• Communications for Statistical Applications and Methods
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• 제4권1호
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• Journal of Electrical Engineering and Technology
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• 제13권4호
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• pp.1724-1731
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• 2018

The conventional polynomial neural network (PNN) is a classical flexible neural structure and self-organizing network, however it is not free from the limitation of overfitting problem. In this study, we propose a space search-optimized polynomial neural network (ssPNN) structure to alleviate this problem. Ranking selection is realized by means of ranking selection-based performance index (RS_PI) which is combined with conventional performance index (PI) and coefficients based performance index (CPI) (viz. the sum of squared coefficient). Unlike the conventional PNN, L2-norm regularization method for estimating the polynomial coefficients is also used when designing the ssPNN. Furthermore, space search optimization (SSO) is exploited here to optimize the parameters of ssPNN (viz. the number of input variables, which variables will be selected as input variables, and the type of polynomial). Experimental results show that the proposed ranking selection-based polynomial neural network gives rise to better performance in comparison with the neuron fuzzy models reported in the literatures.

• 대한수학회보
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• 제53권1호
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• pp.1-20
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• 2016

The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial selection (being used in factoring RSA challenge numbers) is to select a nonlinear polynomial for algebraic sieving and a linear polynomial for rational sieving. There is another method called a nonlinear method which selects two polynomials of the same degree greater than one. In this paper, we generalize Montgomery's method [12] using geometric progression (GP) (mod N) to construct a pair of nonlinear polynomials. We also introduce GP of length d + k with $1{\leq}k{\leq}d-1$ and show that we can construct polynomials of degree d having common root (mod N), where the number of such polynomials and the size of the coefficients can be precisely determined.

• 정보보호학회논문지
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• 제26권3호
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• pp.631-643
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• 2016

현재까지 알려진 가장 효율적인 인수분해 방법은 General Number Field Sieve (GNFS)를 이용하는 방법이다. CADO-NFS는 GNFS를 기반으로 구현된 공개된 소프트웨어로 RSA-704의 인수분해에 사용된 도구이다. CADO-NFS에서 다항식 선택은 크게 다항식을 생성하는 과정과 이를 최적화하는 과정으로 나누어져 있다. 그러나 CADO-NFS에서 다항식의 최적화 과정은 전체 다항식 선택 소요 시간 중 약 90%를 차지할 정도로 큰 부하를 주고 있다. 본 논문에서는 사전 연산 테이블을 이용하여 다항식 최적화 과정의 부하를 줄이는 방안을 제안한다. 제안하는 방법은 기존 CADO-NFS의 다항식과 같은 다항식을 선택하지만, 다항식 선택에 걸리는 시간은 약 40% 감소한다.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권4호
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• pp.327-332
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• 2005

We investigatea new fuzzy-neural networks-Hybrid Fuzzy set based polynomial Neural Networks (HFSPNN). These networks consist of genetically optimized multi-layer with two kinds of heterogeneous neurons thatare fuzzy set based polynomial neurons (FSPNs) and polynomial neurons (PNs). We have developed a comprehensive design methodology to determine the optimal structure of networks dynamically. The augmented genetically optimized HFSPNN (namely gHFSPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of gHFSPNN leads to the selection leads to the selection of preferred nodes (FSPNs or PNs) available within the HFSPNN. In the sequel, the structural optimization is realized via GAs, whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFSPNN is quantified through experimentation where we use a number of modeling benchmarks synthetic and experimental data already experimented with in fuzzy or neurofuzzy modeling.

• 정보보호학회논문지
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• 제26권5호
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• pp.1121-1130
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• 2016

RSA 암호 시스템은 가장 널리 사용되는 공개키 암호 알고리즘 중 하나이며, RSA 암호 시스템의 안전성은 큰 수의 인수분해의 어려움에 기반을 둔다. 따라서 RSA 암호 시스템의 합성수 n을 인수분해하려는 시도는 계속 진행 중에 있다. General Number Field Sieve는 현재까지 알려진 가장 빠른 인수분해 방법이고, RSA-704를 인수분해 하는데 사용된 소프트웨어인 CADO-NFS도 GNFS를 기반으로 설계되어 있다. 그러나 CADO-NFS는 다항식 선택 과정에서 입력된 변수로부터 항상 최적의 다항식을 선택하지 못하는 문제점이 있다. 본 논문에서는 CADO-NFS의 다항식 선택 단계를 분석하고 중국인의 나머지 정리와 유클리드 거리를 사용하여 다항식을 선택하는 방법을 제안한다. 제안된 방법을 이용하면 기존의 방법보다 좋은 다항식이 매번 선택되며, RSA-1024를 인수분해 하는데 적용할 수 있을 것으로 기대한다.

• ETRI Journal
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• 제27권6호
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• pp.747-758
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• 2005

The problem of selection among competing models has been a fundamental issue in statistical data analysis. Good fits to data can be misleading since they can result from properties of the model that have nothing to do with it being a close approximation to the source distribution of interest (for example, overfitting). In this study we focus on the preference among models from a family of polynomial regressors. Three decades of research has spawned a number of plausible techniques for the selection of models, namely, Akaike's Finite Prediction Error (FPE) and Information Criterion (AIC), Schwartz's criterion (SCH), Generalized Cross Validation (GCV), Wallace's Minimum Message Length (MML), Minimum Description Length (MDL), and Vapnik's Structural Risk Minimization (SRM). The fundamental similarity between all these principles is their attempt to define an appropriate balance between the complexity of models and their ability to explain the data. This paper presents an empirical study of the above principles in the context of model selection, where the models under consideration are univariate polynomials. The paper includes a detailed empirical evaluation of the model selection methods on six target functions, with varying sample sizes and added Gaussian noise. The results from the study appear to provide strong evidence in support of the MML- and SRM- based methods over the other standard approaches (FPE, AIC, SCH and GCV).

• Asian-Australasian Journal of Animal Sciences
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• 제24권1호
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• pp.17-27
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• 2011

A selection experiment for reduced residual feed intake (RFI) in Yorkshire pigs consisted of a line selected for lower RFI (LRFI) and a random control line (CTRL). Longitudinal measurements of daily feed intake (DFI) and body weight (BW) from generation 5 of this experiment were used. The objectives of this study were to evaluate the use of random regression (RR) and nonlinear mixed models to predict DFI and BW for individual pigs, accounting for the substantial missing information that characterizes these data, and to evaluate the effect of selection for RFI on BW and DFI curves. Forty RR models with different-order polynomials of age as fixed and random effects, and with homogeneous or heterogeneous residual variance by month of age, were fitted for both DFI and BW. Based on predicted residual sum of squares (PRESS) and residual diagnostics, the quadratic polynomial RR model was identified to be best, but with heterogeneous residual variance for DFI and homogeneous residual variance for BW. Compared to the simple quadratic and linear regression models for individual pigs, these RR models decreased PRESS by 1% and 2% for DFI and by 42% and 36% for BW on boars and gilts, respectively. Given the same number of random effects as the polynomial RR models, i.e., two for BW and one for DFI, the non-linear Gompertz model predicted better than the polynomial RR models but not as good as higher order polynomial RR models. After five generations of selection for reduced RFI, the LRFI line had a lower population curve for DFI and BW than the CTRL line, especially towards the end of the growth period.

• Journal of the Korean Statistical Society
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• 제9권1호
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• pp.61-77
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• 1980

In response surface experiments, a polynomial model is often used to fit the response surface by the method of least squares. However, if the vectors of predictor variables are multicollinear, least squares estimates of the regression parameters have a high probability of being unsatisfactory. Hoerland Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using "ridge" estimates in place of the least squares estimates. Ridge regrssion theory in literature has been mainly concerned with selection of k for the first order polynomial regression model and the precision of $\hat{\beta}(k)$, the ridge estimator of regression parameters. The problem considered in this paper is that of selecting k of ridge regression for a given polynomial regression model with an arbitrary order. A criterion is proposed for selection of k in the context of integrated mean square error of fitted responses, and illustrated with an example. Also, a type of admissibility condition is established and proved for the propose criterion.criterion.

• 디지털산업정보학회논문지
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• 제7권4호
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• pp.7-14
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• 2011

Infinite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rate per fault (hazard function). This infinite non-homogeneous Poisson process is model which reflects the possibility of introducing new faults when correcting or modifying the software. In this paper, polynomial hazard function have been proposed, which can efficiency application for software reliability. Algorithm for estimating the parameters used to maximum likelihood estimator and bisection method. Model selection based on mean square error and the coefficient of determination for the sake of efficient model were employed. In numerical example, log power time model of the existing model in this area and the polynomial hazard function model were compared using failure interval time. Because polynomial hazard function model is more efficient in terms of reliability, polynomial hazard function model as an alternative to the existing model also were able to confirm that can use in this area.