On a perceptron-type learning rule for higher order Hopfield neural networks including dilation and translation

Lenze, Burkhard

doi:10.1016/s0925-2312(01)00604-x

Cited by 1 publication

(5 citation statements)

References 28 publications

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“…The following theorem, which gives a sufficient condition for the termination of this learning rule after a finite number of steps, has also been proved in Ref. 13.…”

Section: Remarkmentioning

confidence: 93%

“…In this paper, we focus our attention on a corresponding generalization of the perceptron learning rule as introduced in Ref. 13. We are especially interested in the question, whether similar results can be obtained in the latter case.…”

Section: Remarkmentioning

confidence: 97%

“…13. In other words, these sections only aim to sketch the general background and to make the paper self-contained.…”

Section: Recall In Hopfield Neural Network With Dilation and Translamentioning

confidence: 99%

“…13, it has been shown that in case of its termination, the perceptron learning rule in Definition 3 will lead to a generalized higher order Hopfield neural network that performs perfectly on the given training set (1). The following theorem, which gives a sufficient condition for the termination of this learning rule after a finite number of steps, has also been proved in Ref.…”

Section: Remarkmentioning

confidence: 99%

“…(iv) As expected, the larger set Γ 2 (cf. (13) leads to better results and to larger intervals for proper λ-values than the smaller set Γ 1 (cf. (12)).…”

Section: Effects Of Dilation and Translation On Perceptron-type Learnmentioning

confidence: 99%

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Effects of Dilation and Translation on a Perceptron-Type Learning Rule for Higher Order Hopfield Neural Networks

Lenze

Raddatz²

2002

Int. J. Neur. Syst.

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In this paper, we will take a further look at a generalized perceptron-like learning rule which uses dilation and translation parameters in order to enhance the recall performance of higher order Hopfield neural networks without significantly increasing their complexity. We will practically study the influence of these parameters on the perceptron learning and recall process, using a generalized version of the Hebbian learning rule for initialization. Our analysis will be based on a pattern recognition problem with random patterns. We will see that in case of a highly correlated set of patterns, there can be gained some improvements concerning the learning and recall performance. On the other hand, we will show that the dilation and translation parameters have to be chosen carefully for a positive result.

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“…The following theorem, which gives a sufficient condition for the termination of this learning rule after a finite number of steps, has also been proved in Ref. 13.…”

Section: Remarkmentioning

confidence: 93%

Section: Remarkmentioning

confidence: 97%

“…13. In other words, these sections only aim to sketch the general background and to make the paper self-contained.…”

Section: Recall In Hopfield Neural Network With Dilation and Translamentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

“…(iv) As expected, the larger set Γ 2 (cf. (13) leads to better results and to larger intervals for proper λ-values than the smaller set Γ 1 (cf. (12)).…”

Section: Effects Of Dilation and Translation On Perceptron-type Learnmentioning

confidence: 99%

See 3 more Smart Citations

Effects of Dilation and Translation on a Perceptron-Type Learning Rule for Higher Order Hopfield Neural Networks

Lenze

Raddatz²

2002

Int. J. Neur. Syst.

Self Cite

View full text Add to dashboard Cite

show abstract

On a perceptron-type learning rule for higher order Hopfield neural networks including dilation and translation

Cited by 1 publication

References 28 publications

Effects of Dilation and Translation on a Perceptron-Type Learning Rule for Higher Order Hopfield Neural Networks

Effects of Dilation and Translation on a Perceptron-Type Learning Rule for Higher Order Hopfield Neural Networks

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