• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.295-309
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• 2010

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.853-868
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• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1193-1198
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• 2012

By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability of the Cohen-Grossberg neural network models. The condition contains and improves some of the previous results in the earlier references.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.10a
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• pp.422-426
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• 2007

CP(Counterpropagation) 알고리즘은 Kohonen의 경쟁 네트워크와 Grossberg의 아웃스타(outstar) 구조의 결합으로 이루어진 것으로 패턴 매칭, 패턴 분류, 통계적인 분석 및 데이터 압축 등 활용분야가 다양하고, 다른 신경망 모델에 비해 학습이 매우 빠르다는 장점이 있다. 하지만 CP 알고리즘은 충분한 경쟁층의 수가 설정되지 않아 경쟁층에서 학습이 불안정하고, 여권 코드와 같이 다양한 패턴으로 그성된 경우에는 패턴들을 정확히 분류할 수 없는 단점이 있다. 그리고 CP 알고리즘은 출력층에서 연결강도를 조정할 때, 학습률에 따라 학습 및 인식 성능이 좌우된다. 따라서 본 논문에서는 패턴 인식 성능을 개선하기 위해 다수의 경쟁층을 설정하고, 입력 벡터와 숭자 뉴런의 대표 벡터간의 차이와 숭자 뉴런의 빈도수를 학습률 조정에 반영하여 학습률을 동적으로 조정하여 경쟁층에서 안정적으로 학습되도록 하고, 출력층의 연결강도 조정시 이전 연결 강도 변화량을 반영하는 모멘텀(momentum)학습법을 적용한 개선된 CP 알고리즘을 제안한다. 학습 성능을 확인하기 위해서 실제 여권에서 추출된 개별 코드를 대상으로 실험한 결과, 본 논문에서 개선한 CP 알고리즘이 기존의 CP 알고리즘보다 패턴 분류의 정확성과 인식 성능이 개선된 것을 확인하였다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.9
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• pp.1682-1688
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• 2008

The Counterpropagation algorithm(CP) is a combination of Kohonen competition network as a hidden layer and the outstar structure of Grossberg as an output layer. CP has been used in many real applications for pattern matching, classification, data compression and statistical analysis since its learning speed is faster than other network models. However, due to the Kohonen layer's winner-takes-all strategy, it often causes instable learning and/or incorrect pattern classification when patterns are relatively diverse. Also, it is often criticized by the sensitivity of performance on the learning rate. In this paper, we propose an enhanced CP that has multiple Kohonen layers and dynamic controlling facility of learning rate using the frequency of winner neurons and the difference between input vector and the representative of winner neurons for stable learning and momentum learning for controlling weights of output links. A real world application experiment - pattern recognition from passport information - is designed for the performance evaluation of this enhanced CP and it shows that our proposed algorithm improves the conventional CP in learning and recognition performance.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.974-976
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• 1995

Segmentation of image data is an important problem in computer vision, remote sensing, and image analysis. Most objects in the real world have textured surfaces. Segmentation based on texture information is possible even if there are no apparent intensity edges between the different regions. There are many existing methods for texture segmentation and classification, based on different types of statistics that can be obtained from the gray-level images. In this paper, we use a neural network model --- ART-2 (Adaptive Resonance Theory) for textures in an image, proposed by Carpenter and Grossberg. In our experiments, we use Walsh matrix as feature value for textured image.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.11
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• pp.1464-1471
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• 1999

This paper introduces complex-valued competitive learning neural network for spatio-temporal pattern recognition. There have been quite a few neural networks for spatio-temporal pattern recognition. Among them, recurrent neural network, TDNN, and avalanche model are acknowledged as standard neural network paradigms for spatio-temporal pattern recognition. Recurrent neural network has complicated learning rules and does not guarantee convergence to global minima. TDNN requires too many neurons, and can not be regarded to deal with spatio-temporal pattern basically. Grossberg's avalanche model is not able to distinguish long patterns, and has to be indicated which layer is to be used in learning. In order to remedy drawbacks of the above networks, unsupervised competitive learning using complex umber is proposed. Suggested neural network also features simultaneous recognition, time-shift invariant recognition, stable categorizing, and learning rate modulation. The network is evaluated by computer simulation with randomly generated patterns.

• Asia pacific journal of information systems
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• v.11 no.4
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• pp.27-41
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• 2001

CRM is at the core of any customer-focused business strategy and includes the people, processes, and technology questions associated with marketing, sales, and service. In today's hyper-competitive world, organizations looking to implement successful CRM strategies need to focus on a common view of the customer using integrated information systems and contact center implementations that allow the customer to communicate via any desired communication channel. A CRM solution contains a number of sophisticated tools that enable to extract detailed information about customers. This information can be used to gain a better understanding of customers. From this we can determine trends, and so refine business toward customers' needs and target new products to particular customer groups. This paper presents an approach for forming the product-customer groups using neural networks for customer relationship management. The Carpenter-Grossberg's neural network, which has been used for manufacturing cell formation in group technology, is modified and applied for product-customer group formation. As a result of numerical experiments, it is also useful for more complex problems in which customers have different preferences for each product.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.42 no.2
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• pp.366-373
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• 2017

In this paper, we propose a variable weighted average (VWA) learning method in order to improve the performance of the fuzzy ART neural network that has been developed by Grossberg. In a conventional method, the Fast Commit Slow Recode (FCSR), when an input pattern falls in a category, the representative pattern of the category is updated at a fixed learning rate regardless of the degree of similarity of the input pattern. To resolve this issue, a variable learning method proposes reflecting the distance between the input pattern and the representative pattern to reduce the FCSR's category proliferation issue and improve the pattern recognition rate. However, these methods still suffer from the category proliferation issue and limited pattern recognition rate due to inevitable excessive learning created by use of fuzzy AND. The proposed method applies a weighted average learning scheme that reflects the distance between the input pattern and the representative pattern when updating the representative pattern of a category suppressing excessive learning for a representative pattern. Our simulation results show that the newly proposed variable weighted average learning method (VWA) mitigates the category proliferation problem of a fuzzy ART neural network by suppressing excessive learning of a representative pattern in a noisy environment and significantly improves the pattern recognition rates.