• 전기학회논문지
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• 제66권12호
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• pp.1772-1781
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• 2017

In this study, the design methodology for alleviating the overfitting problem of Polynomial Neural Networks(PNN) is realized with the aid of two kinds techniques such as L2 regularization and Sum of Squared Coefficients (SSC). The PNN is widely used as a kind of mathematical modeling methods such as the identification of linear system by input/output data and the regression analysis modeling method for prediction problem. PNN is an algorithm that obtains preferred network structure by generating consecutive layers as well as nodes by using a multivariate polynomial subexpression. It has much fewer nodes and more flexible adaptability than existing neural network algorithms. However, such algorithms lead to overfitting problems due to noise sensitivity as well as excessive trainning while generation of successive network layers. To alleviate such overfitting problem and also effectively design its ensuing deep network structure, two techniques are introduced. That is we use the two techniques of both SSC(Sum of Squared Coefficients) and $L_2$ regularization for consecutive generation of each layer's nodes as well as each layer in order to construct the deep PNN structure. The technique of $L_2$ regularization is used for the minimum coefficient estimation by adding penalty term to cost function. $L_2$ regularization is a kind of representative methods of reducing the influence of noise by flattening the solution space and also lessening coefficient size. The technique for the SSC is implemented for the minimization of Sum of Squared Coefficients of polynomial instead of using the square of errors. In the sequel, the overfitting problem of the deep PNN structure is stabilized by the proposed method. This study leads to the possibility of deep network structure design as well as big data processing and also the superiority of the network performance through experiments is shown.

• 한국정밀공학회지
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• 제23권4호
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• pp.168-175
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• 2006

This paper presents surface matching algorithms that can be used to reconstruct the surface topography of an object scanned by an AFM. The essence of the algorithms is to match up neighboring images intentionally overlapped with others. Two performance indexes using the correlation coefficient and the sum of the squared differences are introduced. To compensate for the inaccuracy of the coarse stage implemented to AFM, all the six axes including the rotational degrees of freedom are successively matched so as to maximize the coefficients defined. The results show that the proposed algorithms are useful for measurement range extension of AFM. The results also show that a combined use of the two indexes is beneficial for practical cases.

• Journal of the Korean Statistical Society
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• 제27권1호
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• pp.1-10
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• 1998

In the problem of estimating a vector of unknown regression coefficients under the sum of squared error losses in a hierarchical linear model, we propose the hierarchical Bayes estimator of a vector of unknown regression coefficients in a hierarchical linear model, and then prove the admissibility of this estimator using Blyth's (196\51) method.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권2호
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• pp.103-115
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• 2004

A computational algorithm is developed for fitting given data in the plane or in 3-space by implicitly defined quadrics. Implicity implies that the type of the quadric is part of the model and need not be known in advance. Starting with some estimate for the coefficients of the quadric the method will alternatively determine the shortest distances from the given points onto the quadric and adapt the coefficients such as to reduce the sum of those squared distances. Numerical examples are given.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• 응용통계연구
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• 제30권6호
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• pp.889-899
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• 2017

독립성분분석은 혼합된 신호에서 원신호들을 분리하기 위해서 사용되는 다변량 분석방법으로서, 블라인드 음원 분리 중 가장 널리 사용되는 방법이다. 독립성분분석은 주성분분석이나 요인분석과 같이 선형변환을 사용하지만, 원신호들의 통계적 독립과 비정규성 가정을 필요로 한다는 점에서 다르다. 설명되는 분산의 누적비율이 클수록 더 중요한 성분을 의미하게 되는 주성분분석과 달리, 독립성분분석에서는 독립성분들의 중요순서를 결정하는데 적절한 유일한 기준이 정해지지 않는다. 군집분석이나 차원축소된 그래프 작성 등과 같은 후속 연구를 진행하기 위해서는 일부의 주요 독립성분을 사용하게 되므로, 성분의 순서를 정하는 것은 의미가 있다. 본 연구에서는 성분의 순서를 결정하기 위한 몇 가지 기준의 성능을 비교하였다. 첨도와 첨도의 절댓값, 음의 엔트로피, 콜모고로프-스미르노프 통계량, 계수제곱합을 이용한 방법이 고려되었다. 이들은 알려진 그룹을 분류하는 능력을 기준으로 평가되었다. 두 가지 형태의 자료를 이용한 분석결과를 제시하였다.

• Communications for Statistical Applications and Methods
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• 제22권5호
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• pp.495-506
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• 2015

Volatility is a variation measure in finance for returns of a financial instrument over time. GARCH models have been a popular tool to analyze volatility of financial time series data since Bollerslev (1986) and it is said that volatility is highly persistent when the sum of the estimated coefficients of the squared lagged returns and the lagged conditional variance terms in GARCH models is close to 1. Regarding persistence, numerous methods have been proposed to test if such persistency is due to volatility shifts in the market or natural fluctuation explained by stationary long-range dependence (LRD). Recently, Lee et al. (2015) proposed a residual-based cumulative sum (CUSUM) test statistic to test volatility shifts in GARCH models against LRD. We propose a bootstrap-based approach for the residual-based test and compare the sizes and powers of our bootstrap-based CUSUM test with the one in Lee et al. (2015) through simulation studies.

• 대한치과기공학회지
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• 제21권1호
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• pp.67-75
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• 1999

The purpose of this study is to evaluate the friction coefficients between abutment materials and clasp materials, and to an estimation formula for retention force. The coefficients of friction between three clasp materials and four abutment materials were measured under various conditions, polished and sandblasted and wet and dry. The measurement was repeated for each combination up to a total measurement of 1200 times. Estimation formula for retention force is measured as sum of two terms, which the one time is proportional to the product of friction coefficient ${\mu}$ and undercut u and the other term is proportional to u-squared. Two proportional coefficient were obtained by least square method. The results are as follows: 1. Friction coefficients were ranged from 0.08 to 0.53 under various conditions. 2. Friction coefficients of non-metal abutment materials are greater in wet conditions than dry conditions. 3. Friction coefficients of sandblasted clasp against abutment are greater than that of polished clasp. 4. Clasp retention force can be estimated with the model as F=$F_d(3.0{\mu}u+1.5u^2/h)$ with minor error.

• 대한전자공학회논문지
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• 제26권3호
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• pp.160-166
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• 1989

공간영역 예측기의 계수를 계산하기 위한 적응 알고리듬이 제안되었다. 제안된 방법은 LMS 알고리듬을 사용하여 TDL(tapped-delay-line)과 ESC(escalator) 구조를 갖는 공간영역 예측기의 계수를 계산한다. 기종존의 일반적인 예측기와 다른점은 순방향과 역방향 예측 오차의 평균 자승값의 합을 최소화하며 예측기의 계수를 계산함으로 향상된 선형예측 공간 스펙트럼을 얻을 수 있다. 제안된 방법을 선형으로 배열된 센서에 의하여 얻어진 협대역신호의 입사각 추정문제에 적용시켜 기존의 적응예측 알고리듬과 컴퓨터 시뮬레이션을 통하여 성능을 비교하였다.

• Communications for Statistical Applications and Methods
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• 제27권5호
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.