• ETRI Journal
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• 제34권2호
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• pp.288-291
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• 2012

In this letter, a new online anomaly detection approach for software systems is proposed. The novelty of the proposed approach is to apply a new semantic kernel function for a support vector machine (SVM) classifier to detect fault-suspicious execution paths at runtime in a reasonable amount of time. The kernel uses a new sequence matching algorithm to measure similarities among program execution paths in a customized feature space whose dimensions represent the largest common subpaths among the execution paths. To increase the precision of the SVM classifier, each common subpath is given weights according to its ability to discern executions as correct or anomalous. Experiment results show that compared with the known kernels, the proposed SVM kernel will improve the time overhead of online anomaly detection by up to 170%, while improving the precision of anomaly alerts by up to 140%.

• 대한수학회보
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• 제59권5호
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• pp.1215-1235
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• 2022

In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권6호
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• pp.2709-2729
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• 2016

Representation based classification, kernel method and sparse representation have received much attention in the field of face recognition. In this paper, we proposed an improved kernel principal component analysis method based on sparse representation to improve the accuracy and robustness for face recognition. First, the distances between the test sample and all training samples in kernel space are estimated based on collaborative representation. Second, S training samples with the smallest distances are selected, and Kernel Principal Component Analysis (KPCA) is used to extract the features that are exploited for classification. The proposed method implements the sparse representation under ℓ₂ regularization and performs feature extraction twice to improve the robustness. Also, we investigate the relationship between the accuracy and the sparseness coefficient, the relationship between the accuracy and the dimensionality respectively. The comparative experiments are conducted on the ORL, the GT and the UMIST face database. The experimental results show that the proposed method is more effective and robust than several state-of-the-art methods including Sparse Representation based Classification (SRC), Collaborative Representation based Classification (CRC), KCRC and Two Phase Test samples Sparse Representation (TPTSR).

• 호남수학학술지
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• 제43권4호
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• pp.691-700
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• 2021

In this paper, we compute directly the Hankel matrix representation of the Hankel operator on the Hardy space of the unit disc without using any classical kernel functions with respect to special orthonormal bases for the Hardy space and its orthogonal complement. This gives an elementary proof for the formula.

• 대한수학회논문집
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• 제11권2호
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• pp.367-375
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• 1996

Suppose the kernel function $\kappa$ belongs to $S(R^2)$ and is symmetric such that $ < \otimes x, \kappa >\geq 0$ for all $x \in S'(R)$. Let A be the class of functions f such that the function f is measurable on $S'(R)$ with $\int_{S'(R)}$\mid$f((I + tK)^{\frac{1}{2}}x$\mid$^2d\mu(x) < M$ for some $M > 0$ and for all t > 0, where K is the integral operator with kernel function $\kappa$. We show that the \lambda$-potential $G_Kf$ of f is a weak solution of $(\lambda I - \frac{1}{2} \tilde{\Xi}_{0,2}(\kappa))_u = f$.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.813-821
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• 2010

In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical approaches. First a new reproducing kernel space is constructed to solve this class of tenth-order linear boundary value problems; then the approximate solutions of such problems are given in the form of series using the present method. Three examples compared with those considered by Siddiqi, Twizell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362; S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline, Applied Mathematics and Computation 185 (1)(2007) 115-127] show that the method developed in this paper is more efficient.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권3호
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• pp.1173-1192
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• 2015

The Support Vector Data Description (SVDD) has achieved great success in anomaly detection, directly finding the optimal ball with a minimal radius and center, which contains most of the target data. The SVDD has some limited classification capability, because the hyper-sphere, even in feature space, can express only a limited region of the target class. This paper presents an anomaly detection algorithm for mitigating the limitations of the conventional SVDD by finding the minimum volume enclosing ellipsoid in the feature space. To evaluate the performance of the proposed approach, we tested it with intrusion detection applications. Experimental results show the prominence of the proposed approach for anomaly detection compared with the standard SVDD.

• 핵의학기술
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• 제16권2호
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• pp.29-34
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• 2012

Siemens사의 CT 선량 감소 소프트웨어인 IRIS의 적용을 통하여 CT 선량 감소 시 노이즈 감소 효과와 해상력의 보존 그리고 ACCT에 IRIS 각 kernel의 적용 시 SUV 변화를 확인하는데 목적을 두었다. Biograph mCT 40 slice 스캐너를 이용하여 AAPM CT performance phantom, Anthropomorphic chest phantom을 관전압 120 kVp로 고정하고 100-10 mAs까지 15%감소하여 스캔 후 FBP, IRIS 각 kernel을 적용하여 재구성 하여 영상의 노이즈, 해상력, 영상 평가를 시행하였다. NEMA IEC body phantom을 이용하여 55.5 MBq를 background에 주입하고 열소와 배후 방사의 비를 8:1이 되도록 모형을 제작하였다. 120 kVp, 50 mAs 조건으로 1분, 2분, 3분, 4분 스캔하여 영상을 획득한 후 ACCT에 IRIS 각 kernel을 적용하여 기존 FBP 방식을 적용한 SUV와의 평가를 시행하였다. IRIS의 적용 시 기존 FBP 방식에 비하여 45% 선량을 감소하였음에도 불구하고 해상력 저하 없는 노이즈 감소 효과가 확인 되었으며 SUV 평가 실험에서 IRIS의 I70f kernel을 제외하고는 기존 FBP 방식을 통하여 획득된 SUV와 유의한 차이가 나타나지 않았다. 본 연구를 통하여 IRIS 적용 시 기존 FBP 방식에 비하여 CT 피폭선량 감소와 해상력 저하 없는 노이즈 감소 효과를 입증하였으며 IRIS kernel의 적절한 적용을 통하여 PET/CT 검사 시 환자 피폭선량 감소는 물론 FBP 방식에 비하여 우수한 영상의 획득이 가능할 것이라 사료된다.

• 대한수학회논문집
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• 제3권2호
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• pp.179-187
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• 1988

• Journal of Computing Science and Engineering
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• 제10권2호
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• pp.58-67
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• 2016

With the large amount of complex network data that is increasingly available on the Web, link prediction has become a popular data-mining research field. The focus of this paper is on a link-prediction task that can be formulated as a binary classification problem in complex networks. To solve this link-prediction problem, a sparse-classification algorithm called "Truncated Kernel Projection Machine" that is based on empirical-feature selection is proposed. The proposed algorithm is a novel way to achieve a realization of sparse empirical-feature-based learning that is different from those of the regularized kernel-projection machines. The algorithm is more appealing than those of the previous outstanding learning machines since it can be computed efficiently, and it is also implemented easily and stably during the link-prediction task. The algorithm is applied here for link-prediction tasks in different complex networks, and an investigation of several classification algorithms was performed for comparison. The experimental results show that the proposed algorithm outperformed the compared algorithms in several key indices with a smaller number of test errors and greater stability.