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Learning automata algorithms for pattern classification

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Abstract

This paper considers the problem of learning optimal discriminant functions for pattern classification. The criterion of optimality is minimising the probability of misclassification. No knowledge of the statistics of the pattern classes is assumed and the given classified sample may be noisy. We present a comprehensive review of algorithms based on the model of cooperating systems of learning automata for this problem. Both finite action set automata and continuous action set automata models are considered. All algorithms presented have rigorous convergence proofs. We also present algorithms that converge to global optimum. Simulation results are presented to illustrate the effectiveness of these techniques based on learning automata.

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References

  • Aluffi-Pentini F, Parisi V, Zirilli F 1985 Global optimisation and stochastic differential equations.J. Optim. Theory Appl. 47: 1–26

    Article  MATH  MathSciNet  Google Scholar 

  • Barto A G 1985 Learning by statistical cooperation of self-interested neuron-like computing elements. COINS Tech. Report. 81-11, Univ. of Massachusetts, Amherst, MA

    Google Scholar 

  • Barto A G, Anandan P 1985 Pattern-recognizing stochastic learning automata.IEEE Trans. Syst., Man Cybern. 15: 360–374

    MATH  MathSciNet  Google Scholar 

  • Baum E, Haussler D L 1989 What sized net gives valid generalisation.Neural Comput. 1: 151–160

    Article  Google Scholar 

  • Blum J R 1954 Multidimensional stochastic approximation methods.Ann. Math. Stat. 25: 737–744

    Article  MathSciNet  MATH  Google Scholar 

  • Blumer A, Ehrenfeucht A, Haussler D L, Warmuth M K 1989 Learnability and the Vapnik-Chervonenkis dimension.J. Assoc. Comput. Mach. 36: 929–965

    MATH  MathSciNet  Google Scholar 

  • Borkar V S 1998 Stochastic approximation algorithms: Overview and recent trends.Sadhana 24:

  • Bush R R, Mosteller F 1958Stochastic models for learning (New York: John Wiley)

    Google Scholar 

  • Chiang T, Hwang C, Sheu S 1987 Diffusion for global optimisation in Rn.SIAM J. Control Optim. 25: 737–753

    Article  MATH  MathSciNet  Google Scholar 

  • Duda R O, Hart P E 1973Pattern classification and scene analysis (New York: Wiley)

    MATH  Google Scholar 

  • Haussler D L 1992 Decision theoretic generalization of the PAC model for neural net and learning applications.Inf. Comput. 100: 78–150

    Article  MATH  MathSciNet  Google Scholar 

  • Kashyap R L, Blaydon C C, Fu K S 1970 Stochastic approximation.Adaptive, learning and pattern recognition systems: Theory and applications (eds) J M Mendel, K S Fu (New York: Academic Press)

    Google Scholar 

  • Kiefer J, Wolfowitz J 1952 Stochastic estimation of a regression function.Ann. Math. Stat. 23: 462–466

    Article  MathSciNet  MATH  Google Scholar 

  • Kushner H Y and Yin G G 1997Stochastic approximation algorithms and applications (New York: Springer-Verlag)

    MATH  Google Scholar 

  • Lippmann R P 1987 An introduction to computing with neural nets.IEEE Acoust., Speech Signal Process. Mag. April: 4–22

  • Minsky M L, Papert S A 1969Perceptrons (Cambridge, MA: MIT Press)

    MATH  Google Scholar 

  • Nagendra G D 1997PAC learning with noisy samples. M E thesis, Dept. of Electrical Engineering, Indian Institute of Science, Bangalore

    Google Scholar 

  • Narendra K S, Thathachar M A L 1989Learning automata: An introduction (Englewood Cliffs, NJ: Prentice Hall)

    Google Scholar 

  • Natarajan B K 1991Machine learning: A theoretical approach (San Mateo, CA: Morgan Kaufmann)

    Google Scholar 

  • Phansalkar V V 1991Learning automata algorithms for connectionist suystems — local and global convergence. Ph D thesis, Dept. of Electrical Engineering, Indian Institute of Science, Bangalore

    Google Scholar 

  • Rajaraman K, Sastry P S 1996 Finite time analysis of pursuit algorithm for learning automata.IEEE Trans. Syst., Man Cybern. 27: 590–599

    Google Scholar 

  • Rajaraman K, Sastry P S 1997 A parallel stochastic algorithm for learning logic expressions under noise.J. Indian Inst. Sci. 77: 15–45

    MathSciNet  Google Scholar 

  • Rumelhart D E, Hinton G E, Williams R J 1986 Learning internal representations by error propagation.Parallel distributed processing (eds) D E Rumelhart, J McLlelland (Cambridge, MA: MIT Press) vol. 1

    Google Scholar 

  • Santharam G 1994Distributed learning with connectionist models for optimisation and control. Ph D thesis, Dept. of Electrical Engineering, Indian Institute of Science, Bangalore

    Google Scholar 

  • Santharam G, Sastry P S, Thathachar M A L 1994 Continuous action set learning automata for stochastic optimization.J. Franklin Inst. 331: 607–628

    Article  MathSciNet  Google Scholar 

  • Sastry P S, Rajaram K, Ranjan S R 1993 Learning optimal conjunctive concepts using stochastic automata.IEEE Trans. Syst., Man Cybern. 23: 1175–1184

    Article  Google Scholar 

  • Sastry P S, Phansalkar V V, Thathachar M A L 1994 Decentralised learning of Nash equilibria in multi-person stochastic games with incomplete information.IEEE Trans. Syst., Man Cybern. 24: 769–777

    Article  MathSciNet  Google Scholar 

  • Shapiro I J, Narendera K S 1969 Use of stochastic automata for parameter self optimisation multimodel performance criteria.IEEE Trans. Syst. Sci. Cybern. 5: 352–360

    Google Scholar 

  • Sklansky J, Wassel G N 1981Pattern classification and trainable machines (New York: Springer-Verlag)

    Google Scholar 

  • Thathachar M A L, Sastry P S 1985 A new approach to the design of reinforcement schemes for learning automata.IEEE Trans. Syst., Man Cybern. 15: 168–175

    MATH  MathSciNet  Google Scholar 

  • Thathachar M A L, Sastry P S 1987 Learning optimal discriminant functions through a cooperative game of automata.IEEE Trans. Syst., Man Cybern. 17: 73–85

    Article  MATH  MathSciNet  Google Scholar 

  • Thathachar M A L, Sastry P S 1991 Learning automata in stochastic games with incomplete information.Systems and signal processing (eds) R N Madan, N Vishwanathan, R L Kashyap (New Delhi: Oxford and IBH) pp 417–434

    Google Scholar 

  • Thathachar M A L, Phansalkar V V 1995a Learning the global maximum with parameterised learning automata.IEEE Trans. Neural Networks 6: 398–406

    Article  Google Scholar 

  • Thathachar M A L, Phansalkar V V 1995b Convergence of teams and hierarchies of learning automata in connectionist systems.IEEE Trans. Syst., Man Cybern. 25: 1459–1469

    Article  Google Scholar 

  • Thathachar M A L, Arvind M T 1998 Parallel algorithms for modules of learning automata.IEEE Trans. Syst., Man Cybern. B28: 24–33

    Google Scholar 

  • Vapnik V N 1982Estimation of dependences based on empirical data (New York: Springer-Verlag)

    MATH  Google Scholar 

  • Vapnik V N 1997Nature of statistical learning theory (New York: Springer-Verlag)

    Google Scholar 

  • Williams R J 1992 Simple statistical gradient-following algorithms for connectionist reinforcement learning.Machine learning 8: 229–256

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Science, 560 012, Bangalore, India

    P S Sastry & M A L Thathachar

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  1. P S Sastry
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  2. M A L Thathachar
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Corresponding authors

Correspondence to P S Sastry or M A L Thathachar.

Additional information

This work is supported in part by an Indo-US project under ONR grant number N-00014-J-1324.

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Sastry, P.S., Thathachar, M.A.L. Learning automata algorithms for pattern classification. Sadhana 24, 261–292 (1999). https://doi.org/10.1007/BF02823144

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