• KIPS Transactions on Software and Data Engineering
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• v.5 no.8
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• pp.361-368
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• 2016

While dimension reduction methods on high dimensional data have been widely studied, research on dimension reduction methods for high dimensional streaming data with concept drift is limited. In this paper, we review incremental dimension reduction methods and propose a method to apply dimension reduction efficiently in order to improve classification performance on high dimensional streaming data with concept drift.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.191-202
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• 2024

The goal of this paper is to show how multivariate regression analysis with high-dimensional responses is facilitated by the response dimension reduction. Multivariate regression, characterized by multi-dimensional response variables, is increasingly prevalent across diverse fields such as repeated measures, longitudinal studies, and functional data analysis. One of the key challenges in analyzing such data is managing the response dimensions, which can complicate the analysis due to an exponential increase in the number of parameters. Although response dimension reduction methods are developed, there is no practically useful illustration for various types of data such as so-called large p-small n data. This paper aims to fill this gap by showcasing how response dimension reduction can enhance the analysis of high-dimensional response data, thereby providing significant assistance to statistical practitioners and contributing to advancements in multiple scientific domains.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• Interaction and multiscale mechanics
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• v.3 no.1
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• pp.1-22
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• 2010

In this paper one introduces a method of multiscale modelling called collection of dynamical systems with dimensional reduction. The method is suggested to be an appropriate approach to theoretical modelling of phenomena in mechanics of materials having in mind especially dynamics of processes. Within this method one formalizes scale of averaging of processes during modelling. To this end a collection of dynamical systems is distinguished within an elementary dynamical system. One introduces a dimensional reduction procedure which is designed to be a method of transition between various scales. In order to consider continuum models as obtained by means of the dimensional reduction one introduces continuum with finite-dimensional fields. Owing to geometrical elements associated with the elementary dynamical system we can formalize scale of averaging within continuum mechanics approach. In general presented here approach is viewed as a continuation of the rational mechanics.

• 한국연소학회:학술대회논문집
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• 2012.11a
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• pp.75-78
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• 2012

Rotary kiln furnace is one of the most widely used reactors in industrial field. In this paper, 0-dimensional heat and mass balance for direct coal flame rotary kiln was performed preferentially, then a simplified 1-dimensional model was developed based on 0-dimensional analysis data to proceed additional thermal analysis. Compared the results with the currently operating rotary kiln data to validate 1-dimensional model. Through this procedure, it can help to derive fundamental idea for design and operation of rotary kiln.

• 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.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2868-2872
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• 2007

In this study, a passive control using a boat-tail device is conducted for a three-dimensional car model in ground proximity. We consider various boat-tails and investigate the mechanism of drag reduction by them. By varying the length and slant angle of boat-tail, we obtain drag reductions up to 40%. From the oil-surface flow visualization and hot-wire measurement, the drag reduction by the boat-tail is characterized by the shear-layer instability and reattachment on the boat-tail, forming a small separation bubble at the upstream part of boat-tail surface, resulting in the delay of main separation and drag reduction. At high slant angles, the flow fully separates and drag is nearly same as that of no control.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.87-96
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• 2010

We consider the semilinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the semilinear biharmonic boundary value problem. We show this result by using the critical point theory, the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Publications of The Korean Astronomical Society
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• v.28 no.1
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• pp.7-13
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• 2013

We present a multi-dimensional reduction method of the surveyed cube database obtained using a single- dish radio telescope in Taeduk Radio Astronomy Observatory (TRAO). The multibeam receiver system installed at the 14 m telescope in TRAO was not optimized at the initial stage, though it became more stabilized in the following season. We conducted a Galactic Plane survey using the multibeam receiver system. We show that the noise level of the first part of the survey was higher than expected, and a special reduction process seemed to be definitely required. Along with a brief review of classical methods, a multi-dimensional method of reduction is introduced; It is found that the 'background' task within IRAF (Image Reduction and Analysis Facility) can be applied to all three directions of the cube database. Various statistics of reduction results is tested using several IRAF tasks. The rms value of raw survey data is 0.241 K, and after primitive baseline subtraction and elimination of bad channel sections, the rms value turned out to be 0.210 K. After the one-dimensional reduction using 'background' task, the rms value is estimated to be 0.176 K. The average rms of the final reduced image is 0.137 K. Thus, the image quality is found to be improved about 43% using the new reduction method.

• Structural Monitoring and Maintenance
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• v.5 no.3
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• pp.417-428
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• 2018

In this paper, various model reduction methods were assessed using a shear frame, plane and space truss structures. Each of the structures is one-dimensional, two-dimensional and three-dimensional, respectively. Three scenarios of poor, better, and the best were considered for each of the structures in which 25%, 40%, and 60% of the total degrees of freedom (DOFs) were measured in each of them, respectively. Natural frequencies of the full and reduced order structures were compared in each of the numerical examples to assess the performance of model reduction methods. Generally, it was found that system equivalent reduction expansion process (SEREP) provides full accuracy in the model reduction in all of the numerical examples and scenarios. Iterated improved reduced system (IIRS) was the second-best, providing acceptable results and lower error in higher modes in comparison to the improved reduced system (IRS) method. Although the Guyan's method has very low levels of accuracy. Structures were classified with the excitation frequency. High-frequency structures compared to low-frequency structures have been poor performance in the model reduction methods (Guyan, IRS, and IIRS).