• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.66 no.12
• /
• pp.1772-1781
• /
• 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.

• Journal of the Korean Society for Precision Engineering
• /
• v.23 no.4 s.181
• /
• pp.168-175
• /
• 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
• /
• v.27 no.1
• /
• pp.1-10
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.11 no.2
• /
• pp.103-115
• /
• 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
• /
• v.18 no.6
• /
• pp.733-739
• /
• 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.

• The Korean Journal of Applied Statistics
• /
• v.30 no.6
• /
• pp.889-899
• /
• 2017

Independent component analysis is a multivariate approach to separate mixed signals into original signals. It is the most widely used method of blind source separation technique. ICA uses linear transformations such as principal component analysis and factor analysis, but differs in that ICA requires statistical independence and non-Gaussian assumptions of original signals. PCA have a natural ordering based on cumulative proportion of explained variance; howerver, ICA algorithms cannot identify the unique optimal ordering of the components. It is meaningful to set order because major components can be used for further analysis such as clustering and low-dimensional graphs. In this paper, we compare the performance of several criteria to determine the order of the components. Kurtosis, absolute value of kurtosis, negentropy, Kolmogorov-Smirnov statistic and sum of squared coefficients are considered. The criteria are evaluated by their ability to classify known groups. Two types of data are analyzed for illustration.

• Communications for Statistical Applications and Methods
• /
• v.22 no.5
• /
• pp.495-506
• /
• 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.

• Journal of Technologic Dentistry
• /
• v.21 no.1
• /
• pp.67-75
• /
• 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.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.26 no.3
• /
• pp.160-166
• /
• 1989

We propose adaptive algorithms computing the coefficients of spatial domain predictors. The method uses the LMS approach to compute the coefficients of the predictors realized by using the TDL(tapped-delay-line) and the ESC (escalator) structures. The predictors to be presented differ from the conventional ones in the sense that the relevant weights are updated such that the sum of the mean squared values of the forward and the backward prediction errors is minimized. Using the coefficients of such spatial domain predictors yields improved linear predictive spatial spectrums. The algorithms are applied to the problems of estimating incident angles of multiple narrow-band signals received by a linear array of sensors. Simulation results demonstrating the performances of the proposed methods are presented.

• Communications for Statistical Applications and Methods
• /
• v.27 no.5
• /
• pp.523-533
• /
• 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.