• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.970-976
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• 2007

In this study, Polynomial Network Pattern Classifier(PNC) based on Fuzzy Inference Mechanism is designed and its parameters such as learning rate, momentum coefficient and fuzzification coefficient are optimized by means of Particle Swarm Optimization. The proposed PNC employes a partition function created by Fuzzy C-means(FCM) clustering as an activation function in hidden layer and polynomials weights between hidden layer and output layer. Using polynomials weights can help to improve the characteristic of the linear classification of basic neural networks classifier. In the viewpoint of linguistic analysis, the proposed classifier is expressed as a collection of "If-then" fuzzy rules. Namely, architecture of networks is constructed by three functional modules that are condition part, conclusion part and inference part. The condition part relates to the partition function of input space using FCM clustering. In the conclusion part, a polynomial function caries out the presentation of a partitioned local space. Lastly, the output of networks is gotten by fuzzy inference in the inference part. The proposed PNC generates a nonlinear discernment function in the output space and has the better performance of pattern classification as a classifier, because of the characteristic of polynomial based fuzzy inference of PNC.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.981-989
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• 2010

In this study, we introduce a new architecture of fuzzy inference system. In the fuzzy inference system, we use Fuzzy C-Means clustering algorithm to form the premise part of the rules. The membership functions standing in the premise part of fuzzy rules do not assume any explicit functional forms, but for any input the resulting activation levels of such radial basis functions directly depend upon the distance between data points by means of the Fuzzy C-Means clustering. As the consequent part of fuzzy rules of the fuzzy inference system (being the local model representing input output relation in the corresponding sub-space), four types of polynomial are considered, namely constant, linear, quadratic and modified quadratic. This offers a significant level of design flexibility as each rule could come with a different type of the local model in its consequence. Either the Least Square Estimator (LSE) or the weighted Least Square Estimator (WLSE)-based learning is exploited to estimate the coefficients of the consequent polynomial of fuzzy rules. In fuzzy modeling, complexity and interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. The performance of the fuzzy inference system is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules(clusters) and the order of polynomial in the consequent part of the rules. Accordingly we can obtain preferred model structure through an adjustment of such parameters of the fuzzy inference system. Moreover the comparative experimental study between WLSE and LSE is analyzed according to the change of the number of clusters(rules) as well as polynomial type. The superiority of the proposed model is illustrated and also demonstrated with the use of Automobile Miles per Gallon(MPG), Boston housing called Machine Learning dataset, and Mackey-glass time series dataset.

• The Journal of Information Technology
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• v.5 no.4
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• pp.129-137
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• 2002

In this paper, a public key knapsack cryptosystem algorithm is based on the security to a difficulty of polynomial factorization in computer communication networks is proposed. For the proposed public key knapsack cryptosystem, a polynomial vector Q(x,y,z) is formed by transform of superincreasing vector P, a polynomial g(x,y,z) is selected. Next then, the two polynomials Q(x,y,z) and g(x,y,z) is decided on the public key. The enciphering first selects plaintext vector. Then the ciphertext R(x,y,z) is computed using the public key polynomials and a random integer $\alpha$. For the deciphering of ciphertext R(x,y,z), the plaintext is determined using the roots x, y, z of a polynomial g(x,y,z)=0 and the increasing property of secrety key vector. Therefore a public key knapsack cryptosystem is based on the security to a difficulty of factorization of a polynomial g(x,y,z)=0 with three variables. The propriety of the proposed public key cryptosystem algorithm is verified with the computer simulation.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.3
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• pp.18-31
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• 2002

In this study, we introduce a concept of advanced neurofuzzy polynomial networks(ANFPN), a hybrid modeling architecture combining neurofuzzy networks(NFN) and polynomial neural networks(PNN). These networks are highly nonlinear rule-based models. The development of the ANFPN dwells on the technologies of Computational Intelligence(Cl), namely fuzzy sets, neural networks and genetic algorithms. NFN contributes to the formation of the premise part of the rule-based structure of the ANFPN. The consequence part of the ANFPN is designed using PNN. At the premise part of the ANFPN, NFN uses both the simplified fuzzy inference and error back-propagation learning rule. The parameters of the membership functions, learning rates and momentum coefficients are adjusted with the use of genetic optimization. As the consequence structure of ANFPN, PNN is a flexible network architecture whose structure(topology) is developed through learning. In particular, the number of layers and nodes of the PNN are not fixed in advance but is generated in a dynamic way. In this study, we introduce two kinds of ANFPN architectures, namely the basic and the modified one. Here the basic and the modified architecture depend on the number of input variables and the order of polynomial in each layer of PNN structure. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability. The availability and feasibility of the ANFPN are discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed ANFPN can produce the model with higher accuracy and predictive ability than any other method presented previously.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.424-427
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• 2001

In this study, we introduce a concept of neurofuzzy polynomial networks (NFPN), a hybrid modeling architecture combining neurofuzzy networks (NFN) and polynomial neural networks(PNN). NFN contributes to the formation of the premise part of the rule-based structure of the NFPN. The consequence part of the NFPN is designed using PNN. The parameters of the membership functions, learning rates and momentum coefficients are adjusted with the use of genetic optimization. We introduce two kinds of NFPN architectures, namely the basic and the modified one. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability.

• Journal of Ocean Engineering and Technology
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• v.26 no.2
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• pp.39-47
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• 2012

The objective of this study was to develop a strength prediction model using a polynomial regression analysis based on the experimental results obtained from ninety samples. As the results of a correlation analysis between various mixing factors and unconfined compressive strength using SPSS (statistical package for the social sciences), the governing factors in the strength of lightweight soil were found to be the crumb rubber content, bottom ash content,and water-cement ratio. After selecting the governing factors affecting the strength through the correlation analysis, a strength prediction model, which consisted of the selected governing factors, was developed using the polynomial regression analysis. The strengths calculated from the proposed model were similar to those resulting from laboratory tests (R2=87.5%). Therefore, the proposed model can be used to predict the strength of lightweight mixtures with various mixing ratios without time-consuming experimental tests.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.57-66
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• 2024

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in ℙ^N, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme's degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.8 no.5
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• pp.345-353
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• 2015

There are many software reliability models that are based on the times of occurrences of errors in the debugging of software. It is shown that it is possible to do parameter inference for software reliability models based on finite failure model and non-homogeneous Poisson Processes (NHPP). For someone making a decision to market software, the conditional failure rate is an important variables. In this case, finite failure model are used in a wide variety of practical situations. Their use in characterization problems, detection of outlier, linear estimation, study of system reliability, life-testing, survival analysis, data compression and many other fields can be seen from the many study. Statistical process control (SPC) can monitor the forecasting of software failure and thereby contribute significantly to the improvement of software reliability. Control charts are widely used for software process control in the software industry. In this paper, proposed a control mechanism based on NHPP using mean value function of polynomial hazard function.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.6
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• pp.793-798
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• 2012

In this paper, we explored the new method for extracting feature from the electroencephalography (EEG) signal based on linear regression technique with the orthonormal polynomial bases. At first, EEG signals from electrodes around motor cortex were selected and were filtered in both spatial and temporal filter using band pass filter for alpha and beta rhymic band which considered related to the synchronization and desynchonization of firing neurons population during motor imagery task. Signal from epoch length 1s were fitted into linear regression with Legendre polynomials bases and extract the linear regression weight as final features. We compared our feature to the state of art feature, power band feature in binary classification using support vector machine (SVM) with 5-fold cross validations for comparing the classification accuracy. The result showed that our proposed method improved the classification accuracy 5.44% in average of all subject over power band features in individual subject study and 84.5% of classification accuracy with forward feature selection improvement.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.3
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• pp.87-94
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• 2002

This study presents an MSB(Most Significant Bit) Int multiplier using cellular automata, along with a new MSB first multiplication algorithm over GF($2^m$). The proposed architecture has the advantage of high regularity and a reduced latency based on combining the characteristics of a PBCA(Periodic Boundary Cellular Automata) and with the property of irreducible AOP(All One Polynomial). The proposed multiplier can be used in the effectual hardware design of exponentiation architecture for public-key cryptosystem.