An experimental study on nonlinear function computation for neural/fuzzy hardware design

IEEE Transactions on Neural Networks

Volumn 18, Issue 1, 2007, Pages 266-283

  Basterretxea, Koldo ^a   Tarela, José Manuel ^a   del Campo, Inés ^a   Bosque, Guillermo ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

Approximation capability; Centered recursive interpolation (CRI); Gaussian function; Neurofuzzy hardware; Sigmoid function

Indexed keywords

APPROXIMATION THEORY; BACKPROPAGATION; COMPUTER SIMULATION; INTERPOLATION; LEARNING SYSTEMS; RADIAL BASIS FUNCTION NETWORKS;

CENTERED RECURSIVE INTERPOLATION (CRI); GAUSSIAN FUNCTION; HARDWARE DESIGN; NEUROFUZZY HARDWARE; SIGMOID FUNCTION;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER AIDED DESIGN; ELECTRONICS; EQUIPMENT; EQUIPMENT DESIGN; EVALUATION; FUZZY LOGIC; INSTRUMENTATION; NONLINEAR SYSTEM; SIGNAL PROCESSING;

COMPUTER-AIDED DESIGN; ELECTRONICS; EQUIPMENT DESIGN; EQUIPMENT FAILURE ANALYSIS; FUZZY LOGIC; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 33846105772     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2006.884680     Document Type: Article

References (62)

1. D. Anguita, I. Baturone, and J. Miller, Eds., "Applied soft computing," in Special Issue on Hardware Implementations of Soft Computing Techniques. New York: Elsevier, 2004, vol. 4.
2. B. Linares-Barranco, A. G. Andreou, G. Indiveri, and T. Shibata, Eds., "Guest editorial - Special issue on neural networks hardware implementations," IEEE Trans. Neural Netw., vol. 14, no. 5, pp. 976-979, Sep. 2003.
3. F. Salam and T. Yamakawa, Eds., "Special issue on micro-electronic hardware implementations of soft computing: Neural and fuzzy networks with learning," Comput. Electr. Eng., vol. 25, no. 5, pp. 305-307, 1999.
4. M. J. Patyra, Ed., "Guest editorial: Fuzzy logic hardware implementations," IEEE Trans. Fuzzy Syst., vol. 4, no. 4, p. 401, Nov. 1996.
5. S. K. Halgamuge, T. Hollstein, A. Kirschbaum, and M. Glesner, "Automatic generation of application specific fuzzy controllers for rapid prototyping," in Proc. IEEE Int. Conf. Fuzzy Syst., Orlando, FL, Jun. 1994, pp. 1638-1641.
6. E. Franchi, N. Manaresi, R. Rovatti, A. Bellini, and G. Baccarani, "Analog synthesis of nonlinear functions based on fuzzy logic," IEEE J. Solid-State Circuits, vol. 33, no. 6, pp. 885-895, Jun. 1998.
7. I. Rojas, F. J. Pelayo, J. Ortega, and A. Prieto, "A CMOS implementation of fuzzy controllers based on adaptive membership function ranges," in 5th Int. Conf. Microelectron. Neural Netw. Fuzzy Syst., 1996, pp. 317-321.
8. S. Guo, L. Peters, and H. Surmann, "Design and application of an analog fuzzy logic controller," IEEE Trans. Fuzzy Syst., vol. 4, no. 4, pp. 429-438, Nov. 1996.
9. Y. Ota and M. Wilamowski, "CMOS implementation of a voltage-mode fuzzy min-max controller," J. Circuits, Syst. Comput., vol. 6, no. 2, pp. 171-184, 1996.
10. L. Peters, S. Guo, and R. Camposano, "A novel analog fuzzy controller for intelligent sensors," Fuzzy Sets Syst., no. 70, pp. 235-247, 1995.
11. F. Vidal-Verdú and A. Rodríguez-Vázquez, "Using building blocks to design analog-fuzzy controllers," IEEE Micro, vol. 15, no. 4, pp. 49-57, Aug. 1995.
12. J. Choi, B. J. Sheu, and J. C.-F. Chang, "A Gaussian synapse circuit for analog VLSI neural networks," IEEE Trans. Very Large Scale Integration (VLSI) Syst., vol. 2, no. 2, pp. 129-133, Jun. 1994.
13. T. Yildirim and J. S. Marsland, "An RBF/MLP hybrid neural network implemented in VLSI hardware," in Proc. Conf. Neural Netw. and Their Appl., Saint-Jerome, France, 1996, pp. 156-160.
14. R. Coggins, I. M. Jabr, B. Flower, and S. Pickard, "A low-power network for on-line diagnosis of heart patients," IEEE Micro, vol. 15, no. 3, pp. 18-25, Jun. 1995.
15. C. Lu and B. Shi, "Circuit design of an adjustable neuron activation function and its derivative," Electron. Lett., vol. 36, no. 6, pp. 553-555, 2000.
16. S. M. Fakhaire, H. Farshbaf, and K. C. Smith, "Scalable closed-boundary analog neural networks," IEEE Trans. Neural Netw., vol. 15, no. 2, pp. 492-504, Mar. 2004.
17. F. Girosi and T. Poggio, "Networks and the Best Aproximation Property" Center Biol. Inf. Process., Artif. Intell. Lab, Massachusetts Inst. Technol., Cambridge, MA, Romm 43-787, 1989.
18. G. Cybenco, "Approximation by superposition of a sigmoidal function," Math. Control, Signals, Syst., vol. 2, pp. 303-314, 1989.
19. K.-I. Funahashi, "On the approximate realization of continuous mappings by neural networks," Neural Netw., vol. 2, pp. 183-192, 1989.
20. E. J. Hartman, J. D. Keeler, and J. M. Kowalski, "Layered neural networks with Gaussian hidden units as universal approximations," Neural Comput., vol. 2, pp. 210-215, 1990.
21. J. Park and I. W. Sandberg, "Universal approximation using radial-basis-function networks," Neural Comput., vol. 3, pp. 246-257, 1991.
22. J. Park and I. W. Sandberg, "Approximation and radial-basis-function networks," Neural Comput., vol. 5, pp. 305-316, 1993.
23. L. X. Wang, "Fuzzy systems are universal approximators," in Proc. IEEE Int. Conf. Fuzzy Syst., San Diego, CA, 1992, pp. 1163-1169.
24. J. J. Buckley, "Universal fuzzy controllers," Automatica, vol. 28, no. 6, pp. 1245-1248, 1992.
25. S. G. Cao, N. W. Rees, and G. Feng, "Mamdani-type fuzzy controllers are universal fuzzy controllers," Fuzzy Sets Syst., vol. 123, pp. 359-367, 2001.
26. X.-J. Zeng and M. G. Singh, "Approximation theory of fuzzy systems - SISO case," IEEE Trans. Fuzzy Syst., vol. 2, no. 2, pp. 162-176, May 1994.
27. K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Netw., vol. 2, pp. 359-366, 1989.
28. M. Stinchombe and H. White, "Universal approximation using feedforward networks with nonsigmoid hidden layer activation functions," in Proc. IJCNN, Washington, D.C., 1989, pp. 161-166.
29. T. Chan and H. Chen, "Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks," IEEE Trans. Neural Netw., vol. 6, no. 4, pp. 904-910, Jul. 1995.
30. H. Ying, "Sufficient conditions on general fuzzy systems as function approximators," Automatica, vol. 30, no. 3, pp. 521-525, 1994.
31. J. L. Castro, "Fuzzy logic controllers are universal approximators," IEEE Trans. Syst., Man Cybern., vol. 25, no. 4, pp. 629-635, Apr. 1995.
32. D. Tikk, L. T. Kóczy, and T. D. Gedeon, "A survey on universal approximation and its limits in soft computing techniques," Int. J. Approximate Reasoning, vol. 33, pp. 185-202, 2003.
33. V. Kurková, "Approximation of functions by perceptron networks with bounded number of hidden units," Neural Netw., vol. 8, no. 5, pp. 745-750, 1995.
34. H. Ying, "General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators," IEEE Trans. Fuzzy Syst., vol. 6, no. 4, pp. 582-587, Nov. 1998.
35. K. Zeng, N.-Y. Zhang, and W.-L. Xu, "A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 773-780, Dec. 2000.
36. X.-J. Zeng and M. G. Singh, "Approxiamtion accuracy analysis of fuzzy systems as function approximators," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 44-63, Feb. 1996.
37. R. Rovatti, "Fuzzy piecewise multilinear and peiecewise linear systems as universal approximators in Sobolev norms," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 235-249, May 1998.
38. I. Baturone, S. Sánchez-Solano, A. Barriga, and J. L. Huertas, "Design issues for the VLSI implementation of universal approximator fuzzy systems," in Proc. WSES CSCC'99 Multiconf., 1999, pp. 6471-6476.
39. C. Alippi, "Selecting accurate, robust, and minimal feedforward neural networks," IEEE Trans. Circuits Syst., vol. 49, no. 12, pp. 1799-2002, Dec. 2002.
40. J. M. Tarela, K. Basterretxea, I. del Campo, M. V. Martínez, and E. Alonso, "Optimised PWL recursive approximation and its application to neuro-fuzzy systems," Math. Comput. Model., vol. 35, no. 7-8, pp. 867-883, 2002.
41. K. Basterretxea, J. M. Tarela, and I. del Campo, "Approximation of sigmoid function and the derivative for hardware implementation of artificial neurons," Proc. Inst. Elect. Eng. Circuits Devices Syst., vol. 151, no. 1, pp. 18-24, 2004.
42. K. Basterretxea, J. M. Tarela, and I. del Campo, "PWL approximation of non-linear functions for the implementation of neuro-fuzzy systems," in Proc. CSCC'99 3rd World Multiconf. Circuits, Syst., Commun. Comput., 1999, pp. 3001-3007.
43. S. Guarnieri, F. Piazza, and A. Uncini, "Multilayer feedforward networks with adaptive spline activation function," IEEE Trans. Neural Netw., vol. 10, no. 3, pp. 672-683, May 1999.
44. K. Basterretxea, J. M. Tarela, and I. del Campo, "Digital design of sigmoid approximator for artificial neural networks," Electron. Lett., vol. 38, no. 1, pp. 35-37, 2002.
45. K. Basterretxea, J. M. Tarela, and I. del Campo, "Digital Gaussian membership function circuit for neuro-fuzzy hardware," Electron. Lett., vol. 42, no. 1, pp. 44-46, 2006.
46. M. T. Hagan, H. B. Demuth, and M. Beale, Neural Network Design. Boston, MA: PWS, 1996.
47. C. Xiang, S. Q. Ding, and T. H. Lee, "Geometrical interpretation and architecture selection of MLP," IEEE Trans. Neural Netw., vol. 16, no. 1, pp. 84-96, Jan. 2005.
48. H. Demuth and M. Beale, Neural Network Toolbox User's Guide, 4 ed. Natick, MA: MathWorks Inc., 2003, ch. 5.
49. G. E. P. Box and G. M. Jenkins, "Forecasting using leading indicators," in Time Series Analysis, Forecasting and Control. San Francisco, CA: Holden Day, 1970.
50. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its application to modelling and control," IEEE Trans. Syst. Man, Cybern., vol. 15, no. 1, pp. 116-132, 1985.
51. A. Esposito, M. Marinaro, D. Oricchio, and S. Scarpetta, "Approximation of continuous mappings by a growing neural RBF-based algorithm," Neural Netw., vol. 13, pp. 651-665, 2000.
52. S. Lee and M. K. Rhee, "A Gaussian potential function network with hierarchically self-organizing learning," Neural Netw., vol. 4, pp. 207-224, 1991.
53. C.-L. Chen, W.-C. Chen, and F.-Y. Chang, "Hybrid learning algorithm for Gaussian potential function networks," Proc. Inst. Elect. Eng. - D: Control Theory Appl., vol. 140, no. 6, pp. 442-448, Nov. 1993.
54. L. Yingwei, N. Sundararajan, and P. Saratchandran, "Identification of time-varying nonlinear systems using minimal radial basis function neural networks," IEE Proc. - Control Theory Appl., vol. 144, no. 2, pp. 202-208, 1997.
55. J. S. R. Jang and C. T. Sun, "Functional equivalence between radial basis function networks and fuzzy inference systems," IEEE Trans. Neural Netw., vol. 4, no. 1, pp. 156-159, Jan. 1993.
56. K. J. Hunt, R. Haas, and R. Murray-Smith, "Extending the functional equivalence of radial basis function networks and fuzzy inference systems," IEEE Trans. Neural Netw., vol. 7, no. 3, pp. 776-782, May 1996.
57. J. M. Benitez, J. L. Castro, and I. Requena, "Are artificial neural networks black boxes?," IEEE Trans. Neural Netw., vol. 8, no. 5, pp. 1156-1164, Sep. 1997.
58. H. C. Andersen, A. Lofti, and L. C. Westphal, "Comments on 'functional equivalence between radial basis function networks and fuzzy inference systems'," IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1529-1531, Nov. 1998.
59. J. L. Castro, C. J. Mantas, and J. M. Benitez, "Interpretation of artificial neural networks by means of fuzzy rules," IEEE Trans. Neural Netw., vol. 13, no. 1, pp. 101-116, Jan. 2002.
60. E. Kolman and M. Margaliot, "Are artificial neural networks white boxes?," IEEE Trans. Neural Netw., vol. 16, no. 4, pp. 844-852, Jul. 2005.
61. J. S. R. Jang, "ANFIS: Adaptive-network-based fuzzy inference systems," IEEE Trans. Syst. Man, Cybern., vol. 23, no. 3, pp. 665-685, May/Jun. 1993.
62. S.-J. Lee and C.-S. Ouyang, "A neuro-fuzzy system modeling with selfconstructing rule generation and hybrid SVD-based learning," IEEE Trans. Fuzzy Syst., vol. 11, no. 3, pp. 341-353, Jun. 2003.