Abstract
If the antecedents of a fuzzy classification method are derived from pictures or measured data, it might have too many dimensions to handle. A classification scheme based on such data has to apply a careful selection or processing of the measured results: either a sampling, re-sampling is necessary or the usage of functions, transformations that reduce the long, high dimensional observed data vector or matrix into a single point or to a low number of points. Wavelet analysis can be useful in such cases in two ways.
As the number of resulting points of the wavelet analysis is approximately half at each filters, a consecutive application of wavelet transform can compress the measurement data, thus reducing the dimensionality of the signal, i.e., the antecedent. An SHDSL telecommunication line evaluation is used to demonstrate this type of applicability, wavelets help in this case to overcome the problem of a one dimensional signal sampling.
In the case of using statistical functions, like mean, variance, gradient, edge density, Shannon or Rényi entropies for the extraction of the information from a picture or a measured data set, and they don not produce enough information for performing the classification well enough, one or two consecutive steps of wavelet analysis and applying the same functions for the thus resulting data can extend the number of antecedents, and can distill such parameters that were invisible for these functions in the original data set. We give two examples, two fuzzy classification schemes to show the improvement caused by wavelet analysis: a measured surface of a combustion engine cylinder and a colonoscopy picture. In the case of the first example the wear degree is to be determine, in the case of the second one, the roundish polyp content of the picture. In the first case the applied statistical functions are Rényi entropy differences, the structural entropies, in the second case mean, standard deviation, Canny filtered edge density, gradients and the entropies.
In all the examples stabilized KH rule interpolation was used to treat sparse rulebases.
The preliminary version of this paper was presented at the 3rd Conference on Information Technology, Systems Research and Computational Physics, 2–5 July 2018, Cracow, Poland [1].
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References
Lilik, F., Solecki, L., Sziová, B., Kóczy, L.T., Nagy, Sz.: On wavelet based enhancing possibilities of fuzzy classification of measurement results. In: Kulczycki, P., Kowalski, P.A., Łukasik, S. (eds.) Contemporary Computational Science, AGH-UST Press, Cracow, p. 138 (2018)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X
Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man-Mach. Stud. 7, 1–13 (1975). https://doi.org/10.1016/S0020-7373(75)80002-2
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man and Cybern. SMC–3, 28–44 (1973). https://doi.org/10.1109/TSMC.1973.5408575
Kóczy, L.T., Hirota, K.: Approximate reasoning by linear rule interpolation and general approximation. Int. J. Approx. Reason. 9, 197–225 (1993). https://doi.org/10.1016/0888-613X(93)90010-B
Kóczy, L.T., Hirota, K.: Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases. Inf. Sci. 71, 169–201 (1993). https://doi.org/10.1016/0020-0255(93)90070-3
Tikk, D., Joó, I., Kóczy, L.T., Várlaki, P., Moser, B., Gedeon, T.D.: Stability of interpolative fuzzy KH-controllers. Fuzzy Sets Syst. 125, 105–119 (2002). https://doi.org/10.1016/S0165-0114(00)00104-4
Daubechies, I.: Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics 61. SIAM, Philadelphia (1992)
Christopoulos, C., Skodras, A., Ebrahimi, T.: The JPEG2000 still image coding system: an overview. IEEE Trans. Consum. Electron. 46, 1103–1127 (2000)
Kiely, A., Klimesh, M.: The ICER Progressive Wavelet Image Compressor, IPN Progress Report 42-155, 15 November 2003. http://ipnpr.jpl.nasa.gov/tmo/progressreport/42-155/155J.pdf
Nagy, S., Pipek, J.: An economic prediction of the finer resolution level wavelet coefficients in electronic structure calculations. Phys. Chem. Chem. Phys. 17, 31558–31565 (2015)
Fourier, J-B.J.: Theorie Analitique de la Chaleur, Firmin Didot, Paris (1822)
Haar, A.: Zur Theorie der orthogonalen Funktionensysteme (On the theory of orthogonal function systems, in German). Math. Ann. 69, 331–371 (1910)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Techn. J. 27, 379–423 (1948). https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Rényi, A.: On measures of information and entropy. In: Proceedings of the fourth berkeley symposium on mathematics, statistics and probability 1960, pp. 547–561 (1961)
Pipek, J., Varga, I.: Universal classification scheme for the spatial localization properties of one-particle states in finite d-dimensional systems. Phys. Rev. A 46, 3148–3164 (1992). APS, Ridge NY-Washington DC
Varga, I., Pipek, J.: Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems. Phys. Rev. E 68, 026202 (2003). APS, Ridge NY-Washington DC
Mojzes, I., Dominkonics, Cs., Harsányi, G., Nagy, Sz., Pipek, J., Dobos, L.: Heat treatment parameters effecting the fractal dimensions of AuGe metallization on GaAs. Appl. Phys. Lett. 91(7) (2007). Article No. 073107
Molnár, L.M., Nagy, S., Mojzes, I.: Structural Entropy in Detecting Background Patterns of AFM Images, Vacuum, vol. 84, pp. 179–183. Elsevier, Amsterdam (2010)
Bonyár, A., Molnár, L.M., Harsányi, G.: Localization factor: a new parameter for the quantitative characterization of surface structure with atomic force microscopy (AFM). MICRON 43, 305–310 (2012). Elsevier, Amsterdam
Bonyár, A.: AFM characterization of the shape of surface structures with localization factor. Micron 87, 1–9 (2016)
Lilik, F., Botzheim, J.: Fuzzy based prequalification methods for EoSHDSL technology. Acta Technica Jaurinensis 4(1), 135–144 (2011)
Lilik, F., Nagy, Sz., Kóczy, L.T.: Wavelet based fuzzy rule bases in pre-qualification of access networks’ wire pairs. In: IEEE Africon 2015, Addis Ababa, Ethiopia, 14–17 September 2015, Paper P-52 (2015)
Lilik, F., Nagy, S., Kóczy, L.T.: Improved method for predicting the performance of the physical links in telecommunications access networks. Complexity 2018, 1–14 (2018). ID 3685927
Dreyer, M.R., Solecki, L.: Verschleissuntersuchungen an Zylinderlaufbahnen von Verbrennungsmotoren. In: 3. Symposium Produktionstechnik – Innovativ und Interdisziplinär, Zwickau, 6–7 April 2011, pp. 69–74 (2011)
Nagy, Sz., Solecki, L.: Wavelet analysis and structural entropy based intelligent classification method for combustion engine cylinder surfaces. In: Proceedings of the 8th European Symposium on Computational Intelligence and Mathematics, ESCIM, Sofia, 5–8 October 2016, pp. 115–120 (2016)
Nagy, Sz., Lilik, F., Kóczy, L.T.: Entropy based fuzzy classification and detection aid for colorectal polyps. In: IEEE Africon 2017, Cape Town, South Africa, 15–17 September 2017 (2017)
Silva, J.S., Histace, A., Romain, O., Dray, X., Granado, B.: Towards embedded detection of polyps in WCE images for early diagnosis of colorectal cancer. Int. J. Comput. Assist. Radiol. Surg. 9, 283–293 (2014)
Georgieva, V.M., Draganov, I.: Multistage approach for simple kidney cysts segmantation in CT images. In: Kountchev, R., Nakamatsu, K. (eds.) Intelligent Systems Reference Library, New Approaches in Intelligent Image Analysis, vol. 108, pp. 223–252. Springer Nature (2016)
Georgieva, V.M., Vassilev, S.G.: Kidney segmentation in ultrasound images via active contours. In: 11th International Conference on Communications, Electromagnetics and Medical Applications, Athens, Greece, 13–15 October 2016, pp. 48–53 (2016)
Acknowledgment
The authors would like to thank the financial support of the projects GINOP-2.3.4-15-2016-00003 and the ÚNKP-18-4 New National Excellence Programme of the Ministry of Human Capacities of Hungary. This work was supported by National Research, Development and Innovation Office (NKFIH) K124055. The authors would like to thank to EFOP-3.6.1-16-2016-00017 1 “~Internationalisation, initiatives to establish a new source of researchers and graduates, and development of knowledge and technological transfer as instruments of intelligent specialisations at Széchenyi István University” for the support of the research.
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Lilik, F., Solecki, L., Sziová, B., Kóczy, L.T., Nagy, S. (2020). On Wavelet Based Enhancing Possibilities of Fuzzy Classification Methods. In: Kulczycki, P., Kacprzyk, J., Kóczy, L., Mesiar, R., Wisniewski, R. (eds) Information Technology, Systems Research, and Computational Physics. ITSRCP 2018. Advances in Intelligent Systems and Computing, vol 945. Springer, Cham. https://doi.org/10.1007/978-3-030-18058-4_5
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