• 한국경영과학회지
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• 제31권2호
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• pp.69-85
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• 2006

Transductive Support Vector Machine(TSVM) is one of semi-supervised learning algorithms which exploit the domain structure of the whole data by considering labeled and unlabeled data together. Although it was proposed several years ago, there has been no efficient algorithm which can handle problems with more than hundreds of training examples. In this paper, we propose an efficient branch-and-bound algorithm which can solve large-scale TSVM problems with thousands of training examples. The proposed algorithm uses two bounding techniques: min-cut bound and reduced SVM bound. The min-cut bound is derived from a capacitated graph whose cuts represent a lower bound to the optimal objective function value of the dual problem. The reduced SVM bound is obtained by constructing the SVM problem with only labeled data. Experimental results show that the accuracy rate of TSVM can be significantly improved by learning from the optimal solution of TSVM, rather than an approximated solution.

• Management Science and Financial Engineering
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• 제16권1호
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• pp.81-117
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• 2010

Semi-supervised learning incorporates unlabeled examples, whose labels are unknown, as well as labeled examples into learning process. Although transductive support vector machine (TSVM), one of semi-supervised learning models, was proposed about a decade ago, its application to large-scaled data has still been limited due to its high computational complexity. Our previous research addressed this limitation by introducing a branch-and-bound algorithm for finding an optimal solution to TSVM. In this paper, we propose three new techniques to enhance the performance of the branch-and-bound algorithm. The first one tightens min-cut bound, one of two bounding strategies. Another technique exploits a graph-based approximation to a support vector machine problem to avoid the most time-consuming step. The last one tries to fix the labels of unlabeled examples whose labels can be obviously predicted based on labeled examples. Experimental results are presented which demonstrate that the proposed techniques can reduce drastically the number of subproblems and eventually computational time.

• 한국컴퓨터정보학회논문지
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• 제21권9호
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• pp.79-84
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• 2016

In this paper we consider the problem of finding the triplet (S,${\pi}$,f), where $S{\subseteq}V$, ${\pi}$ is a sequence of nodes in S and $f:V{\backslash}S{\rightarrow}S$ for a given complete graph G=(V,E). In particular, there exist two costs, $c^V_{uv}$ and $c^D_{uv}$ for $(u,v){\in}E$, and the cost of triplet (S,${\pi}$,f) is defined as $\sum_{i=1}^{{\mid}S{\mid}}c^V_{{\pi}(i){\pi}(i+1)}+2$ ${\sum_{u{\in}V{\backslash}S}c^D_{uf(u)}$. This problem is motivated by the integrated routing of the vehicle and drone for urban delivery services. Since a well-known NP-complete TSP (Traveling Salesman Problem) is a special case of our problem, we cannot expect to have any polynomial-time algorithm unless P=NP. Furthermore, for practical purposes, we may not rely on time-exhaustive enumeration method such as branch-and-bound and branch-and-cut. This paper suggests the simple heuristic which is motivated by the MST (minimum spanning tree)-based approximation algorithm and neighborhood search heuristic for TSP.

• Geomechanics and Engineering
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• 제38권4호
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• pp.367-380
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• 2024

In this study, a prediction model for the cutting force evolution in brittle rocks was developed. This model is based on indentation tests using a conical pick at a cutting depth of 9 mm. The behavior of the indentation mechanism was analyzed in three phases by using Evans' cutting mode. The peak values in the force history identified these phases. The variation in the local strength of the rock caused a large offset in the model prediction of chipping. Regression analyses showed that there is a strong power relationship between the upper bound of the cutting force along with chipping and depth of cut. The slope of the three crushing phases has been found to increase sequentially (α₁<α₂<α₃). In addition, a positive correlation existed between the Schmidt hardness and brittleness index that affects the lower and upper bounds of chipping. Consequently, the results clearly demonstrate that the new model can reasonably predict the evolution of the cutting force based on experimental data. These results would be beneficial for engineers to design and select the optimum excavation machine to reduce mechanical vibration and enhance cutting efficiency.