Abstract

A Ho-Kashyap (H-K) associative processor (AP) is shown to have a larger storage capacity than the pseudoinverse and correlation APs and to accurately store linearly dependent key vectors. Prior APs have not demonstrated good performance on linearly dependent key vectors. The AP is attractive for optical implementation. A new robust H-K AP is proposed to improve noise performance. These results are demonstrated both theoretically and by Monte Carlo simulation. The H-K AP is also shown to outperform the pseudoinverse AP in an aircraft recognition case study. A technique is developed to indicate the least reliable output vector elements and a new AP error correcting synthesis technique is advanced.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. S. Stiles, D.-L. Denq, “A Quantitative Comparison of the Performance of Three Discrete Distributed Associative Memory Models,” IEEE Trans. Comput. C-36, 257–263 (1987).
    [CrossRef]
  2. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
    [CrossRef] [PubMed]
  3. R. McEliece et al., “The Capacity of the Hopfield Associative Memory,” IEEE Trans. Info. Theory IT-33, 461–482 (1987).
    [CrossRef]
  4. B. Telfer, D. Casasent, “Ho-Kashyap Associative Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1005, 77–87 (1988).
  5. T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, Berlin, 1987).
  6. G. Stiles, D.-L. Denq, “On the Effect of Noise on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Pat. Anal. and Mach. Int. PAMI-7, 358–360 (1985).
    [CrossRef]
  7. K. Murakami, T. Aibara, “An Improvement on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Syst. Man and Cybern. SMC-17, 699–707 (1987).
    [CrossRef]
  8. D. Casasent, B. Telfer, “Key and Recollection Vector Effects on Heteroassociative Memory Performance,” Appl. Opt. 28, 272–283 (1989).
    [CrossRef] [PubMed]
  9. Y.-C. Ho, R. Kashyap, “An Algorithm for Linear Inequalities and Its Applications,” IEEE Trans. Electron. Comput. EC-14, 683–688 (1965).
    [CrossRef]
  10. T. Cover, “Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition,” IEEE Trans. Electron. Comput. EC-14, 326–334 (1965).
    [CrossRef]
  11. M. Hassoun, “Two-Level Neural Network for Deterministic Logic Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 258–264 (1988).
  12. M. Hassoun, D. Clark, “An Adaptive Attentive Learning Algorithm for Single-Layer Neural Networks,” IEEE Int. Conf. Neural Networks I431–440 (1988).
    [CrossRef]
  13. M. Hassoun, “A High-Performance Associative Neural Memory (ANM) for Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 956 (1988).
  14. M. Hassoun, A. Youssef, “High Performance Recording Algorithm for Hopfield Model Associative Memories,” Opt. Eng. 28, 46–54 (1989).
    [CrossRef]
  15. M. H. Hassoun, “Adaptive Dynamic Heteroassociative Neural Memories for Pattern Classification,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 75–83 (1989).
  16. A. M. Youssef, M. H. Hassoun, “Dynamic Autoassociative Neural Memory Performance vs. Capacity,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 52–59 (1989).
  17. B. Kosko, “Bidirectional Associative Memories,” IEEE Trans. Syst. Man and Cybern. SMC-18, 49–60 (1988).
    [CrossRef]
  18. B. L. Montgomery, B. V. K. Vijaya Kumar, “An Evaluation of the Use of the Hopfield Neural Network Model as a Nearest-Neighbor Algorithm,” Appl. Opt. 25, 3759–3766 (1986).
    [CrossRef] [PubMed]
  19. R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag. 4, 4–22 (1987).
    [CrossRef]
  20. A. D. Fisher, W. L. Lippincott, J. W. Lee, “Optical Implementations of Associative Networks with Versatile Adaptive Learning Capabilities,” Appl. Opt. 26, 5039–5054 (1987).
    [CrossRef] [PubMed]
  21. G. Strang, Linear Algebra and Its Applications (Harcourt, Brace, Jovanovich, New York, 1980).
  22. R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  23. Y.-C. Ho, R. Kashyap, “A Class of Iterative Procedures for Linear Inequalities,” J. SIAM Control 4, 112–115 (1966).
    [CrossRef]
  24. J. Goodman et al., “Parallel Incoherent Optical Vector-Matrix Multiplier,” Technical Report L-723-1, BMD (1979).
  25. D. Casasent, J. Jackson, C. Neuman, “Frequency-Multiplexed and Pipelined Iterative Optical Systolic Array Processors,” Appl. Opt. 22, 115–124 (1983).
    [CrossRef] [PubMed]
  26. D. Casasent, J. Jackson, “Space and Frequency-Multiplexed Optical Linear Algebra Processor: Fabrication and Initial Tests,” Appl. Opt. 25, 2258–2263 (1986).
    [CrossRef] [PubMed]
  27. K. Wagner, D. Psaltis, “A Space Integrating Acousto-Optic Matrix-Matrix Multiplier,” Opt. Commun. 52, 173–177 (1984).
    [CrossRef]
  28. R. Winder, “Bounds on Threshold Gate Realizability,” IEEE Trans. Electron. Comput. EC-12, 561–564 (1963).
    [CrossRef]
  29. C. Giles, T. Maxwell, “Learning, Invariance, and Generalization in High-Order Neural Networks,” Appl. Opt. 26, 4972–4978 (1987).
    [CrossRef] [PubMed]
  30. D. Psaltis, C. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
    [CrossRef]
  31. Y. Kosugi, Y. Naito, “An Associative Memory as a Model for the Cerebellar Cortex,” IEEE Trans. Syst. Man Cybern. SMC-7, 95–98 (1977).
  32. H. Kasden, “Industrial Applications of Diffraction Pattern Sampling,” Opt. Eng. 18, 496–503 (1979).

1989

M. Hassoun, A. Youssef, “High Performance Recording Algorithm for Hopfield Model Associative Memories,” Opt. Eng. 28, 46–54 (1989).
[CrossRef]

M. H. Hassoun, “Adaptive Dynamic Heteroassociative Neural Memories for Pattern Classification,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 75–83 (1989).

A. M. Youssef, M. H. Hassoun, “Dynamic Autoassociative Neural Memory Performance vs. Capacity,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 52–59 (1989).

D. Casasent, B. Telfer, “Key and Recollection Vector Effects on Heteroassociative Memory Performance,” Appl. Opt. 28, 272–283 (1989).
[CrossRef] [PubMed]

1988

B. Kosko, “Bidirectional Associative Memories,” IEEE Trans. Syst. Man and Cybern. SMC-18, 49–60 (1988).
[CrossRef]

M. Hassoun, “Two-Level Neural Network for Deterministic Logic Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 258–264 (1988).

M. Hassoun, D. Clark, “An Adaptive Attentive Learning Algorithm for Single-Layer Neural Networks,” IEEE Int. Conf. Neural Networks I431–440 (1988).
[CrossRef]

M. Hassoun, “A High-Performance Associative Neural Memory (ANM) for Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 956 (1988).

B. Telfer, D. Casasent, “Ho-Kashyap Associative Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1005, 77–87 (1988).

D. Psaltis, C. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

1987

K. Murakami, T. Aibara, “An Improvement on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Syst. Man and Cybern. SMC-17, 699–707 (1987).
[CrossRef]

R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag. 4, 4–22 (1987).
[CrossRef]

G. S. Stiles, D.-L. Denq, “A Quantitative Comparison of the Performance of Three Discrete Distributed Associative Memory Models,” IEEE Trans. Comput. C-36, 257–263 (1987).
[CrossRef]

C. Giles, T. Maxwell, “Learning, Invariance, and Generalization in High-Order Neural Networks,” Appl. Opt. 26, 4972–4978 (1987).
[CrossRef] [PubMed]

A. D. Fisher, W. L. Lippincott, J. W. Lee, “Optical Implementations of Associative Networks with Versatile Adaptive Learning Capabilities,” Appl. Opt. 26, 5039–5054 (1987).
[CrossRef] [PubMed]

R. McEliece et al., “The Capacity of the Hopfield Associative Memory,” IEEE Trans. Info. Theory IT-33, 461–482 (1987).
[CrossRef]

1986

1985

G. Stiles, D.-L. Denq, “On the Effect of Noise on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Pat. Anal. and Mach. Int. PAMI-7, 358–360 (1985).
[CrossRef]

1984

K. Wagner, D. Psaltis, “A Space Integrating Acousto-Optic Matrix-Matrix Multiplier,” Opt. Commun. 52, 173–177 (1984).
[CrossRef]

1983

1982

J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

1979

H. Kasden, “Industrial Applications of Diffraction Pattern Sampling,” Opt. Eng. 18, 496–503 (1979).

1977

Y. Kosugi, Y. Naito, “An Associative Memory as a Model for the Cerebellar Cortex,” IEEE Trans. Syst. Man Cybern. SMC-7, 95–98 (1977).

1966

Y.-C. Ho, R. Kashyap, “A Class of Iterative Procedures for Linear Inequalities,” J. SIAM Control 4, 112–115 (1966).
[CrossRef]

1965

Y.-C. Ho, R. Kashyap, “An Algorithm for Linear Inequalities and Its Applications,” IEEE Trans. Electron. Comput. EC-14, 683–688 (1965).
[CrossRef]

T. Cover, “Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition,” IEEE Trans. Electron. Comput. EC-14, 326–334 (1965).
[CrossRef]

1963

R. Winder, “Bounds on Threshold Gate Realizability,” IEEE Trans. Electron. Comput. EC-12, 561–564 (1963).
[CrossRef]

Aibara, T.

K. Murakami, T. Aibara, “An Improvement on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Syst. Man and Cybern. SMC-17, 699–707 (1987).
[CrossRef]

Casasent, D.

Clark, D.

M. Hassoun, D. Clark, “An Adaptive Attentive Learning Algorithm for Single-Layer Neural Networks,” IEEE Int. Conf. Neural Networks I431–440 (1988).
[CrossRef]

Cover, T.

T. Cover, “Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition,” IEEE Trans. Electron. Comput. EC-14, 326–334 (1965).
[CrossRef]

Denq, D.-L.

G. S. Stiles, D.-L. Denq, “A Quantitative Comparison of the Performance of Three Discrete Distributed Associative Memory Models,” IEEE Trans. Comput. C-36, 257–263 (1987).
[CrossRef]

G. Stiles, D.-L. Denq, “On the Effect of Noise on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Pat. Anal. and Mach. Int. PAMI-7, 358–360 (1985).
[CrossRef]

Duda, R.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Fisher, A. D.

Giles, C.

Goodman, J.

J. Goodman et al., “Parallel Incoherent Optical Vector-Matrix Multiplier,” Technical Report L-723-1, BMD (1979).

Hart, P.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Hassoun, M.

M. Hassoun, A. Youssef, “High Performance Recording Algorithm for Hopfield Model Associative Memories,” Opt. Eng. 28, 46–54 (1989).
[CrossRef]

M. Hassoun, D. Clark, “An Adaptive Attentive Learning Algorithm for Single-Layer Neural Networks,” IEEE Int. Conf. Neural Networks I431–440 (1988).
[CrossRef]

M. Hassoun, “Two-Level Neural Network for Deterministic Logic Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 258–264 (1988).

M. Hassoun, “A High-Performance Associative Neural Memory (ANM) for Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 956 (1988).

Hassoun, M. H.

M. H. Hassoun, “Adaptive Dynamic Heteroassociative Neural Memories for Pattern Classification,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 75–83 (1989).

A. M. Youssef, M. H. Hassoun, “Dynamic Autoassociative Neural Memory Performance vs. Capacity,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 52–59 (1989).

Ho, Y.-C.

Y.-C. Ho, R. Kashyap, “A Class of Iterative Procedures for Linear Inequalities,” J. SIAM Control 4, 112–115 (1966).
[CrossRef]

Y.-C. Ho, R. Kashyap, “An Algorithm for Linear Inequalities and Its Applications,” IEEE Trans. Electron. Comput. EC-14, 683–688 (1965).
[CrossRef]

Hong, J.

D. Psaltis, C. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

Hopfield, J.

J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Jackson, J.

Kasden, H.

H. Kasden, “Industrial Applications of Diffraction Pattern Sampling,” Opt. Eng. 18, 496–503 (1979).

Kashyap, R.

Y.-C. Ho, R. Kashyap, “A Class of Iterative Procedures for Linear Inequalities,” J. SIAM Control 4, 112–115 (1966).
[CrossRef]

Y.-C. Ho, R. Kashyap, “An Algorithm for Linear Inequalities and Its Applications,” IEEE Trans. Electron. Comput. EC-14, 683–688 (1965).
[CrossRef]

Kohonen, T.

T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, Berlin, 1987).

Kosko, B.

B. Kosko, “Bidirectional Associative Memories,” IEEE Trans. Syst. Man and Cybern. SMC-18, 49–60 (1988).
[CrossRef]

Kosugi, Y.

Y. Kosugi, Y. Naito, “An Associative Memory as a Model for the Cerebellar Cortex,” IEEE Trans. Syst. Man Cybern. SMC-7, 95–98 (1977).

Lee, J. W.

Lippincott, W. L.

Lippmann, R. P.

R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag. 4, 4–22 (1987).
[CrossRef]

Maxwell, T.

McEliece, R.

R. McEliece et al., “The Capacity of the Hopfield Associative Memory,” IEEE Trans. Info. Theory IT-33, 461–482 (1987).
[CrossRef]

Montgomery, B. L.

Murakami, K.

K. Murakami, T. Aibara, “An Improvement on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Syst. Man and Cybern. SMC-17, 699–707 (1987).
[CrossRef]

Naito, Y.

Y. Kosugi, Y. Naito, “An Associative Memory as a Model for the Cerebellar Cortex,” IEEE Trans. Syst. Man Cybern. SMC-7, 95–98 (1977).

Neuman, C.

Park, C.

D. Psaltis, C. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

Psaltis, D.

D. Psaltis, C. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

K. Wagner, D. Psaltis, “A Space Integrating Acousto-Optic Matrix-Matrix Multiplier,” Opt. Commun. 52, 173–177 (1984).
[CrossRef]

Stiles, G.

G. Stiles, D.-L. Denq, “On the Effect of Noise on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Pat. Anal. and Mach. Int. PAMI-7, 358–360 (1985).
[CrossRef]

Stiles, G. S.

G. S. Stiles, D.-L. Denq, “A Quantitative Comparison of the Performance of Three Discrete Distributed Associative Memory Models,” IEEE Trans. Comput. C-36, 257–263 (1987).
[CrossRef]

Strang, G.

G. Strang, Linear Algebra and Its Applications (Harcourt, Brace, Jovanovich, New York, 1980).

Telfer, B.

D. Casasent, B. Telfer, “Key and Recollection Vector Effects on Heteroassociative Memory Performance,” Appl. Opt. 28, 272–283 (1989).
[CrossRef] [PubMed]

B. Telfer, D. Casasent, “Ho-Kashyap Associative Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1005, 77–87 (1988).

Vijaya Kumar, B. V. K.

Wagner, K.

K. Wagner, D. Psaltis, “A Space Integrating Acousto-Optic Matrix-Matrix Multiplier,” Opt. Commun. 52, 173–177 (1984).
[CrossRef]

Winder, R.

R. Winder, “Bounds on Threshold Gate Realizability,” IEEE Trans. Electron. Comput. EC-12, 561–564 (1963).
[CrossRef]

Youssef, A.

M. Hassoun, A. Youssef, “High Performance Recording Algorithm for Hopfield Model Associative Memories,” Opt. Eng. 28, 46–54 (1989).
[CrossRef]

Youssef, A. M.

A. M. Youssef, M. H. Hassoun, “Dynamic Autoassociative Neural Memory Performance vs. Capacity,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 52–59 (1989).

Appl. Opt.

IEEE ASSP Mag.

R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag. 4, 4–22 (1987).
[CrossRef]

IEEE Int. Conf. Neural Networks

M. Hassoun, D. Clark, “An Adaptive Attentive Learning Algorithm for Single-Layer Neural Networks,” IEEE Int. Conf. Neural Networks I431–440 (1988).
[CrossRef]

IEEE Trans. Comput.

G. S. Stiles, D.-L. Denq, “A Quantitative Comparison of the Performance of Three Discrete Distributed Associative Memory Models,” IEEE Trans. Comput. C-36, 257–263 (1987).
[CrossRef]

IEEE Trans. Electron. Comput.

Y.-C. Ho, R. Kashyap, “An Algorithm for Linear Inequalities and Its Applications,” IEEE Trans. Electron. Comput. EC-14, 683–688 (1965).
[CrossRef]

T. Cover, “Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition,” IEEE Trans. Electron. Comput. EC-14, 326–334 (1965).
[CrossRef]

R. Winder, “Bounds on Threshold Gate Realizability,” IEEE Trans. Electron. Comput. EC-12, 561–564 (1963).
[CrossRef]

IEEE Trans. Info. Theory

R. McEliece et al., “The Capacity of the Hopfield Associative Memory,” IEEE Trans. Info. Theory IT-33, 461–482 (1987).
[CrossRef]

IEEE Trans. Pat. Anal. and Mach. Int.

G. Stiles, D.-L. Denq, “On the Effect of Noise on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Pat. Anal. and Mach. Int. PAMI-7, 358–360 (1985).
[CrossRef]

IEEE Trans. Syst. Man and Cybern.

K. Murakami, T. Aibara, “An Improvement on the Moore-Penrose Generalized Inverse Associative Memory,” IEEE Trans. Syst. Man and Cybern. SMC-17, 699–707 (1987).
[CrossRef]

B. Kosko, “Bidirectional Associative Memories,” IEEE Trans. Syst. Man and Cybern. SMC-18, 49–60 (1988).
[CrossRef]

IEEE Trans. Syst. Man Cybern.

Y. Kosugi, Y. Naito, “An Associative Memory as a Model for the Cerebellar Cortex,” IEEE Trans. Syst. Man Cybern. SMC-7, 95–98 (1977).

J. SIAM Control

Y.-C. Ho, R. Kashyap, “A Class of Iterative Procedures for Linear Inequalities,” J. SIAM Control 4, 112–115 (1966).
[CrossRef]

Neural Networks

D. Psaltis, C. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

Opt. Commun.

K. Wagner, D. Psaltis, “A Space Integrating Acousto-Optic Matrix-Matrix Multiplier,” Opt. Commun. 52, 173–177 (1984).
[CrossRef]

Opt. Eng.

H. Kasden, “Industrial Applications of Diffraction Pattern Sampling,” Opt. Eng. 18, 496–503 (1979).

M. Hassoun, A. Youssef, “High Performance Recording Algorithm for Hopfield Model Associative Memories,” Opt. Eng. 28, 46–54 (1989).
[CrossRef]

Proc. Natl. Acad. Sci. USA

J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng.

B. Telfer, D. Casasent, “Ho-Kashyap Associative Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1005, 77–87 (1988).

M. Hassoun, “Two-Level Neural Network for Deterministic Logic Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 258–264 (1988).

M. H. Hassoun, “Adaptive Dynamic Heteroassociative Neural Memories for Pattern Classification,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 75–83 (1989).

A. M. Youssef, M. H. Hassoun, “Dynamic Autoassociative Neural Memory Performance vs. Capacity,” Proc. Soc. Photo-Opt. Instrum. Eng. 1053, 52–59 (1989).

M. Hassoun, “A High-Performance Associative Neural Memory (ANM) for Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 956 (1988).

Other

J. Goodman et al., “Parallel Incoherent Optical Vector-Matrix Multiplier,” Technical Report L-723-1, BMD (1979).

G. Strang, Linear Algebra and Its Applications (Harcourt, Brace, Jovanovich, New York, 1980).

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, Berlin, 1987).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Analog optical matrix-vector multiplier for associative processor recall.

Fig. 2
Fig. 2

Fraction of (a) all dichotomies of M N-dimensional vectors that are linearly separable, and (b) all groups of K dichotomies of M N-dimensional vectors that are linearly separable.

Fig. 3
Fig. 3

Recall accuracy vs M/N for exact and noisy key vector inputs using (a) pseudoinverse associative memory and (b) basic Ho-Kashyap associative memory.

Fig. 4
Fig. 4

Recall accuracy vs M/N for exact and noisy key vector inputs using (a) robust pseudoinverse associative memory and (b) robust Ho-Kashyap associative memory.

Fig. 5
Fig. 5

Fraction of output vectors that are completely correct vs M/N for exact and noisy key vector inputs using (a) robust pseudoinverse associative memory and (b) robust Ho-Kashyap associative memory.

Fig. 6
Fig. 6

Images used in the aircraft recognition problem: (a) Phantom and (b) DC-10 aircraft.

Fig. 7
Fig. 7

Wedge samples for the (a) Phantom and (b) DC-10 images in Fig. 6.

Tables (5)

Tables Icon

Table I Ho-Kashyap AP Algorithm

Tables Icon

Table II Average Rank of the Modified Key Matrix X ˜ for Different M/N, with σ = 0.1 for the Singular Value Threshold

Tables Icon

Table III Average Number of Iterations Required by Robust Ho-Kashyap Algorithm for Different M/N

Tables Icon

Table IV Misclassification Results for Pseudoinverse and Ho-Kashyap Memories with ±50° Training Set

Tables Icon

Table V Misclassification Results for Pseudoinverse and Ho-Kashyap Memories with ±80° Training Set

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

y k = sgn ( M x k ) ,
Y = sgn ( MX ) .
M = Y X + ,
μ i < M σ
M = Y X ˜ + ,
Y n + 1 = Y n + E n M n + 1 = M n + ρ ( S E n ) X T R ,
f ( M , N ) = { 1 M N 2 1 - M i = 0 N - 1 ( M - 1 i ) M > N .
g ( M , N , K ) = { 1 M N 2 K - M K [ i = 0 N - 1 ( M - 1 i ) ] K M > N .
g ( M , N , N ) = { 1 M / N < 2 0 M / N 2.
M = 2 N .
m n = Z ˜ + b n ,
e n = Z m n - b n ,
e n = ( 1 / 2 ) ( e n + e n ) ,
b n + 1 = b n + 2 ρ e n ,
If e n 0 go to 1.
e n = ( Z Z ˜ + - I ) b n .
e n + 1 = e n + 2 ρ ( Z Z ˜ + - I ) e n .
¼ e n + 1 2 = ¼ e n T e n + ρ e n T ( Z Z ˜ + - I ) e n + ρ 2 e n T ( Z Z ˜ + - I ) T ( Z Z ˜ + - I ) e n ,
¼ ( e n 2 - e n + 1 2 ) = ρ e n T e n - ρ e n T Z Z ˜ + e n - ρ 2 e n T ( Z Z ˜ + - I ) T ( Z Z ˜ + - I ) e n .
- ρ e n T Z Z ˜ + e n = - ρ b n T ( Z Z ˜ + - I ) Z Z ˜ + e n = ρ b n T ( Z Z ˜ + - Z Z ˜ + ) e n = 0 ,
- ρ 2 e n T [ ( Z Z ˜ + ) T ( Z Z ˜ + ) - ( Z Z ˜ + ) T - Z Z ˜ + + I ] e n T .
- ρ 2 e n T ( I - Z Z ˜ + ) e n .
¼ ( e n 2 - e n + 1 2 ) = ρ ( 1 - ρ ) e n 2 + ρ 2 e n T Z Z ˜ + e n .

Metrics