Periodicity and stability issues of a chaotic pattern recognition neural network

Calitoiu, Dragos; Oommen, B. John; Nussbaum, Doron

doi:10.1007/s10044-007-0060-3

Cited by 15 publications

(37 citation statements)

References 12 publications

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“…The AdNN's power as a PR system requires excessive computationsof the order of O(N 2 ). For the examples cited by Adachi et al and Calitoiu et al [1][2][3][4][5][6][7], which use 10 × 10 pixel arrays, this involves 10, 000 computations per time step. 2.…”

Section: Limitations Of the Current Schemesmentioning

confidence: 99%

Section: Limitations Of the Current Schemesmentioning

confidence: 99%

“…It is also appropriate that the PR limitations of the work of Calitoiu et al [7] are mentioned. Although the experimental results cited in [7] display a reduction in the transient phase (when compared to the AdNN), unfortunately, the M-AdNN does not achieve PR for untrained patterns. It turns out that although unreported in [7], the M-AdNN always reproduces the input patterns periodically independent of whether the input is a trained or an untrained pattern.…”

Section: Limitations Of the Current Schemesmentioning

confidence: 99%

“…This paper deals with the Adachi Neural Network AdNN [1][2][3][4][5], which possesses a spectrum of very interesting chaotic, AM and PR properties, as described in [6,7]. The fundamental "problem" associated with the AdNN and its variants is its quadratic computational requirement.…”

Section: Introductionmentioning

confidence: 99%

“…The Adachi Neural Network (AdNN) [1][2][3][4][5], is a fascinating Neural Network (NN) which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and Pattern Recognition (PR) characteristics. Variants of the AdNN [6,7] have also been used to obtain other PR phenomena, and even blurring. A significant problem associated with the AdNN and its variants, is that all of them require a quadratic number of computations.…”

mentioning

confidence: 99%

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An Enhanced Tree-Shaped Adachi-Like Chaotic Neural Network Requiring Linear-Time Computations

Qin¹,

Oommen²

2010

Chaotic Systems

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Abstract. The Adachi Neural Network (AdNN) [1][2][3][4][5], is a fascinating Neural Network (NN) which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and Pattern Recognition (PR) characteristics. Variants of the AdNN [6,7] have also been used to obtain other PR phenomena, and even blurring. A significant problem associated with the AdNN and its variants, is that all of them require a quadratic number of computations. This is essentially because all their NNs are completely connected graphs. In this paper we consider how the computations can be significantly reduced by merely using a linear number of computations. To do this, we extract from the original complete graph, one of its spanning trees. We then compute the weights for this spanning tree in such a manner that the modified tree-based NN has approximately the same input-output characteristics, and thus the new weights are themselves calculated using a gradient-based algorithm. By a detailed experimental analysis, we show that the new linear-time AdNN-like network possesses chaotic and PR properties for different settings. As far as we know, such a tree-based AdNN has not been reported, and the results given here are novel.

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Section: Limitations Of the Current Schemesmentioning

confidence: 99%

Section: Limitations Of the Current Schemesmentioning

confidence: 99%

Section: Limitations Of the Current Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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An Enhanced Tree-Shaped Adachi-Like Chaotic Neural Network Requiring Linear-Time Computations

Qin¹,

Oommen²

2010

Chaotic Systems

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Chaotic Pattern Recognition: The Spectrum of Properties of the Adachi Neural Network

Qin

Oommen

2008

Lecture Notes in Computer Science

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Abstract. Chaotic Pattern Recognition (PR) is a relatively new subfield of PR in which a system, which demonstrates chaotic behavior under normal conditions, resonates when it is presented with a pattern that it is trained with. The Adachi Neural Network (AdNN) is a classic neural structure which has been proven to demonstrate the phenomenon of Associative Memory (AM). In their pioneering paper [1,2], Adachi and his co-authors showed that the AdNN also emanates periodic outputs on being exposed to trained patterns. This was later utilized by Calitoiu et al [4,5] to design systems which possibly possessed PR capabilities. In this paper, we show that the previously reported properties of the AdNN do not adequately describe the dynamics of the system. Rather, although it possesses far more powerful PR and AM properties than was earlier known, it goes through a spectrum of characteristics as one of its crucial parameters, α, changes. As α increases, the AdNN which is first an AM become quasi-chaotic 1 . The system is then distinguished by two phases which really do not have clear boundaries of demarcation. In the former of these phases it is quasi-chaotic for some patterns and periodic for others. In the latter of these, it exhibits properties that have been unknown (or rather, unreported) till now, namely, a PR capability (which even recognizes masked or occluded patterns) in which the network resonates sympathetically for trained patterns while it is quasi-chaotic for untrained patterns. Finally, the system becomes completely periodic. All these results are, to the best of our knowledge, novel.

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Ideal Chaotic Pattern Recognition Is Achievable: The Ideal-M-AdNN - Its Design and Properties

Qin

Oommen

2013

Transactions on Computational Collective Intelligence XI

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Abstract. This paper deals with the relatively new field of designing a Chaotic Pattern Recognition (PR) system. The benchmark of such a system is the following: First of all, one must be able to train the system with a set of "training" patterns. Subsequently, as long as there is no testing pattern, the system must be chaotic. However, if the system is, thereafter, presented with an unknown testing pattern, the behavior must ideally be as follows. If the testing pattern is not one of the trained patterns, the system must continue to be chaotic. As opposed to this, if the testing pattern is truly one of the trained patterns (or a noisy version of a trained pattern), the system must switch to being periodic, with the specific trained pattern appearing periodically at the output. This is truly an ambitious goal, with the requirement of switching from chaos to periodicity being the most demanding. Some related work has been done in this regard. The Adachi Neural Network (AdNN) [1][2][3][4][5] has properties which are pseudo-chaotic, but it also possesses limited PR characteristics. As opposed to this, the Modified Adachi Neural Network (M-AdNN) proposed by Calitoiu et al [6], is a fascinating NN which has been shown to possess the required periodicity property desirable for PR applications. However, in this paper, we shall demonstrate that the PR properties claimed in [6] are not as powerful as originally reported. Indeed, the claim of the authors of [6] is true, in that it resonates periodically for trained input patterns. But unfortunately, the M-AdNN also resonates for unknown patterns and produces these unknown patterns at the output periodically. However, we describe how the parameters of the M-AdNN for its weights, steepness and external inputs, can be specified so as to yield a new NN, which we shall refer to as the Ideal-M-AdNN.

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Periodicity and stability issues of a chaotic pattern recognition neural network

Cited by 15 publications

References 12 publications

An Enhanced Tree-Shaped Adachi-Like Chaotic Neural Network Requiring Linear-Time Computations

An Enhanced Tree-Shaped Adachi-Like Chaotic Neural Network Requiring Linear-Time Computations

Chaotic Pattern Recognition: The Spectrum of Properties of the Adachi Neural Network

Ideal Chaotic Pattern Recognition Is Achievable: The Ideal-M-AdNN - Its Design and Properties

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