• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.471-479
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• 2008

Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.

• 로봇학회논문지
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• 제2권4호
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• pp.327-333
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• 2007

We propose a navigation algorithm using image-based visual servoing utilizing a fixed camera. We define the mobile robot navigation problem as an unconstrained optimization problem to minimize the image error between the goal position and the position of a mobile robot. The residual function which is the image error between the position of a mobile robot and the goal position is generally large for this navigation problem. So, this navigation problem can be considered as the nonlinear least squares problem for the large residual case. For large residual, we propose a method to find the second-order term using the secant approximation method. The performance was evaluated using the simulation.

• Smart Structures and Systems
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• 제4권3호
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• pp.279-290
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• 2008

The modeling and parameter estimation of a damped one-degree-of-freedom mass-spring system is examined. This paper presents a method for estimating the system parameters (damping coefficients and natural frequency) from measured free-vibration motion of a system that is modeled to include both subcritical viscous damping and kinetic Coulomb friction. The method applies a commercially available least-squares curve-fitting software function to fit the known solution of the equations of motion to the measured response. The method was tested through numerical simulation, and it was applied to experimental data collected from a laboratory mass-spring apparatus. The mass of this apparatus translates on linear bearings, which are the primary source of light inherent damping. Results indicate that the curve-fitting method is effective and accurate for both perfect and noisy measurements from a lightly damped mass-spring system.

• 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.

• 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.

• Journal of the Optical Society of Korea
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• 제16권1호
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• pp.57-62
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• 2012

Using continuous wave near-infrared spectroscopy, we measured time-resolved concentration changes of oxy-hemoglobin and deoxy-hemoglobin from the primary motor cortex following finger tapping tasks. These data were processed using partial least squares-discriminant analysis (PLS-DA) to develop a prediction model for a brain-computer interface. The tasks were composed of a series of finger tapping for 15 sec and relaxation for 45 sec. The location of the motor cortex was confirmed by the anti-phasic behavior of the oxy- and deoxy-hemoglobin changes. The results were compared with those obtained using the hidden Markov model (HMM) which has been known to produce the best prediction model. Our data imply that PLS-DA makes better judgments in determining the onset of the events than HMM.

• 한국CDE학회논문집
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• 제17권4호
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• pp.282-293
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• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.

• 한국정밀공학회지
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• 제15권5호
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• pp.128-136
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• 1998

A mathematical model for investigating the form generation mechanism in the centerless infeed grinding process is described. For 3-D modeling of form generation, contact points are assumed to be on least squares contact lines at the grinding wheel, regulating wheel, and work-rest blade. Using force and deflection analysis, the validity of this assumption is shown. Based on the 2-D simulation model developed in the previous work and the least squares contact line assumption, a 3-D model is presented. To validate this model, simulation results were compared with the experimental works. The experiments and computer simulations were carried out using three types of cylindrical workpiece shapes with varying flat length. The experimental results agree well with the simulation. It can be seen that the effect of flat end propagated to the opposite end through workpiece reorientation.

• 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.

• Journal of the Korean Data and Information Science Society
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• 제21권4호
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• pp.813-818
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• 2010

The least squares estimation method for model parameters under failure step-stress accelerated life tests is studied and a numerical example will be given to illustrate the proposed inferential procedures under the compound linear plans proposed as an alternative to the optimal quadratic plan, assuming that the exponential distribution with a quadratic relationship between stress and log-mean lifetime. The proposed compound linear plan for constant stress accelerated life tests and 4:2:1 plan are compared for various situations. Even though the compound linear plan was proposed under constant stress accelerated life tests, we found that this plan did well relatively in failure step-stress accelerated life tests.