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Optimal association with partly missing key vectors

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Abstract

A new association scheme which can still recall appropriate data when some key elements are missing (blank) is presented. The traditional associative memory models are designed to deal with complete (memorized) keys, but in the real world, key elements are often missing due to error, equipment failure, observation difficulty, etc. The traditional models, in this case, can not have an optimal association except for special cases. When an incomplete key containing blanks is given, we wish to get the same data, as nearly as possible, as would be obtained with the complete key. In this paper, the optimal associative memory model which operates with partly missing keys is proposed. The model is constructed on the basis of the theory of the pseudoinverse of matrices. Even from the incomplete keys which contain a large percentage of blanks, the model recalls the appropriate data optimally under the MSE criterion. From the results of computer simulations, we can show that the model has the expected ability.

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References

  • Dixon, J.: Pattern recognition with partly missing data. IEEE Trans. Syst. Man Cybern.9, 617–621 (1979)

    Google Scholar 

  • Greville, T.N.E.: Some applications of the pseudoinverse of a matrix. SIAM Rev.2, 15–22 (1960)

    Google Scholar 

  • Kittler, J.: Classification of incomplete pattern vectors using modified discriminant functions. IEEE Trans. Comput.27, 367–375 (1978)

    Google Scholar 

  • Kohonen, T.: Correlation matrix memories. IEEE Trans. Comput.21, 353–359 (1972)

    Google Scholar 

  • Kohonen, T., Ruohonen, M.: Representation of associated data by matrix operators. IEEE Trans. Comput.22, 701–702 (1973)

    Google Scholar 

  • Kohonen, T.: An adaptive associative memory principle. IEEE Trans. Comput.23, 444–445 (1974)

    Google Scholar 

  • Kohonen, T., Reuhkala, E., Mäkisara, K., Vainio, L.: Associative recall of images. Biol. Cybern.22, 159–168 (1976)

    Google Scholar 

  • Kohonen, T.: Associative memory: a system theoretical approach. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  • Nakano, K.: Associatron-a model of associative memory. IEEE Trans. Syst. Man Cybern.2, 380–388 (1972)

    Google Scholar 

  • Murakami, K., Akaishi, S., Aibara, T.: On optimal assoviative recall by an incomplete key. Biol. Cybern.30, 95–97 (1978)

    Google Scholar 

  • Murakami, K., Aibara, T.: Construction of a distributed associative memory on the basis of Bayes discriminant rule. IEEE Trans. Pattern Anal. Mach. Intellig.3, 210–214 (1981)

    Google Scholar 

  • Penrose, R.: On best approximate solutions of linear matrix equations. Proc. Cambridge Philos. Soc.52, 17–19 (1956)

    Google Scholar 

  • Poggio, T.: On optimal nonlinear associative recall. Biol. Cybern.19, 201–209 (1975)

    Google Scholar 

  • Reid, R.J., Frame, J.S.: Convergence in iteratively formed correlation matrix memories. IEEE Trans. Comput.24, 827–830 (1975)

    Google Scholar 

  • Steinbuch, K., Piske, U.A.W.: Learning matrices and their applications. IEEE Trans. Electron. Comput.12, 846–862 (1963)

    Google Scholar 

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Murakami, K., Aibara, T. Optimal association with partly missing key vectors. Biol. Cybernetics 44, 151–155 (1982). https://doi.org/10.1007/BF00317975

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  • DOI: https://doi.org/10.1007/BF00317975

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