Functional linear regression for functional response via sparse basis selection

한경희,신혜진 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.3

We study a sparse estimation in functional linear regression model for functional response where the bivariate regression coefficient function takes zero values in a certain region of domain, so it is generated by a sparse set of basis functions. From a variable selection perspective, we construct a sparse basis representation for the coefficient function using the penalized least squares method. The proposed method enables us to simultaneously estimate the regression parameters and select basis functions. For a given basis, we show that our approach consistently identifies true subset of basis functions and the resulting estimator has asymptotically the same properties as the oracle estimator derived from the true underlying model. Simulation studies and a real data application are provided to demonstrate a finite sample performance of the proposed method.

서로 다른 두 개의 2차원 CAT 기저함수를 이용한 컬러영상 암호화

남태희(Tae-Hee Nam),김영민(Young-Min Kim) 한국의료정보교육협회 2018 보건의료생명과학논문지 Vol.6 No.1

본 논문에서는 서로 다른 두개의 2차원 CAT(Two-Dimensional Cellular Automata Transform) 기저함수(Basis Functions)를 단계적으로 이용하여 컬러 영상을 암호화하는 방법을 제안한다. 암호화 방법은 먼저, 서로 다른 두개의 게이트웨이 값들을 설정하여 2차원 CAT 기저함수들을 생성한다. 생성된 기저함수를 컬러 영상에 단계적으로 곱하여 2차원 CAT 암호화를 한다. 마지막으로, 키 공간 분석, 엔트로피 분석 및 민감도 분석을 통해 제안한 방법이 효율적이고 매우 안전함을 검증한다. In this paper, we propose the color image encryption method which gradually uses two different 2D CAT(Two-Dimensional Cellular Automata Transform) basis functions. The encryption method is processed in the following order. First, two different gateway values ​​are set to produce 2D CAT basis functions. The produced basis functions is gradually multiplied by color image that has been process the 2D CAT encipherment. Lastly, the results of the experiment which are key space analysis, entropy analysis, and sensitivity analysis verify that the proposed method is efficient and very secure.

SOME FORMULAS FOR BESSEL AND HYPER-BESSEL FUNCTIONS RELATED TO THE PROPER LORENTZ GROUP

I. A. Shilin,최준상 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.1

In a representation space of the proper Lorentz group, we consider the so-called spherical and two parabolic bases and compute the matrix elements of restriction of the representation to matrix diag(1, 1, 1, -1) with respect to one of the above parabolic basis in the following three particular cases: matrix elements belong to ‘zero row’; lie on the ‘main diagonal’; lie on the ‘anti-diagonal’. Taking the relations between above bases, we give a group theoretical treatment of one known formula and derive two new formulas for series involving modified hyper-Bessel functions of the first kind, which converge to products of (usual) cylinder functions. Some results here are pointed out to be able to be rewritten in terms of Bessel-Clifford functions.

암호화를 위한 정규기저 기반 부호계열 발생 알고리즘 분석 및 발생기 구성

이정재,Lee, Jeong-Jae 한국융합신호처리학회 2014 융합신호처리학회 논문지 (JISPS) Vol.15 No.2

For the element ${\alpha}{\in}GF(p^n)$, two kinds of bases are known. One is a conventional polynomial basis of the form $\{1,{\alpha},{\alpha}^2,{\cdots},{\alpha}^{n-1}\}$, and the other is a normal basis of the form $\{{\alpha},{\alpha}^p,{\alpha}^{p^2},{\cdots},{\alpha}^{p^{n-1}}\}$. In this paper we consider the method of generating normal bases which construct the finite field $GF(p^n)$, as an n-dimensional extension of the finite field GF(p). And we analyze the code sequence generating algorithm and derive the implementation functions of code sequence generator based on the normal bases. We find the normal polynomials of degrees, n=5 and n=7, which can generate normal bases respectively, design, and construct the code sequence generators based on these normal bases. Finally, we produce two code sequence groups(n=5, n=7) by using Simulink, and analyze the characteristics of the autocorrelation function, $R_{i,i}(\tau)$, and crosscorrelation function, $R_{i,j}(\tau)$, $i{\neq}j$ between two different code sequences. Based on these results, we confirm that the analysis of generating algorithms and the design and implementation of the code sequence generators based on normal bases are correct. 원소 ${\in}F(p)$에 대하여 두 종류의 기저함수가 알려져 있다. 통상적인 다항식 기저(polynomial bases)는 $\{1,{\alpha},{\alpha}^2,{\cdots},{\alpha}^{n-1}\}$로 이루어지고 이와 다르게 정규 기저(normal bases)는 $\{{\alpha},{\alpha}^p,{\alpha}^{p^2},{\cdots},{\alpha}^{p^{n-1}}\}$의 형태를 갖는다. 본 논문에서는 소수 p의 원소로 이루어지는 유한장 GF(p)상에서 n차원 벡터공간인 확대장 $GF(p^n)$을 이룰 수 있는 정규기저의 발생과 생성에 대하여 검토하고 정규기저를 기반으로 부호계열 발생알고리즘을 분석하여 발생기구성함수를 도출하였다. 차수 n=5와 n=7인 두 종류의 정규기저를 생성할 수 있는 정규다항식을 발견하고 부호계열 발생기를 설계 구성하였다. 마지막으로 Simulink를 이용하여 두 종류(n=5, n=7)의 부호계열 그룹을 발생시키고 발생된 부호계열간의 자기상관함수, $R_{i,i}(\tau)$와 상호상관함수, $R_{i,j}(\tau)$, $i{\neq}j$ 특성을 분석하였다. 이 결과로부터 정규기저를 이용한 부호계열 발생알고리즘의 분석, 그리고 부호계열 발생기 설계와 구성이 타당함을 확인하였다.

Selecting Optimal Basis Function with Energy Parameter in Image Classification Based on Wavelet Coefficients

Hee Young Yoo,Ki Won Lee,Hong Sung Jin,Byung Doo Kwon 大韓遠隔探査學會 2008 大韓遠隔探査學會誌 Vol.24 No.5

Land-use or land-cover classification of satellite images is one of the important tasks in remote sensing application and many researchers have tried to enhance classification accuracy. Previous studies have shown that the classification technique based on wavelet transform is more effective than traditional techniques based on original pixel values, especially in complicated imagery. Various basis functions such as Haar, daubechies, coiflets and symlets are mainly used in 20 image processing based on wavelet transform. Selecting adequate wavelet is very important because different results could be obtained according to the type of basis function in classification. However, it is not easy to choose the basis function which is effective to improve classification accuracy. In this study, we first computed the wavelet coefficients of satellite image using ten different basis functions, and then classified images. After evaluating classification results, we tried to ascertain which basis function is the most effective for image classification. We also tried to see if the optimum basis function is decided by energy parameter before classifying the image using all basis functions. The energy parameters of wavelet detail bands and overall accuracy are clearly correlated. The decision of optimum basis function using energy parameter in the wavelet based image classification is expected to be helpful for saving time and improving classification accuracy effectively.

Selecting Optimal Basis Function with Energy Parameter in Image Classification Based on Wavelet Coefficients

유희영,이기원,진홍성,권병두 대한원격탐사학회 2008 大韓遠隔探査學會誌 Vol.24 No.5

Land-use or land-cover classification of satellite images is one of the important tasks inremote sensing application and many researchers have tried to enhance classification accuracy. Previousstudies have shown that the classification technique based on wavelet transform is more effective thantraditional techniques based on original pixel values, especially in complicated imagery. Various basisfunctions such as Haar, daubechies, coiflets and symlets are mainly used in 2D image processing based onwavelet transform. Selecting adequate wavelet is very important because different results could be obtainedaccording to the type of basis function in classification. However, it is not easy to choose the basis functionwhich is effective to improve classification accuracy. In this study, we first computed the wavelet coefficientsof satellite image using ten different basis functions, and then classified images. After evaluating classificationresults, we tried to ascertain which basis function is the most effective for image classification. We also triedto see if the optimum basis function is decided by energy parameter before classifying the image using allbasis functions. The energy parameters of wavelet detail bands and overall accuracy are clearly correlated.The decision of optimum basis function using energy parameter in the wavelet based image classification isexpected to be helpful for saving time and improving classification accuracy effectively.

Physics based basis function for vibration analysis of high speed rotating beams

R. Ganesh,Ranjan Ganguli 국제구조공학회 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.39 No.1

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

A Comparative Study of 3D DWT Based Space-borne Image Classification for Differnet Types of Basis Function

Hee Young Yoo,Ki Won Lee,Byung Doo Kwon 大韓遠隔探査學會 2008 大韓遠隔探査學會誌 Vol.24 No.1

In the previous study, the Haar wavelet was used as the sole basis function for the 3D discrete wavelet transform because the number of bands is too small to decompose a remotely sensed image in band direction with other basis functions. However, it is possible to use other basis functions for wavelet decomposition in horizontal and vertical directions because wavelet decomposition is independently performed in each direction. This study aims to classify a high spatial resolution image with the six types of basis function including the Haar function and to compare those results. The other wavelets are more helpful to classify high resolution imagery than the Haar wavelet. In overall accuracy, the Coif4 wavelet has the best result. The improvement of classification accuracy is different depending on the type of class and the type of wavelet. Using the basis functions with long length could be effective for improving accuracy in classification, especially for the classes of small area. This study is expected to be used as fundamental information for selecting optimal basis function according to the data properties in the 3D DWT based image classification.

Physics based basis function for vibration analysis of high speed rotating beams

Ganesh, R.,Ganguli, Ranjan Techno-Press 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.39 No.1

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

A Comparative Study of 3D DWT Based Space-borne Image Classification for Differnet Types of Basis Function

Yoo, Hee-Young,Lee, Ki-Won,Kwon, Byung-Doo The Korean Society of Remote Sensing 2008 大韓遠隔探査學會誌 Vol.24 No.1

In the previous study, the Haar wavelet was used as the sole basis function for the 3D discrete wavelet transform because the number of bands is too small to decompose a remotely sensed image in band direction with other basis functions. However, it is possible to use other basis functions for wavelet decomposition in horizontal and vertical directions because wavelet decomposition is independently performed in each direction. This study aims to classify a high spatial resolution image with the six types of basis function including the Haar function and to compare those results. The other wavelets are more helpful to classify high resolution imagery than the Haar wavelet. In overall accuracy, the Coif4 wavelet has the best result. The improvement of classification accuracy is different depending on the type of class and the type of wavelet. Using the basis functions with long length could be effective for improving accuracy in classification, especially for the classes of small area. This study is expected to be used as fundamental information for selecting optimal basis function according to the data properties in the 3D DWT based image classification.