• 제목/요약/키워드: Least Squares Methods

검색결과 624건 처리시간 0.04초

Choice of Statistical Calibration Procedures When the Standard Measurement is Also Subject to Error

  • Lee, Seung-Hoon;Yum, Bong-Jin
    • Journal of the Korean Statistical Society
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    • 제14권2호
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    • pp.63-75
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    • 1985
  • This paper considers a statistical calibration problem in which the standard as wel as the nonstandard measurement is subject to error. Since the classicla approach cannot handle this situation properly, a functional relationship model with additional feature of prediction is proposed. For the analysis of the problem four different approaches-two estimation techniques (ordinary and grouping least squares) combined with two prediction methods (classical and inverse prediction)-are considered. By Monte Carlo simulation the perromance of each approach is assessed in term of the probability of concentration. The simulation results indicate that the ordinary least squares with inverse prediction is generally preferred in interpolation while the grouping least squares with classical prediction turns out to be better in extrapolation.

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부호유향그래프와 동적 부분최소자승법에 기반한 화학공정의 다중이상진단 (Multiple-Fault Diagnosis for Chemical Processes Based on Signed Digraph and Dynamic Partial Least Squares)

  • 이기백;신동일;윤인섭
    • 제어로봇시스템학회논문지
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    • 제9권2호
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    • pp.159-167
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    • 2003
  • This study suggests the hybrid fault diagnosis method of signed digraph (SDG) and partial least squares (PLS). SDG offers a simple and graphical representation for the causal relationships between process variables. The proposed method is based on SDG to utilize the advantage that the model building needs less information than other methods and can be performed automatically. PLS model is built on local cause-effect relationships of each variable in SDG. In addition to the current values of cause variables, the past values of cause and effect variables are inputted to PLS model to represent the Process armies. The measured value and predicted one by dynamic PLS are compared to diagnose the fault. The diagnosis example of CSTR shows the proposed method improves diagnosis resolution and facilitates diagnosis of masked multiple-fault.

음향 신호를 이용한 수중로봇의 위치추정 (Localization of an Underwater Robot Using Acoustic Signal)

  • 김태균;고낙용
    • 로봇학회논문지
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    • 제7권4호
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    • pp.231-242
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    • 2012
  • This paper proposes particle filter(PF) method using acoustic signal for localization of an underwater robot. The method uses time of arrival(TOA) or time difference of arrival(TDOA) of acoustic signals from beacons whose locations are known. An experiment in towing tank uses TOA information. Simulation uses TDOA information and it reveals dependency of the localization performance on the uncertainty of robot motion and senor data. Also, comparison of the PF method with the least squares method of spherical interpolation(SI) and spherical intersection(SX) is provided. Since PF uses TOA or TDOA which comes from measurement of external information as well as internal motion information, its estimation is more accurate and robust to the sensor and motion uncertainty than the least squares methods.

A Study on Support Vectors of Least Squares Support Vector Machine

  • Seok, Kyungha;Cho, Daehyun
    • Communications for Statistical Applications and Methods
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    • 제10권3호
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    • pp.873-878
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    • 2003
  • LS-SVM(Least-Squares Support Vector Machine) has been used as a promising method for regression as well as classification. Suykens et al.(2000) used only the magnitude of residuals to obtain SVs(Support Vectors). Suykens' method behaves well for homogeneous model. But in a heteroscedastic model, the method shows a poor behavior. The present paper proposes a new method to get SVs. The proposed method uses the variance of noise as well as the magnitude of residuals to obtain support vectors. Through the simulation study we justified excellence of our proposed method.

Combining Ridge Regression and Latent Variable Regression

  • Kim, Jong-Duk
    • Journal of the Korean Data and Information Science Society
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    • 제18권1호
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    • pp.51-61
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    • 2007
  • Ridge regression (RR), principal component regression (PCR) and partial least squares regression (PLS) are among popular regression methods for collinear data. While RR adds a small quantity called ridge constant to the diagonal of X'X to stabilize the matrix inversion and regression coefficients, PCR and PLS use latent variables derived from original variables to circumvent the collinearity problem. One problem of PCR and PLS is that they are very sensitive to overfitting. A new regression method is presented by combining RR and PCR and PLS, respectively, in a unified manner. It is intended to provide better predictive ability and improved stability for regression models. A real-world data from NIR spectroscopy is used to investigate the performance of the newly developed regression method.

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Geographically weighted least squares-support vector machine

  • Hwang, Changha;Shim, Jooyong
    • Journal of the Korean Data and Information Science Society
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    • 제28권1호
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    • pp.227-235
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    • 2017
  • When the spatial information of each location is given specifically as coordinates it is popular to use the geographically weighted regression to incorporate the spatial information by assuming that the regression parameters vary spatially across locations. In this paper, we relax the linearity assumption of geographically weighted regression and propose a geographically weighted least squares-support vector machine for estimating geographically weighted mean by using the basic concept of kernel machines. Generalized cross validation function is induced for the model selection. Numerical studies with real datasets have been conducted to compare the performance of proposed method with other methods for predicting geographically weighted mean.

WorldView-2 pan-sharpening by minimization of spectral distortion with least squares

  • Choi, Myung-Jin
    • 대한원격탐사학회지
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    • 제27권3호
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    • pp.353-357
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    • 2011
  • Although the intensity-hue-saturation (IHS) method for pan-sharpening has a spectral distortion problem, it is a popular method in the remote sensing community and has been used as a standard procedure in many commercial packages due to its fast computing and easy implementation. Recently, IHS-like approaches have tried to overcome the spectral distortion problem inherited from the IHS method itself and yielded a good result. In this paper, a similar IHS-like method with least squares for WorldView-2 pan-sharpening is presented. In particular, unlike the previous methods with three or four-band multispectral images for pan-sharpening, six bands of WorldView-2 multispectral image located within the range of panchromatic spectral radiance responses are considered in order to reduce the spectral distortion during the merging process. As a result, the new approach provides a satisfactory result, both visually and quantitatively. Furthermore, this shows great value in spectral fidelity of WorldView-2 eight-band multispectral imagery.

적응 쌍선형 격자필터 (II) - 최소자승 격자 알고리즘 (Adaptive Bilinear Lattice Filter(II)-Least Squares Lattice Algorithm)

  • Heung Ki Baik
    • 전자공학회논문지B
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    • 제29B권1호
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    • pp.34-42
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    • 1992
  • This paper presents two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models. The lattice filters perform a Gram-Schmidt orthogonalization of the input data and have very good numerical properties. Furthermore, the computational complexity of the algorithms is an order of magnitude snaller than previously algorithm is an order of magnitude smaller than previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to comprte the adaptive filter outputs. This method is conceptually very simple`however, it will result in biased system models in the presence of measurement noise. The second approach is an approximate least-squares output error solution. In this case, the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results of several experiments that demonstrate and compare the properties of the adaptive bilinear filters are also presented in this paper. These results indicate that the output error algorithm is less sensitive to output measurement noise than the squation error method.

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Multiclass Classification via Least Squares Support Vector Machine Regression

  • Shim, Joo-Yong;Bae, Jong-Sig;Hwang, Chang-Ha
    • Communications for Statistical Applications and Methods
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    • 제15권3호
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    • pp.441-450
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    • 2008
  • In this paper we propose a new method for solving multiclass problem with least squares support vector machine(LS-SVM) regression. This method implements one-against-all scheme which is as accurate as any other approach. We also propose cross validation(CV) method to select effectively the optimal values of hyper-parameters which affect the performance of the proposed multiclass method. Experimental results are then presented which indicate the performance of the proposed multiclass method.

Kernel Ridge Regression with Randomly Right Censored Data

  • Shim, Joo-Yong;Seok, Kyung-Ha
    • Communications for Statistical Applications and Methods
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    • 제15권2호
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    • pp.205-211
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    • 2008
  • This paper deals with the estimations of kernel ridge regression when the responses are subject to randomly right censoring. The iterative reweighted least squares(IRWLS) procedure is employed to treat censored observations. The hyperparameters of model which affect the performance of the proposed procedure are selected by a generalized cross validation(GCV) function. Experimental results are then presented which indicate the performance of the proposed procedure.