no. 13, pp. 1871–1883, Jul. 2010.
[16] E. Delgado, F. A. Sepúlveda, S. Röthlisberger, and G. Castellanos, “The Rademacher Complexity Model over Acoustic Features for Improving Robustness in Hypernasal Speech Detection. Volume. Editors: Ni,” in Computers and Simulation in Modern Science. UK: WSEAS Press, University of Cambridge, 2011, pp. 130-135.
[17] T. Wagner, “Nonparametric estimates of probability densities,” Information Theory, IEEE Transactions on, vol. 21, no. 4, pp. 438- 440, Jul 1975.
[18] B. Xia, D. Hong, and K. Hongfa, “Study on Grey Parameter Estimation Approach of Small Samples,” in Grey Systems and Intelligent Services, 2009. GSIS 2009., Nov.2009, pp. 311-315.
[19] D. C. Caccia, D. Percival, M. J. Cannon, R. Gary, and J. B. Bassingthwaighte, “Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods,” Physica A: Statistical and Theoretical Physics, vol. 246, no. 3-4, pp. 609-632, December 1997.
[20] J. B. Bassingthwaighte and G. M. Raymond, “Evaluating rescaled range analysys for time series,” Annals of Biomedical Engineering, vol. 22, no. 4, pp. 432-444, July 1994.
[21] D. Peña and F. J. Prieto, “Multivariate Outlier Detection and Robust Covariance Matrix Estimation,” Technometrics, vol. 43, no. 3, pp. 286-310, Aug. 2001.
[22] A. C. Rencher, Methods of Multivariate Analysis. , 2nd ed. New York: Wiley Series in Probability and Statistics, 2002.
[23] D. Peña, Análisis de datos multivariantes.: Mc Graw Hill, 2002.
[24] Z. M. Bokal and R.B. Sinitsyn, “Nonparametric method for estimating spoken language sound multivariate probability density function,” in Microwaves, Radar and Remote Sensing Symposium, 2008. MRRS 2008, Kiev , Sept. 2008, pp. 170-171, 22-24.
[25] V. Babovic, M. Keijzer, and M. Stefansson, “Chaos theory, optimal embedding and evolutionary algorithms,” Tech. Rep. TR-9800463, Danish Technical Research Council (STVF), January 2001.
[26] M. L. Petrovich and M. I. Davidovich, Estimación Estadística y Prueba de Hipótesis en el Computador (Rus). Moscú: Finansy i Statistika, 1989.
[27] L. Baringhaus and N. Henze, “Limit Distributions for Measures of Multivariate Skewness and Kurtosis Based on Projections,” Journal of Multivariate Analysis, vol. 38, no. 1, pp. 51–69, July 1991.
[28] K. Umayahara and Y. Nakamori, “N-dimensional views in fuzzy data analysis,” in Intelligent Processing Systems1997. ICIPS ‘97. 1997 IEEE International Conference on, vol. 1, Oct. 1997., pp. 54-57.
[29] T. W. Anderson and Bahadur R. R., “Classification Into Two Multivariate Normal Distributions With Different Covariance Matrices,” The Annals of Mathematical Statistics, vol. 33, no. 2, pp. 420–431, 1962.
[30] E. Delgado, A. Perera, M. Vallverdú, P. Caminal, and G. Castellanos, “Dimensionality reduction oriented toward the feature visualization for ischemia detection,” IEEE Transactions on Information Technology in Biomedicine, vol. 13, no. 4, pp. 590-598, Mar. 2009.
[31] R. Jensen and Q. Shen, “Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches,” IEEE Transactions On Knowledge and Data Engineering, vol. 16, no. 12, pp. 1457-1471, Dec. 2004.
[32] F. S. Tsai and K. L. Chan, “Dimensionality Reduction Techniques for Data Exploration,” in Information, Communications & Signal Processing, 2007 6th International Conference on, Dec. 2007, pp. 1-5, 10-13.
[33] G. Hu and S. Yuemei, “An Attribute Reduction Method based on Fuzzy-Rough Sets Theories,” in First International Workshop on Education Technology and Computer Science, vol. 3, China, Mar. 2009., pp. 828-831.
[34] I.K Sethi, “Entropy nets: from decision trees to neural networks,” Proceedings of the IEEE, vol. 78, no. 10, pp. 1605-1613, Oct. 1990.
[35] I. Guyon, S. Gunn, M. Nikravesh, and L. A. Zadeh, Feature Extraction Foundations and Applications. Netherlands: Springer-Verlag, 2006.
[36] D. Gering. (2002., Apr. ) Linear and Nonlinear Data Dimensionality Reduction. [Online]. http://people.csail. mit.edu/gering/
[37] K. Pearson, “On lines and planes of closest fit to systems of points in space,” Philosophical Magazine, vol. 2, no. 6, pp. 559-572, 1901.
[38] T. Cox and M. Cox, Multidimensional Scaling, Second Edition ed. New York: Chapman & Hall, 2001.
[39] S. T. Roweis and Saul L. K., “Nonlinear Dimensionality Reduction by Locally Linear Embedding,” Science, vol. 290, pp. 2323-2326, Dec. 2000.
[40] J. Tenenbaum, V. de Silva, and J. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction,” Science, vol. 290, pp. 2319-2323, Dec. 2000.
[41] F. S. Tsai, “Dimensionality reduction techniques for blog visualization,” Expert Systems with Applications, vol. 38, no. 3, pp. 2766–2773, 2011.
[42] N. Kwak, C. Kim, and H. Kim, “Dimensionality reduction based on ICA for regression problems,” Neurocomputing, vol. 71, no. 13-15, pp. 2596-2603, August 2008.
[43] I. Joliffe, Principal Component Analysis, Second edition ed. New York: Springer-Verlag, 1986.
[44] A. Hyvarinen, J. Karhunen, and E. Oja, Independent component analysis. Canada: John Wiley & Sons, 2001.
[45] K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd ed.: Academic Press, 1990.
[46] A. H. Sahoolizadeh, B. Z. Heidari, and C. H. Dehghani, “A New Face Recognition Method using PCA, LDA and Neural Network,” International Journal of Electrical and Electronics Engineering, vol. 2, no. 8, pp. 507- 512, 2008.
[47] L. H. Chan, S. H. Salleh, and C. M. Ting, “PCA, LDA and neural network for face identification,” in Industrial Electronics and Applications, ICIEA 2009. 4th IEEE Conference on, xi’an, May. 2009., pp. 1256-1259, 25- 27.
[48] M. Soo Park, J. H. Na, and J. Y. Cho, “PCA-based Feature Extraction using Class Information,” in Systems, Man and Cybernetics, 2005 IEEE International Conference on, vol. 1, Oct. 2005., pp. 341- 345.
[49] W. Jiao and Y. Chang, “Fault diagnosis of rotor systems Using ICA Based Feature Extraction ,” in Proceedings of the 2009 IEEE International Conference on Robotics and Biomimetics, Dec. 2009. , pp. 1286-1291.
[50] W. Liao and J. Jiang, “Image Feature Extraction based on Kernel ICA,” in Image and Signal Processing, 2008. CISP ‘08. Congress on, vol. 2, Sanya, May. 2008., pp. 763-767.
[51] F.R. Bach and M.I. Jordan, “Kernel Independent Component Analysis,” Journal of Machine Learning Research, vol. 3, pp. 1-48., 2002.
[52] W. Yang, L. Zhang, and C. Sun, “Fuzzy 2DLDA for Face Recognition,” in Pattern Recognition, 2009. CCPR 2009, Chinese Conference on, Nov. 2009., pp. 1-4, 4-6.
[53] J.H. Friedman, “Regularized discriminant analysis,” Journal of the American Statistical Association, vol. 84, no. 405, pp. 165–175., Mar. 1989.
[54] J. Yang, D. Zhang, A. F. Frangi, and J. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 26, no. 1, pp. 131-137, Jan. 2004.
[55] H. Kong et al., “Generalized 2D principal component analysis,” in Neural Networks, 2005. IJCNN ‘05. Proceedings. 2005 IEEE International Joint Conference on, vol. 1, Jul. 2005., pp. 108- 113.
[56] L. Wang, X. Wang, X. Zhang, and J. Feng, “The equivalence of two-dimensional PCA to line-based PCA,” Pattern Recognition Letters, vol. 26, no. 1, pp. 57-60, January 2005.
[57] J. Yang and L. Chengjun, “Horizontal and Vertical 2DPCA-Based Discriminant Analysis for Face Verification on a Large-Scale Database,” Information Forensics and Security, IEEE Transactions on, vol. 2, no. 4, pp. 781-792, Dec. 2007.
[58] W.S. Zheng, J.H. Lai, and Z. Li Stan, “1D-LDA vs. 2DLDA: when is vector-based linear discriminant analysis better than matrix-based,” Pattern Recognition, vol. 41, no. 7, pp. 2156–2172, 2008.
[59] W. Yan, X. Yan, L. Zhang , and C. Sun, “Feature extraction based on fuzzy 2DLDA,” Neurocomputing, vol. 73, no. 10-12, pp. 1556–1561, Jun. 2010.
[60] C. Deisy, B. Subbulakshmi, S. Baskar, and N. Ramaraj, “Efficient Dimensionality Reduction Approaches for Feature Selection,” in International Conference on Computational Intelligence and Multimedia Applications, vol. 2, Sivakasi, Tamil Nadu, Dec. 2007, pp. 121-127.
[61] M. Dash and H. Liu, “Feature Selection for Classification,” Intelligent Data Analysis: An Internat. J., vol. 1, no. 1, pp. 131-156, 1997.
[62] M. Dash and H. Liu, “Consistency-based search in feature selection,” Artificial Intelligence, vol. 151, no. 1-2, pp. 155-176, Dec. 2003.
[63] K. Jaber, R. Abdullah, and N.A. Rashid, “A framework for decision tree-based method to index data from large protein sequence databases,” in Biomedical Engineering and Sciences (IECBES), 2010 IEEE EMBS Conference on, Kuala Lumpur, Nov.2011, pp. 120-125.
[64] I.K Sethi, “Entropy nets: from decision trees to neural networks,” Proceedings of the IEEE, vol. 78, no. 10, pp. 1605-1613, Oct. 1990.
[65] T. Kohonen, Self-Organizing Maps, Third Edition ed. Berlin: Springer, 1995.
[66] R. Kohav and G.H. John, “Wrappers for Feature Subset Selection,” Artificial Intelligence, vol. 97, pp. 273-324, May. 1997.
[67] M. Blachnik, W. Duch, A. Kachel, and J. Biesiada, “Feature Selection for Supervised Classification: A Kolmogorov-Smirnov Class Correlation-Based Filter,” in AIMeth Series 2009, Symposium On Method of Artificial Intelligence, Gliwice, Nov.2009, pp. 18-19.
[68] P. A. Devijver and J. Kittler, Pattern Recognition: A Statistical Aproach, Prmera edición ed.: Englrwood Cliffs: Pretince Hall, 1982.
[69] D. W. Aha and R. L. Bankert, “A Comparative Evaluation of Sequential Feature Selection Algorithms,” in Learning from data: artificial intelligence and statistics V. New York: Springer Verlag, 1996., ch. 19, pp. 199-206.
[70] P. Pudil, J. Novovicova, and J. Kittle, “Floating Search Methods in Feature Selection,” Pattern Recognition Letters, vol. 15, no. 11, pp. 1,119-1,125, Nov. 1994.
[71] M. Kudo and J. Sklansky, “Comparison of Algorithms that Selects Features for Pattern Classifiers,” Pattern Recognition, vol. 33, no. 1, pp. 25-41, Jan. 2000.
[72] S. K. Pal, R. K. De, and J. Basak, “Unsupervised Feature Evaluation: A Neuro-Fuzzy Approach,” IEEE Trans. Neural Network, vol. 11, no. 2, pp. 366-376, Mar. 2000.
[73] K. Kira and L. Rendell, “A practical Approach to Feature Selection,” in Proc. Ninth Int’l. Workshop Machine Learning, San Francisco, 1992., pp. 249-256.
[74] D. Koller and M. Sahami, “Towards Optimal Feature Selection,” in Proc. 13th Int’l. Conf. Machine Learning, 1996, pp. 284-292.
[75] P. Mitra, P. Murthy, and S. K. Pal, “Unsupervised feature selection using feature similarity,” IEEE Transactions On Pattern Analysis And Machine Intelligente, vol. 24, no. 6, pp. 301-312, Jun. 2002.
[76] L. A. Zadeh, “FuzzySets,” Information and Control, vol. 8, pp. 338-353, 1965.
[77] Z. Wang, Q. Wang, M Bai, Z. Chen, and Z. Sun, “Further exploration on relationship between crisp sets and fuzzy sets,” in Computer and Automation Engineering (ICCAE), 2010 The 2nd International Conference on, vol. 2, 2010, pp. 609-613.
[78] W. Pedricz, A. Skowron, and V. Kreinovich, Handbook of Granular Computing. England: A Jhon Wiley & Sons, 2008.
[79] L. Zehua, J. Hai, and Y. Pingpeng, “The Theory of Triangle Type-2 Fuzzy Sets,” in Computer and Information Technology, 2009. CIT ‘09. Ninth IEEE International Conference on, Oct. 2009, pp. 57-62, 11-14.
[80] J.M. Mendel and Wu Hongwei, “Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems,” Fuzzy Systems, IEEE Transactions on , vol. 14, no. 6, pp. 781-792, Dec. 2006.
[81] J.M. Mendel, “Type-2 fuzzy sets and systems: An overview.,” IEEE Comput. Intell. Mag., vol. 2, no. 1, pp. 20– 29., Feb. 2007.
[82] H. Hagras, “Type-2 FLCs: A New Generation of Fuzzy Controllers ,” Computational Intelligence Magazine, IEEE , vol. 2, no. 1, pp. 30-43, Feb. 2007.
[83] J.M. Mendel, R.I. John, and Liu Feilong, “On using type1 fuzzy set mathematics to derive interval type-2 fuzzy logic systems,” in Fuzzy Information Processing Society, 2005. NAFIPS 2005. Annual Meeting of the North American, 2005, pp. 528- 533.
[84] K. W. Reed, “Type-1 And Type-2 Fuzzy Systems For Detecting Visitors In An Uncertain Environment,” Dissertations, Academic, University of Missouri, Columbia , Computer engineering, Columbia, Tesis Maestria 2009.
[85] H. Wu, H. Wu, and J. Luo, “An Interval Type-2 Fuzzy Rough Set Model for Attribute Reduction,” IEEE Transactions on Fuzzy System, vol. 17, no. 2, pp. 301-315, 2009.
[86] E. C. Tsang, D. Chen, D. S. Yeung, X. Z. Wang, and J. W. Lee, “Attributes Reduction Using Fuzzy Rough Sets,” IEEE Transactions On Fuzzy Systems, vol. 16, no. 5, pp. 1130-1141, 2008.
[87] R. Jensen and Q. Shen, “Fuzzy-Rough Sets for descriptive Dimensionality Reduction,” in Fuzzy Systems, IEEE International Conference, Honolulu, HI , USA , 2002, pp. 29-34.
[88] R. B. Bhatt and M. Gopa, “On fuzzy-rough sets approach to feature selection,” Pattern Recognition Letters, vol. 26, no. 7, pp. 965-975, May 2005.
[89] G. C. Tsang, C. Degang, E. C. Tsang, J. W. Lee, and D. S. Yeung, “On attributes reduction with fuzzy rough sets,” in IEEE Conferences, vol. 3, 2005, pp. 2775-2780.
[90] P. Maji and S. K. Pal, “Feature Selection Using F-information Measures in Fuzzy Approximation Spaces,” IEEE Transaction on Knowledge and data Engineering, vol. 22, no. 6, pp. 854-867, Jun. 2010.
Published
2011-12-12
How to Cite
Orrego Metaute, D., & Delgado Trejos, E. (2011). Effective representation of physiological dynamics by fuzzy rough set: a review. ITECKNE, 8(2), 204-215. https://doi.org/https://doi.org/10.15332/iteckne.v8i2.2737
Issue
Section
Research and Innovation Articles
