• Title/Summary/Keyword: The Least Squares Method

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LS-SVM for large data sets

  • Park, Hongrak;Hwang, Hyungtae;Kim, Byungju
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.2
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    • pp.549-557
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    • 2016
  • In this paper we propose multiclassification method for large data sets by ensembling least squares support vector machines (LS-SVM) with principal components instead of raw input vector. We use the revised one-vs-all method for multiclassification, which is one of voting scheme based on combining several binary classifications. The revised one-vs-all method is performed by using the hat matrix of LS-SVM ensemble, which is obtained by ensembling LS-SVMs trained using each random sample from the whole large training data. The leave-one-out cross validation (CV) function is used for the optimal values of hyper-parameters which affect the performance of multiclass LS-SVM ensemble. We present the generalized cross validation function to reduce computational burden of leave-one-out CV functions. Experimental results from real data sets are then obtained to illustrate the performance of the proposed multiclass LS-SVM ensemble.

Multiclass LS-SVM ensemble for large data

  • Hwang, Hyungtae
    • Journal of the Korean Data and Information Science Society
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    • v.26 no.6
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    • pp.1557-1563
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    • 2015
  • Multiclass classification is typically performed using the voting scheme method based on combining binary classifications. In this paper we propose multiclass classification method for large data, which can be regarded as the revised one-vs-all method. The multiclass classification is performed by using the hat matrix of least squares support vector machine (LS-SVM) ensemble, which is obtained by aggregating individual LS-SVM trained on each subset of whole large data. The cross validation function is defined to select the optimal values of hyperparameters which affect the performance of multiclass LS-SVM proposed. We obtain the generalized cross validation function to reduce computational burden of cross validation function. Experimental results are then presented which indicate the performance of the proposed method.

The Analysis of Townsend Enuation Based on Linealized Least Squares Method (최소자승법을 적응한 Townsend법의 해석)

  • 백용현;하성철
    • 전기의세계
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    • v.27 no.2
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    • pp.69-74
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    • 1978
  • There have been a number of experimental or theorethical investigations of transport coefficient for electrons in the field of gas. In this paper the authors present the method by which Townsend first ionization doefficient (.alpha.) or attachment coefficient (.eta.) can be deduced easily and precisely by means of analyzing Townsend equation based on linealized least squares method. The apparent ionization coefficient (.alpha.-.eta.)/p have been analyzed from the experimental data by applying the new method above mentioned. And the values of (.alpha.-.eta.)/p in SF$_{6}$ as a function of E/p were agreement with the values measured by Bhalla et al. who analyzed th experimental pre-breakdown currents. In the same way (.alpha.-.eta.)/p in N$_{2}$O had a same tendency to that of Folkard et al.l.

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Lens design by using damped least squares method with special procedure for estimating numerical adequacy of derivative increments of variables (미분증가치의 최적성 평가법을 도입한 감쇠최소자승법에 의한 광학 설계)

  • 김태희;김경찬;박진원;최옥식;이윤구;조현모;이인원
    • Korean Journal of Optics and Photonics
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    • v.8 no.2
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    • pp.88-94
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    • 1997
  • Photographic lenses and an aspheric optical pickup-lens are designed by using damped least-squares(DLS) method. We start optimization with arbitrary initial damping factor. To improve the rate of convergence and the stability in optimization, we apply the special procedure that estimates numerical adequacy of derivative increments of variables to the DLS method. When the initial damping factor is almost equal to the median of series of eigenvalues, the convergence and the stability of the method significantly are improved. Optimized lenses have the performance of each target.

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Estimation of Residual Stresses in Micromachined Films (마이크로머시닝 기술에 의해 형성된 막에 있어서의 잔류응력 추정)

  • Min, Yeong-Hun;Kim, Yong-Gwon
    • The Transactions of the Korean Institute of Electrical Engineers C
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    • v.49 no.6
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    • pp.354-359
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    • 2000
  • A new method of measuring residual stress in micromachined film is proposed. An estimation of residual stress is performed by using least squares fit with an appropriate deflection modeling. an exact value of residual stress is obtained without any of the ambiguities that exist in conventional buckling method, and a good approximation is also obtained by using a few data points. Therefore, the test structures area could be greatly decreased by using this method. The measurement can be done more easily and simply without any actuation or any specific measuring equipment. The structure and fabrication processes described in this paper are simple and widely used in surface micromachining. In addition, in-situ measurement is available by using the proposed method when the test structure and the measurement structure are fabricated on a wafer simultaneously.

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Analysis of Dynamic Crack Propagation using MLS Difference Method (MLS 차분법을 이용한 동적균열전파 해석)

  • Yoon, Young-Cheol;Kim, Kyeong-Hwan;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.1
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    • pp.17-26
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    • 2014
  • This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

Combining Empirical Feature Map and Conjugate Least Squares Support Vector Machine for Real Time Image Recognition : Research with Jade Solution Company

  • Kim, Byung Joo
    • International Journal of Internet, Broadcasting and Communication
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    • v.9 no.1
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    • pp.9-17
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    • 2017
  • This paper describes a process of developing commercial real time image recognition system with company. In this paper we will make a system that is combining an empirical kernel map method and conjugate least squares support vector machine in order to represent images in a low-dimensional subspace for real time image recognition. In the traditional approach calculating these eigenspace models, known as traditional PCA method, model must capture all the images needed to build the internal representation. Updating of the existing eigenspace is only possible when all the images must be kept in order to update the eigenspace, requiring a lot of storage capability. Proposed method allows discarding the acquired images immediately after the update. By experimental results we can show that empirical kernel map has similar accuracy compare to traditional batch way eigenspace method and more efficient in memory requirement than traditional one. This experimental result shows that proposed model is suitable for commercial real time image recognition system.

Performance Analysis of Quaternion-based Least-squares Methods for GPS Attitude Estimation (GPS 자세각 추정을 위한 쿼터니언 기반 최소자승기법의 성능평가)

  • Won, Jong-Hoon;Kim, Hyung-Cheol;Ko, Sun-Jun;Lee, Ja-Sung
    • Proceedings of the KIEE Conference
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    • 2001.07d
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    • pp.2092-2095
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    • 2001
  • In this paper, the performance of a new alternative form of three-axis attitude estimation algorithm for a rigid body is evaluated via simulation for the situation where the observed vectors are the estimated baselines of a GPS antenna array. This method is derived based on a simple iterative nonlinear least-squares with four elements of quaternion parameter. The representation of quaternion parameters for three-axis attitude of a rigid body is free from singularity problem. The performance of the proposed algorithm is compared with other eight existing methods, such as, Transformation Method (TM), Vector Observation Method (VOM), TRIAD algorithm, two versions of QUaternion ESTimator (QUEST), Singular Value Decomposition (SVD) method, Fast Optimal Attitude Matrix (FOAM), Slower Optimal Matrix Algorithm (SOMA).

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Parametric Blind Restoration of Bi-level Images with Unknown Intensities

  • Kim, Daeun;Ahn, Sohyun;Kim, Jeongtae
    • IEIE Transactions on Smart Processing and Computing
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    • v.5 no.5
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    • pp.319-322
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    • 2016
  • We propose a parametric blind deconvolution method for bi-level images with unknown intensity levels that estimates unknown parameters for point spread functions and images by minimizing a penalized nonlinear least squares objective function based on normalized correlation coefficients and two regularization functions. Unlike conventional methods, the proposed method does not require knowledge about true intensity values. Moreover, the objective function of the proposed method can be effectively minimized, since it has the special structure of nonlinear least squares. We demonstrate the effectiveness of the proposed method through simulations and experiments.