Developing an Evolutionary Algorithm to Search for an Optimal Multi-Mother Wavelet Packets Combination

Ohad Bar Siman Tov^1*, J. David Schaffer², Kenneth J. McLeod^1,2

¹Department of Electrical and Computer Engineering, State University of New York at Binghamton, Binghamton, NY, USA.
²Department of Bioengineering, State University of New York at Binghamton, Binghamton, NY, USA.

DOI: 10.4236/jbise.2015.87043                

Abstract

The wavelet transform is a popular analysis tool for non-stationary data, but in many cases, the choice of the mother wavelet and basis set remains uncertain, particularly when dealing with physiological data. Furthermore, the possibility exists for combining information from numerous mother wavelets so as to exploit different features from the data. However, the combinatorics become daunting given the large number of basis sets that can be utilized. Recent work in evolutionary computation has produced a subset selection genetic algorithm specifically aimed at the discovery of small, high-performance, subsets from among a large pool of candidates. Our aim was to apply this algorithm to the task of locating subsets of packets from multiple mother wavelet decompositions to estimate cardiac output from chest wall motions while avoiding the computational cost of full signal reconstruction. We present experiments which show how a continuous assessment metric can be extracted from the wavelets coefficients, but the dual-objective nature of the algorithm (high accuracy with small feature sets) imposes a need to restrict the sensitivity of the continuous accuracy metric in order to achieve the small subset size desired. A possibly subtle tradeoff seems to be needed to meet the dual objectives.

Keywords

Wavelet Transform, Data Mining, Genetic Algorithm

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Graps, A. (1995) An Introduction to Wavelets. IEEE Computational Science and Engineering, 2, 18 p.
[2]	Ruqiang Y. and Gao, R.X. (2009) Tutorial 21 Wavelet Transform: A Mathematical Tool for Non-Stationary Signal Processing in Measurement Science Part 2 in a Series of Tutorials in Instrumentation and Measurement. IEEE Instrumentation & Measurement Magazine, 12, 35-44.
[3]	Kadambe, S., Murray, R. and Boudreaux-Bartels, G.F. (1999) Wavelet Transform-Based QRS Complex Detector, IEEE Transactions on Biomedical Engineering, 46, 838-848. http://dx.doi.org/10.1109/10.771194
[4]	Chen, W., Mo, Z. and Guo, W. (2012) Detection of QRS Complexes Using Wavelet Transforms and Golden Section Search Algorithm. International Journal of Engineering and Advanced Technology (IJEAT), 1, 2249-8958
[5]	Mithun, P., Pandey, P.C., Sebastian, T., Mishra, P. and Pandey, V.K. (2011) A Wavelet Based Technique for Suppression of EMG Noise and Motion Artifact in Ambulatory ECG. 33rd Annual International Conference of the IEEE EMBS, 2011, 7087-7090.
[6]	Frère, J., Gopfert, B., Slawinski, J. and Tourny-Chollet, C. (2012) Shoulder Muscles Recruitment during a Power Backward Giant Swing on High Bar: A Wavelet-EMG-Analysis. Human Movement Science, 31, 472-485. http://dx.doi.org/10.1016/j.humov.2012.02.002
[7]	Beck, T.W., Housh, T.J., Fry, A.C., Cramer, J.T., Weir, J.P., Schilling, B.K., Falvo, M.J. and Moore, C.A. (2009) A Wavelet-Based Analysis of Surface Mechanomyographic Signals from the Quadriceps Femoris. Muscle Nerve, 39, 355-363. http://dx.doi.org/10.1002/mus.21208
[8]	Kannan, S., Dauwels, J. and Ramasubba, R. (2012) Multichannel EEG Compression: Wavelet-Based Image and Volumetric Coding Approach. IEEE Journal of Biomedical and Health Informatics, 17, 113-120.
[9]	Nguyen-Ky, T., Wen, P., Li, Y. and Malan, M. (2012) Measuring the Hypnotic Depth of Anaesthesia Based on the EEG Signal Using Combined Wavelet Transform, Eigenvector and Normalisation Techniques. Computers in Biology and Medicine, 42, 680-691. http://dx.doi.org/10.1016/j.compbiomed.2012.03.004
[10]	Sandham, W., Hamilton, D., Fisher, A., Wei, X. and Conway, M., (1998) Multiresolution Wavelet Decomposition of the Seismocardiogram. IEEE Transactions on Signal Processing, 46, 2541-2543. http://dx.doi.org/10.1109/78.709542
[11]	Parashar, K. (2013) Discrete Wavelet Transform. http://www.thepolygoners.com/tutorials/dwavelet/DWTTut.html
[12]	Valens, C. (1999) A Really Friendly Guide to Wavelets, 1999. http://math.ecnu.edu.cn/~qgu/friendintro.pdf
[13]	Domingues, M.O., Mendes Jr., O. and da Costa A.M. (2005) On Wavelet Techniques in Atmospheric Sciences. Advances in Space Research, 35, 831-842.
[14]	Chourasia, V.S. and Mittra, A.K. (2009) Selection of Mother Wavelet and Denoising Algorithm for Analysis of Foetal Phonocardiographic Signals. Journal of Medical Engineering & Technology, 33, 442-448. http://dx.doi.org/10.1080/03091900902952618
[15]	Heidari, N., Azmi, R. and Pishgoo, B. (2011) Fabric Textile Defect Detection, by Selecting a Suitable Subset of Wavelet Coefficients, through Genetic Algorithm. International Journal of Image Processing, 5, 23-27.
[16]	Amjad Ali, S., Vathsal, S. and Lal Kishore, K. (2010) A GA-Based Window Selection Methodology to Enhance Window-Based Multi-Wavelet Transformation and Thresholding Aided CT Image Denoising Technique. International Journal of Computer Science and Information Security, 7, 280-288.
[17]	Hosseini, P.T., Almasganj, F., Emami, T., Behroozmand, R., Gharibzade, S. and Torabinezhad, F. (2008) Local Discriminant Wavelet Packet Basis for Voice Pathology Classification. Proceedings of the 2nd International Conference on Bioinformatics and Biomedical Engineering, Shanghai, 16-18 May 2008, 2052-2055.
[18]	Jiang, M.Y., Li, C.C., Yuan, D.F. and Lagunas, M.A. (2007) Multiuser Detection Based on Wavelet Packet Modulation and Artificial Fish Swarm Algorithm. Proceedings of the IET Conference on Wireless, Mobile and Sensor Networks, Shanghai, 12-14 December 2007, 117-120.
[19]	Jiang, M.Y., Yuan, D.F., Jiang, Z. and Wei, M.M. (2005) Determination of Wavelet Denoising Threshold by PSO and GA. Proceedings of the IEEE International Symposium on Antenna, Propagation and EMC Technologies for Wireless Communications, Beijing, 8-12 August 2005, 1426-1429. http://dx.doi.org/10.1109/MAPE.2005.1618192
[20]	Schaffer, J.D., Janevski, A. and Simpson, M.R. (2005) A Genetic Algorithm Approach for Discovering Diagnostic Patterns in Molecular Measurement Data. Proceedings of the 2005 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology, San Diego, 14-15 November 2005, 1-8.
[21]	Punyadeera, C., Schneider, E.M., Schaffer, J.D., Hsin-Yun, H., Joos, T.O., Kriebel, F., Weiss, M. and Verhaegh, W.F.J. (2010) A Biomarker Panel to Discriminate between Systemic Inflammatory Response Syndrome and Sepsis and Sepsis Severity. Journal of Emergencies, Trauma & Shock, 3, 26. http://dx.doi.org/10.4103/0974-2700.58666
[22]	Boroczky, L., Zhao, L. and Lee, K.P. (2006) Feature Subset Selection for Improving the Performance of False Positive Reduction in Lung Nodule CAD. IEEE Transactions on Information Technology in Biomedicine, 10, 504-511.
[23]	Janevski, A., Kamalakaran, S., Banerjee, N., Varadan, V. and Dimitrova, N. (2009) PAPAyA: A Platform for Breast Cancer Biomarker Signature Discovery, Evaluation and Assessment. BMC Bioinformatics, 10, 7-8. http://dx.doi.org/10.1186/1471-2105-10-S9-S7
[24]	Kac, G., Durain, E., Amrein, C., Hérisson, E., Fiemeyer, A. and Buu-Hoi, A. (2001) Colonization and Infection of Pulmonary Artery Catheter in Cardiac Surgery Patients: Epidemiology and Multivariate Analysis of Risk Factors. Critical Care Medicine, 29, 971-975. http://dx.doi.org/10.1097/00003246-200105000-00014
[25]	Dalen, J.E. (2001) The Pulmonary Artery Catheter—Friend, Foe, or Accomplice. Journal of the American Medical Association, 286, 348-350.
[26]	Salerno, D.M. and Zanetti, J. (1990) Seismocardiography: A New Technique for Recording Cardiac Vibrations. Concept, Method, and Initial Observations. Journal of Cardiovascular Technology, 9, 111-118.
[27]	Korzeniowska-Kubacka, I. and Piotrowicz, R. (2002) Seismocardiography—A Noninvasive Technique for Estimating Left Ventricular Function. Preliminary Results. Przeglad Lekarski, 59, 774-776.
[28]	Raval, N.Y., Squara, P., Cleman, M., Yalamanchili, K., Winklmaier, M. and Burkhoff, D. (2008) Multicenter Evaluation of Noninvasive Cardiac Output Measurement by Bioreactance Technique. Journal of Clinical Monitoring and Computing, 22, 113-119. http://dx.doi.org/10.1007/s10877-008-9112-5
[29]	Keren, H., Burkhoff, D. and Squara, P. (2007) Evaluation of a Noninvasive Continuous Cardiac Output Monitoring System Based on Thoracic Bioreactance. AJP: Heart and Circulatory Physiology, 293, H583-H589. http://dx.doi.org/10.1152/ajpheart.00195.2007
[30]	Squara, P., Denjean, D., Estagnasie, P., Brusset, A., Dib, J.C. and Dubois, C. (2007) Noninvasive Cardiac Output Monitoring (NICOM): A Clinical Validation. Intensive Care Medicine, 33, 1191-1194. http://dx.doi.org/10.1007/s00134-007-0640-0
[31]	Eshelman, L.J. (1991) The CHC Adaptive Search Algorithm: How to Have Safe Search When Engaging in Nontraditional Genetic Recombination. In: Rawlings, G.J.E., Ed., Foundations of Genetic Algorithms, Morgan Kaufmann, San Francisco, 265-283.
[32]	Mathias, K.E., Eshelman, L.J., Schaffer, J.D., Augusteijn, L., Hoogendijk, P. and van de Wiel, R. (2000) Code Compaction Using Genetic Algorithms. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2000), Las Vegas, 10-12 July 2000, 710-717.
[33]	Schaffer, J.D., Mani, M., Eshelman, L.J. and Mathias, K. (1998) The Effect of Incest Prevention on Genetic Drift. In: Banzhaf, W. and Reeves, C., Eds., Foundations of Genetic Algorithms, Volume 5, Morgan Kaufmann, San Mateo, 235-243.
[34]	Radcliffe, N. (1994) The Algebra of Genetic Algorithms. Annals of Maths and Artificial Intelligence, 10, 339-384. http://dx.doi.org/10.1007/BF01531276
[35]	Radcliffe, N. (1991) Forma Analysis of Random respectful Recombination. Proceedings of the Fourth International Conference on Genetic Algorithms, San Diego, 13-16 July 1991, 222-229.
[36]	Eshelman, L.J. and Schaffer, J.D. (1993) Real-Coded Genetic Algorithms and Interval Schemata. In: Whitley, D., Ed., Foundations of Genetic Algorithms, Volume 2, Morgan Kaufmann, San Mateo, 187-202. http://dx.doi.org/10.1016/b978-0-08-094832-4.50018-0