• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.7
• /
• pp.3076-3092
• /
• 2020

An IKPCA-ELM-based intrusion detection method is developed to address the problem of the low accuracy and slow speed of intrusion detection caused by redundancies and high dimensions of data in the network. First, in order to reduce the effects of uneven sample distribution and sample attribute differences on the extraction of KPCA features, the sample attribute mean and mean square error are introduced into the Gaussian radial basis function and polynomial kernel function respectively, and the two improved kernel functions are combined to construct a hybrid kernel function. Second, an improved particle swarm optimization (IPSO) algorithm is proposed to determine the optimal hybrid kernel function for improved kernel principal component analysis (IKPCA). Finally, IKPCA is conducted to complete feature extraction, and an extreme learning machine (ELM) is applied to classify common attack type detection. The experimental results demonstrate the effectiveness of the constructed hybrid kernel function. Compared with other intrusion detection methods, IKPCA-ELM not only ensures high accuracy rates, but also reduces the detection time and false alarm rate, especially reducing the false alarm rate of small sample attacks.

• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.661-667
• /
• 2013

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in $L^2([-1,1],\mathbb{C})$ using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.429-437
• /
• 2001

In [1, 2], described a Chebyshev series method for the numerical solution of integral equations with three automatic algorithms for computing tow regularization parameters, C/sub f/ and r. Here we describe a Fourier series expansion method for a class singular integral equations with Hilbert kernel and constant coefficients with using a new automatic algorithm.

• Journal of Information Processing Systems
• /
• v.15 no.2
• /
• pp.422-432
• /
• 2019

A hybrid kernel function of support vector machine is proposed to improve the classification performance of power quality disturbances. The kernel function mathematical model of support vector machine directly affects the classification performance. Different types of kernel functions have different generalization ability and learning ability. The single kernel function cannot have better ability both in learning and generalization. To overcome this problem, we propose a hybrid kernel function that is composed of two single kernel functions to improve both the ability in generation and learning. In simulations, we respectively used the single and multiple power quality disturbances to test classification performance of support vector machine algorithm with the proposed hybrid kernel function. Compared with other support vector machine algorithms, the improved support vector machine algorithm has better performance for the classification of power quality signals with single and multiple disturbances.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.641-666
• /
• 2003

We develop a method of calculating explicitly the singularity of Szego and Bergman kernel by using the process developed by Boutet de Monvel and Sjostrand.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.32 no.9C
• /
• pp.861-866
• /
• 2007

A clustering algorithm for Gaussian Probability Distribution Function (GPDF) data called Centroid Neural Network with a Bhattacharyya Kernel (BK-CNN) is proposed in this paper. The proposed BK-CNN is based on the unsupervised competitive Centroid Neural Network (CNN) and employs a kernel method for data projection. The kernel method adopted in the proposed BK-CNN is used to project data from the low dimensional input feature space into higher dimensional feature space so as the nonlinear problems associated with input space can be solved linearly in the feature space. In order to cluster the GPDF data, the Bhattacharyya kernel is used to measure the distance between two probability distributions for data projection. With the incorporation of the kernel method, the proposed BK-CNN is capable of dealing with nonlinear separation boundaries and can successfully allocate more code vector in the region that GPDF data are densely distributed. When applied to GPDF data in an image classification probleml, the experiment results show that the proposed BK-CNN algorithm gives 1.7%-4.3% improvements in average classification accuracy over other conventional algorithm such as k-means, Self-Organizing Map (SOM) and CNN algorithms with a Bhattacharyya distance, classed as Bk-Means, B-SOM, B-CNN algorithms.

• Journal of IKEEE
• /
• v.25 no.4
• /
• pp.664-671
• /
• 2021

This paper proposes a GPGPU structure that can reduce the number of operations and memory access by effectively applying a data reuse method to a convolutional neural network(CNN). Convolution is a two-dimensional operation using kernel and input data, and the operation is performed by sliding the kernel. In this case, a reuse method using an internal register is proposed instead of loading kernel from a cache memory until the convolution operation is completed. The serial operation method was applied to the convolution to increase the effect of data reuse by using the principle of GPGPU in which instructions are executed by the SIMT method. In this paper, for register-based data reuse, the kernel was fixed at 4×4 and GPGPU was designed considering the warp size and register bank to effectively support it. To verify the performance of the designed GPGPU on the CNN, we implemented it as an FPGA and then ran LeNet and measured the performance on AlexNet by comparison using TensorFlow. As a result of the measurement, 1-iteration learning speed based on AlexNet is 0.468sec and the inference speed is 0.135sec.

• The Korean Journal of Applied Statistics
• /
• v.13 no.2
• /
• pp.447-455
• /
• 2000

We propose a weighted kernel pattern recognition method using the K -means clustering algorithm to reduce computation and storage required for the full kernel classifier. This technique finds a set of reference vectors and weights which are used to approximate the kernel classifier. Since the hierarchical clustering method implemented in the 'Weighted Parzen Window (WP\V) classifier is not able to rearrange the proper clusters, we adopt the K -means algorithm to find reference vectors and weights from the more properly rearranged clusters \Ve find that the proposed method outperforms the \VP\V method for the repre~entativeness of the reference vectors and the data reduction.

• Journal of the Korean Data and Information Science Society
• /
• v.21 no.1
• /
• pp.155-162
• /
• 2010

In this paper we propose a doubly penalized kernel method which estimates both the mean function and the variance function simultaneously by kernel machines for heteroscedastic autoregressive data. We also present the model selection method which employs the cross validation techniques for choosing the hyper-parameters which aect the performance of proposed method. Simulated examples are provided to indicate the usefulness of proposed method for the estimation of mean and variance functions.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.813-821
• /
• 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.