• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1047-1065
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• 2022

For two dimensional lattices, a Gaussian basis achieves all two successive minima. For dimension larger than two, constructing a pairwise Gaussian basis is useful to compute short vectors of the lattice. For three dimensional lattices, Semaev showed that one can convert a pairwise Gaussian basis to a basis achieving all three successive minima by one simple reduction. A pairwise Gaussian basis can be obtained from a given basis by executing Gauss algorithm for each pair of basis vectors repeatedly until it returns a pairwise Gaussian basis. In this article, we prove a necessary and sufficient condition for a pairwise Gaussian basis to achieve the first k successive minima for three dimensional lattices for each k ∈ {1, 2, 3} by modifying Semaev's condition. Our condition directly checks whether a pairwise Gaussian basis contains the first k shortest independent vectors for three dimensional lattices. LLL is the most basic lattice basis reduction algorithm and we study how to use LLL to compute a pairwise Gaussian basis. For δ ≥ 0.9, we prove that LLL(δ) with an additional simple reduction turns any basis for a three dimensional lattice into a pairwise SV-reduced basis. By using this, we convert an LLL reduced basis to a pairwise Gaussian basis in a few simple reductions. Our result suggests that the LLL algorithm is quite effective to compute a basis with all three successive minima for three dimensional lattices.

• Journal of information and communication convergence engineering
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• v.5 no.1
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• pp.12-16
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• 2007

In this paper, a new method is proposed for tracking the direction-of-arrival (DOA) of the wideband moving source incident on uniform linear array sensors. DOA is estimated by focusing transformation matrices. To update focusing matrices along with new data snap shots, we use the FAST (Fast Approximate Subspace Tracking) method. Present focusing matrices are constructed by previous signal and its orthogonal basis vectors as well as present signal and its orthogonal basis vectors, which are the left and right singular vectors of the inner product of two approximated matrices. Simulation results are shown to illustrate the performance of the proposed method.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.6
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• pp.267-271
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• 2002

The Hotelling transform is based on statistical properties of an image. The principal uses of this transform are in data compression. The basic concept of the Hotelling transform is that the choice of basis vectors pointing the direction of maximum variance of the data. This property can be used for rotation normalization. Many objects of interest in pattern recognition applications can be easily standardized by performing a rotation normalization that aligns the coordinate axes with the axes of maximum variance of the pixels in the object. However, this transform can not be used to rotation normalization of color images directly. In this paper, we propose a new method for rotation normalization of color images based on the Hotelling transform. The Hotelling transform is performed to calculate basis vectors of each channel. Then the summation of vectors of all channels are processed. Rotation normalization is performed using the result of summation of vectors. Experimental results showed the proposed method can be used for rotation normalization of color images effectively.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.679-698
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• 2002

In this paper some techniques for the dynamic analysis of non-classically damped linear systems are reviewed and compared. All these methods are based on a transformation of the governing equations using a basis of complex or real vectors. Complex and real vector bases are presented and compared. The complex vector basis is represented by the eigenvectors of the complex eigenproblem obtained considering the non-classical damping matrix of the system. The real vector basis is a set of Ritz vectors derived either as the undamped normal modes of vibration of the system, or by the load dependent vector algorithm (Lanczos vectors). In this latter case the vector basis includes the static correction concept. The rate of convergence of these bases, with reference to a parametric structural system subjected to a fixed spatial distribution of forces, is evaluated. To this aim two error norms are considered, the first based on the spatial distribution of the load and the second on the shear force at the base due to impulsive loading. It is shown that both error norms point out that the rate of convergence is strongly influenced by the spatial distribution of the applied forces.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.866-871
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• 1994

B-spline curves and surfaces are effective solutions for design and modelling of the freeform models. The control methods of these are using with control points, knot vectors and weight of NURBS. Using control point is easy and resonable for representation of general models. But the movement of control points bring out the reformation of original convex hull. The B-splines with nonuniform knot vector provide good result of the shape modification without convex hull reforming. B-splines are constructed with control points and basis functions. Nonuniform knot vectors effect on the basis functions. And the blending curves describe the prorities of knot vectors. Applying of these, users will forecast of the reformed curves after modifying controllabler primitives.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.6 no.6
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• pp.986-991
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• 2002

This paper presents off-line handwritten numeral recognition method by using Eigen-Vectors. In this method, numeral features are extracted statistically by using Eigen-Vectors through KL transform and input numeral is recognized in the feature space by the nearest-neighbor classifier. In our feature extraction method, basis vectors which express best the property of each numeral type within the extensive database of sample numeral images are calculated, and the numeral features are obtained by using this basis vectors. Through the experiments with the unconstrained handwritten numeral database of Concordia University, we have achieved a recognition rate of 96.2%.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.1
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• pp.45-60
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• 1995

It is attempted to estimate excitation force of a linear vibratory system using measured vibration responses. The excitation force is estimated from the relationship between the vibration response and system characteristic matrices which are extracted from both the mathematical model of the system and actual response in contrast to the usual approach of inverting the frequency response matrices. This extraction scheme is based on the fact that the vibration response can be expressed in term of linear combination of frequency domain modal vectors defined as mutually orthonormal basis vectors in frequency domain. The extracted frequency domain basis vectors are very stable in computational manipulation. It is found that the estimated excitation force is in good agreement with actually measured force except at the natural frequencies the structure, which is the common feature still to be overcome by the research efforts in this area. From the results of this paper, this disagreement is considered to come from the discrepancy between the model and actual value of the mass, damping and stiffness of the structure.

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1825-1834
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• 2022

Performing high-fidelity computational fluid dynamics (HF-CFD) to predict the flow and heat transfer state of the coolant in the reactor core is expensive, especially in scenarios that require extensive parameter search, such as uncertainty analysis and design optimization. This work investigated the performance of utilizing a multi-fidelity reduced-order model (MF-ROM) in PWR rod bundles simulation. Firstly, basis vectors and basis vector coefficients of high-fidelity and low-fidelity CFD results are extracted separately by the proper orthogonal decomposition (POD) approach. Secondly, a surrogate model is trained to map the relationship between the extracted coefficients from different fidelity results. In the prediction stage, the coefficients of the low-fidelity data under the new operating conditions are extracted by using the obtained POD basis vectors. Then, the trained surrogate model uses the low-fidelity coefficients to regress the high-fidelity coefficients. The predicted high-fidelity data is reconstructed from the product of extracted basis vectors and the regression coefficients. The effectiveness of the MF-ROM is evaluated on a flow and heat transfer problem in PWR fuel rod bundles. Two data-driven algorithms, the Kriging and artificial neural network (ANN), are trained as surrogate models for the MF-ROM to reconstruct the complex flow and heat transfer field downstream of the mixing vanes. The results show good agreements between the data reconstructed with the trained MF-ROM and the high-fidelity CFD simulation result, while the former only requires to taken the computational burden of low-fidelity simulation. The results also show that the performance of the ANN model is slightly better than the Kriging model when using a high number of POD basis vectors for regression. Moreover, the result presented in this paper demonstrates the suitability of the proposed MF-ROM for high-fidelity fixed value initialization to accelerate complex simulation.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.853-861
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• 2003

An improved K-means document clustering method has been presented, where a concept vector is manipulated for each cluster on the basis of cosine similarity of text documents. The concept vectors are unit vectors that have been normalized on the n-dimensional sphere. Because the standard K-means method is sensitive to initial starting condition, our improvement focused on starting condition for estimating the modes of a distribution. The improved K-means clustering algorithm has been applied to a set of text documents, called Classic3, to test and prove efficiency and correctness of clustering result, and showed 7% improvements in its worst case.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2002.11a
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• pp.912-915
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• 2002

This paper presents off-line handwritten numeral recognition method by using Eigen-Vectors. In this method, numeral features are extracted statistically by using Eigen-Vectors through KL transform and input numeral is recognized in the feature space by the nearest-neighbor classifier. In our feature extraction method, basis vectors which express best the property of each numeral type within the extensive database of sample numeral images are calculated, and the numeral features are obtained by using this basis vectors. Through the experiments with the unconstrained handwritten numeral database of Concordia University, we have achieved a recognition rate of 96.2%.