New Recording Algorithm For Hopfield Model Associative Memories

Hassoun, M.H.; Youssef, Abbas M.

doi:10.1117/12.944101

Cited by 14 publications

(15 citation statements)

References 11 publications

(15 reference statements)

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“…Conventional memory stores values in individual addresses, while associative memory stores contents and relationships in shared addresses [14], [15]. The latter form of memory is more suitable to our case since, although the human head has virtually infinite appearances, they share a common set of features.…”

Section: This Observation Suggests That Is Continuous With Respect Tomentioning

confidence: 99%

“…The desired candidate is the one with a smaller . Using the above results, we can now explicitly express by (13) with for otherwise (14) where . The case for mapping the two dipole positions and (see Fig.…”

Section: Appendix Mapping Points Between the Spherical And Spheroidalmentioning

confidence: 99%

“…2) can be similarly derived. The results are the same as shown in (13) and (14) except that , and are all multiplied by the modulus .…”

Section: Appendix Mapping Points Between the Spherical And Spheroidalmentioning

confidence: 99%

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The forward EEG solutions can be computed using artificial neural networks

Sun

Sclabassi

2000

IEEE Trans. Biomed. Eng.

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Abstract-Study of electroencenphalogarphy (EEG) is the one of the most utilized methods in both basic brain research and clinical diagnosis of neurological disorders. Recent technological advances in computer and electronic systems have allowed the EEG to be recorded from large electrode arrays. Modeling the brain waves using a head volume conductor model provides an effective method to localize functional generators within the brain. However, the forward solutions to this model, which represent theoretical potentials in response to current sources within the volume conductor, are difficult to compute because of time-consuming numerical procedures utilized in either the boundary element method (BEM) or the finite element method (FEM). This paper presents a novel computational approach using an artificial neural network (ANN) to map two vectors of forward solutions. These two vectors correspond to different head models but with respect to the same current source. The input vector to the ANN is based on the spherical head model, which can be computed efficiently but involves large errors. The output vector from the ANN is based on the spheroidal model, which is more precise, but difficult to compute directly using the traditional means. Our experiments indicate that this ANN approach provides a remarkable improvement over the BEM and FEM methods: 1) the mean-square error of computation was only approximately 0.3% compared to the exact solution; 2) the online computation was extremely efficient, requiring only 168 floating point operations per channel to compute the forward solution, and 10.2 K-bytes of storage to represent the entire ANN. Using this approach it is possible to perform real-time EEG modeling accurately on personal computers.

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Section: This Observation Suggests That Is Continuous With Respect Tomentioning

confidence: 99%

Section: Appendix Mapping Points Between the Spherical And Spheroidalmentioning

confidence: 99%

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The forward EEG solutions can be computed using artificial neural networks

Sun

Sclabassi

2000

IEEE Trans. Biomed. Eng.

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“…Thus the well known Rosenblatt's perceptron learning rule is the right one for learning the Hamming-stability. Different approaches to Cl-C3 were proposed by Hassoun and Youssef (1988), Cottrell (1988), Jiang et al (1990), and Kam et al (1990). Among them, only Cottrell (1988) correctly established the connection between three criteria Cl-C3 and the Hamming-stability.…”

Section: Introductionmentioning

confidence: 95%

Optimal learning for Hopfield associative memory

Zhuang

Huang

Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol.II. Conference B: Pattern Recognition Methodology

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I n the paper, we are t o design the optimal learning rule for the Hopfield associative memories ( H A M ) based o n three well recognized criteria, that is, all desired attractors must be made not only isolately stable but also asymptotically stable, and the spurious stable states should be the fewest possible. To construct a satisfactory H A M , those criteria are crucial. I n the paper, we first analyze the real cause of the unsatisfactory performance of the Hebb rule and m a n y other existing learning rules designed f o r HAM's and then show that three criteria actually amount to widely expanding the basin of attraction around each desired attractor. One effective way to widely expand basins of attraction of all desired attractors is t o appropriately dig their respective steep kernal basin of attraction. For this, we introduce a concept called by the Hamming-stability. Surprisingly, we find that the Hamming-stability for all desired attractors can be reduced to a moderately expansive linear separability condition at each neuron and thus the well known Rosenblatt's perceptron learning rule is the right one f o r learning the Hamming-stability. Extensive and systematic experiments were conducted, convincingly showing that the proposed perceptron Hamming-stability learning rule did take a good care of three optimal criteria.

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“…Thus the well known Rosenblatt's perceptron learning rule is the right one for learning the Hamming-stability. Different approaches to Cl-C3 were proposed by Hassoun and Youssef (1988), Cottrell Cottrell (1988) correctly established the connection between three criteria Cl-C3 and the Hammingstability. But Cottrell(l988) didn't realize the Hammingstability around each desired attractor was equivalent to a certain linear separability condition at each neuron; as known, the latter was a well-solved problem back to 1960's.…”

Section: Introductionmentioning

confidence: 99%

Design of Hopfield content-addressable memories

Zhuang

Huang

IEEE International Conference on Neural Networks

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In the paper, we design the optimal learning rule for the Hopfield content-addressable memories (CAM) based on three well recognized criteria. After analyzing the real cause of the unsatisfactory performance of the Hebb rule and many other existing learning rules, we show that three criteria actually amount to widely expanding the basin of attraction around each desired attractor. For this, we introduce a concept called by the Hamming-stability. Surprisingly, we And that the Hamming-stability for all desired attractors can be reduced to a moderately expansive linear separability condition at each neuron and thus the well known Rosenblatt's perceptron learning rule is the right one for learning the Hammingstability. Computer experiments were conducted, convincingly shpwing that the proposed perceptron Hamming-stability learning rule did take a good care of three optimal criteria.

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New Recording Algorithm For Hopfield Model Associative Memories

Cited by 14 publications

References 11 publications

The forward EEG solutions can be computed using artificial neural networks

The forward EEG solutions can be computed using artificial neural networks

Optimal learning for Hopfield associative memory

Design of Hopfield content-addressable memories

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