A binary pattern classification using potts model

Kryzhanovsky, Boris; Kryzhanovsky, Vladimir

doi:10.3103/s1060992x08040115

Cited by 5 publications

(8 citation statements)

References 13 publications

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“…The following conclusions can be drawn from expressions ( 12)- (21). The surface transformation is most likely to make minima deeper and, therefore, the probability of finding them higher.…”

Section: Conclusion and Their Verificationmentioning

confidence: 87%

“…From (21) it follows that the smallest shifts are expected for the deepest minima. For example, in case N = 100, k = 2 the experiment shows that for different matrices the shift of global minima varies from 0 to 6 bits and its average value is d 2 ∼ 3.5 bits, which corresponds well to (21). Figure 5 shows the relation between the shift and transformation parameter k. It is seen that the smallest shift occurs when k = 3.…”

Section: Conclusion and Their Verificationmentioning

confidence: 97%

“…The shift of the minimum caused by the surface transformation is relatively small. From (21) it follows that the smallest shifts are expected for the deepest minima. For example, in case N = 100, k = 2 the experiment shows that for different matrices the shift of global minima varies from 0 to 6 bits and its average value is d 2 ∼ 3.5 bits, which corresponds well to (21) We see that all the theoretical conclusions agree with the experimental results, providing good grounds for the use of the DDK algorithm.…”

Section: Conclusion and Their Verificationmentioning

confidence: 97%

“…From (21) it follows that the smallest shifts are expected for the deepest minima. For example, in case N = 100, k = 2 the experiment shows that for different matrices the shift of global minima varies from 0 to 6 bits and its average value is d 2 ∼ 3.5 bits, which corresponds well to (21) We see that all the theoretical conclusions agree with the experimental results, providing good grounds for the use of the DDK algorithm. In the following sections we will give information on how to apply the algorithm for different types of matrices.…”

Section: Conclusion and Their Verificationmentioning

confidence: 97%

“…Let us follow [21] and continue expanding (3). Let the configuration S 1 be an extreme of a quadratic functional built around T 1 .…”

Section: Basic Relationsmentioning

confidence: 99%

See 4 more Smart Citations

Increasing the attraction area of the global minimum in the binary optimization problem

Karandashev

Kryzhanovsky

2012

J Glob Optim

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The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power the matrix it is based on. We demonstrate that this brings about changes of the energy surface: deep minima displace slightly in the space and become still deeper and their attraction areas grow significantly. Experiments show that this approach results in a considerable displacement of the spectrum of the sought-for minima to the area of greater depth, and the probability of finding the global minimum increases abruptly (by a factor of 10 3 in the case of the 10 × 10 Edwards-Anderson spin glass).

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Section: Conclusion and Their Verificationmentioning

confidence: 87%

Section: Conclusion and Their Verificationmentioning

confidence: 97%

Section: Conclusion and Their Verificationmentioning

confidence: 97%

“…From (21) it follows that the smallest shifts are expected for the deepest minima. For example, in case N = 100, k = 2 the experiment shows that for different matrices the shift of global minima varies from 0 to 6 bits and its average value is d 2 ∼ 3.5 bits, which corresponds well to (21) We see that all the theoretical conclusions agree with the experimental results, providing good grounds for the use of the DDK algorithm. In the following sections we will give information on how to apply the algorithm for different types of matrices.…”

Section: Conclusion and Their Verificationmentioning

confidence: 97%

“…Let us follow [21] and continue expanding (3). Let the configuration S 1 be an extreme of a quadratic functional built around T 1 .…”

Section: Basic Relationsmentioning

confidence: 99%

See 3 more Smart Citations

Increasing the attraction area of the global minimum in the binary optimization problem

Karandashev

Kryzhanovsky

2012

J Glob Optim

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Estimates of storage capacity in theq-state Potts-glass neural network

Xiong¹,

Zhao²

2010

J. Phys. A: Math. Theor.

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We study the absolute storage capacity of the q-state Potts-glass neural network which determines how many memory patterns can be really retrieved. By using theoretical analysis combined with a characteristic of the distribution of local field, a general formula for estimating the storage capacity is proposed, and dynamical simulations for q = 2 and q = 3 are presented for comparison. Compared with the previous theory, it is found that in the case of q = 2 our estimate is in good agreement with the simulation result, while for the case of q = 3 it provides a lower boundary of the storage capacity instead. The result may provide useful information for possible applications of neural networks.

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A trade-off formula in designing asymmetric neural networks

Xiong¹,

Zhao²

2013

J. Phys. A: Math. Theor.

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We show that for asymmetric neural networks the symmetric degree η of the synaptic coupling can be related to the two main network parameters, the storage capacity α and another designing parameter κ by the formula η = ακ 2 . Such a relation has been well verified by the simulations of our neural network designing. The formula suggests that we cannot improve the network performances by tuning the parameters α and κ simultaneously. The result may provide useful information for optimizing the designing of asymmetric neural networks.

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A binary pattern classification using potts model

Cited by 5 publications

References 13 publications

Increasing the attraction area of the global minimum in the binary optimization problem

Increasing the attraction area of the global minimum in the binary optimization problem

Estimates of storage capacity in theq-state Potts-glass neural network

A trade-off formula in designing asymmetric neural networks

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