Neural Computing and Applications

, Volume 21, Issue 2, pp 305–317 | Cite as

Plane-Gaussian artificial neural network

  • Xubing Yang
  • Songcan Chen
  • Bin Chen
Original Article


Multilayer perceptrons (MLPs) and radial basis functions networks (RBFNs) have been widely concerned in recent years. In this paper, based on k-plane clustering (kPC) algorithm, we propose a novel artificial network model termed as Plane-Gaussian network to enlarge the arsenal of the neural networks. This network adopts a so-called Plane-Gaussian activation function (PGF) in hidden neurons. Replacing traditional central point of Gaussian radial basis function (RBF) with central hyperplane, PGF forms a band-shaped rather than spheral-shaped receptive field in RBF, which makes PGF able to express its peculiar geometrical characteristics: locality and globality. Importantly, it is also proved that PGF network (PGFN) having one hidden layer is capable of universal approximation. As a universal approximator, PGFN gives an informal way of bridging the gap between MLP and RBFN. The experiments report comparison between training time and classification accuracies on some artificial and UCI datasets and conclude that (1) PGFN runs significantly faster than MLP and (2) PGFN has comparable or better classification performance than MLP and RBFN, especially in subspace-distributed datasets.


Multilayer perceptron (MLP) Radial basis function (RBF) network Activation function Plane-Gaussian function (PGF) 



We thank the anonymous reviewers for their valuable comments and suggestions. We are grateful to the Neural Computing Research Group of Aston university for allowing us to freely use Netlab software. This research was supported by Natural Science Foundation of China (60773061, 60903130), the Jiangsu Science Foundation BK2009393, and Science Foundation of Nanjing Forestry University 163070053 and 163070657.


  1. 1.
    Haykin S (1999) Neural networks: a comprehensive foundation, 2nd edn. Prentice Hall, NJzbMATHGoogle Scholar
  2. 2.
    Bishop CM (1995) Neural networks and pattern recognition. Oxford University Press, OxfordGoogle Scholar
  3. 3.
    Barreto AMS, Barbosa HJC, Ebecken NFF (2006) GOLS-Genetic orthogonal least squares algorithm for training RBF networks. Neurocomputing 69(16–18):2041–2064CrossRefGoogle Scholar
  4. 4.
    Sarimveis H, Doganis P, Alexandridis A (2006) A classification technique based on radial basis function neural networks. Adv Eng Softw 37(4):218–221CrossRefGoogle Scholar
  5. 5.
    Smyrnakis MG, Evans DJ (2007) Classifying Ischemic events using a Bayesian inference multilayer percetron and input variable evaluation using automatic relevance determination. Comput Cardiol 34:305–308Google Scholar
  6. 6.
    Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 5(4):303–314MathSciNetCrossRefGoogle Scholar
  7. 7.
    Funahashi K (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2(3):183–192zbMATHCrossRefGoogle Scholar
  8. 8.
    Hornik K, Stinchcombe M, White H (1990) Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks 3(5):551–560CrossRefGoogle Scholar
  9. 9.
    Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257CrossRefGoogle Scholar
  10. 10.
    Nam MD, Thanh TC (2003) Approximation of function and its derivatives using radial basis function networks. Appl Math Modell 27(3):197–220zbMATHCrossRefGoogle Scholar
  11. 11.
    Lehtokangas M, Saarinen J (1998) Centroid based multilayer perceptron networks. Neural Process Lett 7:101–106CrossRefGoogle Scholar
  12. 12.
    Irigoyen E, Pinzolas M (in press) Numerical bounds to assure initial local stability of NARX multilayer perceptrons and radial basis functions. Neurocomputing Google Scholar
  13. 13.
    Oliveira ALI, Melo BJM, Meira SRL (2005) Improving constructive training of RBF networks through selective pruning and model selection. Neurocomputing 64:537–541CrossRefGoogle Scholar
  14. 14.
    Delogu R, Fanni A, Montisci A (2008) Geometrical synthesis of MLP neural networks. Neurocomputing 71(4–6):919–930CrossRefGoogle Scholar
  15. 15.
    De Silva CR, Ranganath S, De Silva LC (2008) Cloud basis function neural network: a modified RBF network architecture for holistic facial expression recognition. Pattern Recogn 41(4):1241–1253zbMATHCrossRefGoogle Scholar
  16. 16.
    Qu N, Wang L, Zhu M et al (2008) Radial basis function networks combined with genetic algorithm applied to nondestructive determination of compound erythromycin ethylsuccinate powder. Chemom Intell Lab Syst 90(2):145–152CrossRefGoogle Scholar
  17. 17.
    Huan HX, Hien DTT, Huynh HT (2007) A novel efficient two-phase algorithm for training interpolation radial basis function networks. Signal Process 87(11):2708–2717zbMATHCrossRefGoogle Scholar
  18. 18.
    Yeung DS, Chan PPK, Ng WWY (2009) Radial basis function network learning using localized generalization error bound. Inf Sci 179:3199–3217zbMATHCrossRefGoogle Scholar
  19. 19.
    Yeung DS, Wang D, Ng WWY, Tsang ECC, Wang X (2007) Structured large margin machines: sensitive to data distributions. Mach Learn 68(2):171–200CrossRefGoogle Scholar
  20. 20.
    Duda RO, Hart RE, Stock DG (2001) Pattern classification, 2nd edn. Wiley, New YorkzbMATHGoogle Scholar
  21. 21.
    Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New YorkzbMATHGoogle Scholar
  22. 22.
    Bradley PS, Mangasarian OL (2000) k-plane clustering. J Global Optim 16(1):23–32MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Castillo PA, Merelo JJ, Arenas MG, Romero G (2007) Comparing evolutionary hybrid systems for design and optimization of multilayer perceptron structure along training parameters. Inf Sci 177(14):2884–2905CrossRefGoogle Scholar
  24. 24.
    Gao D, Ji Y (2005) Classification methodologies of multilayer perceptrons with sigmoid activation functions. Pattern Recognit 38(10):1469–1482Google Scholar
  25. 25.
    Kiernan L, Mason JD, Warwick K (1996) Robust initialization of Gaussian radial basis function networks using partitioned k-means clustering. Electron Lett 32(7): 671–673Google Scholar
  26. 26.
    Bruzzone L, Prieto DF (1999) A technique for the selection of kernel-function parameters in RBF neural networks for classification of remote-sensing images. IEEE Trans Vol Geosci Remote Sensing 37(2):1179–1184CrossRefGoogle Scholar
  27. 27.
    Jeffreys H, Jeffreys BS (1988) Methods of mathematical physics, 3rd edn. Cambridge University Press, CambridgeGoogle Scholar
  28. 28.
    Chen TP, Chen H (1995) Approximation capability to functions of several variables nonlinear functionals and operators by radial basis function neural networks. IEEE Trans Neural Netw 6(4):904–910CrossRefGoogle Scholar
  29. 29.
    Rudin W (1987) Real and complex analysis, 3rd edn. McGraw-Hill, Inc., New YorkzbMATHGoogle Scholar
  30. 30.
    Blake C, Keogh E, Merz CJ (1998) UCI repository of machine learning databases []. Department of Information and Computer Science, University of California, Irvine
  31. 31.
    Draghici S (2002) On the capabilities of neural networks using limited precision weights. Neural Netw 15:395–414CrossRefGoogle Scholar
  32. 32.
    Mirchandani G, Cao W (1989) On hidden nodes for neural Nets. IEEE Trans Circuits Syst 36(5):661–664MathSciNetCrossRefGoogle Scholar
  33. 33.
    Huang GB, Babri HA (1998) Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions. IEEE Trans Neural Netw 9(1):224–229CrossRefGoogle Scholar
  34. 34.
    Teoh EJ, Xiang C, Tan KC (2006) Estimating the number of hidden neurons in a feedforward network using the singular value decomposition. LNCS 3971. Springer, Berlin, pp 858–865Google Scholar
  35. 35.
    Trenn S (2008) Multilayer perceptrons: approximation order and necessary number o hidden units. IEEE Trans Neural Netw 19(5):836–844CrossRefGoogle Scholar
  36. 36.
    Mehrabi S, Maghsoudloo M, Arabalibeik H et al (2009) Application of multilayer perceptron and radial basis function neural networks in differentiation between chronic obstructive pulmonary and congestive heart failure diseases. Expert Syst Appl 36:6956–6959CrossRefGoogle Scholar
  37. 37.
    Bartlett PL (1998) The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network. IEEE Trans Inf Theory 44(2):525–536MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Bishop CM, Nabney I (2004) Netlab neural network software. Neural computing research group, Information engineering, Aston UniversityGoogle Scholar
  39. 39.
    Moody TJ, Darken CJ (1988) Learning with localized receptive fields. In: Hinton G, Sejnowski T, and Touretzsky D (eds) Proceedings of the 1988 connectionist models summer school. Morgan Kaufmann, pp 133–143Google Scholar
  40. 40.
    Bellman RE, Roth RS (1969) Curve fitting by segmented straight lines. Am Stat Assoc J 64:1079–1084MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.College of Information Science and TechnologyNanjing Forestry UniversityNanjingPeople’s Republic of China
  2. 2.Department of Computer Science and EngineeringNanjing University of Aeronautics & AstronauticsNanjingPeople’s Republic of China
  3. 3.Information Engineering CollegeYangzhou UniversityYangzhouPeople’s Republic of China

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