• Journal of the Korea Society of Computer and Information
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• v.14 no.8
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• pp.11-18
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• 2009

This paper proposes the way of improving learning speed in Levenberg-Marquardt algorithm using the principal submatrix of Jacobian matrix. The Levenberg-Marquardt learning uses Jacobian matrix for Hessian matrix to get the second derivative of an error function. To make the Jacobian matrix an invertible matrix. the Levenberg-Marquardt learning must increase or decrease ${\mu}$ and recalculate the inverse matrix of the Jacobian matrix due to these changes of ${\mu}$. Therefore, to have the proper ${\mu}$, we create the principal submatrix of Jacobian matrix and set the ${\mu}$ as the eigenvalues sum of the principal submatrix. which can make learning speed improve without calculating an additional inverse matrix. We also showed that our method was able to improve learning speed in both a generalized XOR problem and a handwritten digit recognition problem.

• Communications of Mathematical Education
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• v.18 no.3 s.20
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• pp.95-102
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• 2004

수학영재교육이 활성화되기 위해서는 학습자료, 특히 보충 ${\cdot}$ 심화 학습자료의 개발이 시급하다. 이 논문에서는 교육과정에 나타난 행렬의 위치를 파악하여, 문제해결력 신장에 도움이 되는, 행렬을 소재로 한몇 가지 예를 영재교육용 보충 ${\cdot}$ 심화 학습자료로 제시하였다.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.5
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• pp.70-77
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• 1999

본 논문에서는 Wavelet을 이용한 위장 영상의 질환 부위 특징을 추출하여 질환 부위 패턴을 인식할 수 있는 알고리즘을 제안하였다. 전처리 과정으로서 위장 영상이 형태정보는 입력 영상을 DWT(Discrete wavelet transform)에 의해 4레벨 DWT 계수 행렬을 구하고 계수 행렬의 특징에 따라 저주파 계수 행렬로부터 저주파 특징 파라미터 32개, 수평 고주파 계수 행렬로부터 수평 고주파 특징 파라미터 16개, 수직 고주파 계수 행렬로부터 수직 고주파 특징 파라미터 16개, 그리고, 대각 고주파 계수 행렬로부터 대각 고주파 특징 파라미터 32개 등 모두 96개의 특징 파라미터를 추출한 후 각각의 특징 파라미터를 최대 값+0.5로 최소 값을 -0.5로 정규화 하여 신경회로망의 입력 벡터로 사용하였다. 위장 영상 패턴 인식을 위한 신경회로망은 교사 학습을 요구하는 다층 구조의 오차 역전파(Error back propagation)알고리즘으로 하였고 구조적 특성을 이용하여 입력층, 중간층, 출력층의 계층 구조로 설계하였다. 설계된 신경회로망의 학습은 학습계수를 0.2로 모우멘텀을 0.6으로 설정하여 출력층 최대오차가 0.01보다 작을 때까지 수행하였으며 약 8000회 정도 학습한 결과 설정값 보다 작은 결과를 얻었고 질환의 종류나 위치, 크기에 관계없이 100%의 인식률을 얻었다.

• Journal of the Korean School Mathematics Society
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• v.13 no.1
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• pp.125-141
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• 2010

The aim of this paper is to develop a web-based Virtual Learning System for discrete mathematics learning using CAS (Computer Algebra System), The system contains a series of contents that are common between secondary und university curriculum in discrete mathematics such as sets, relations, matrices, graphs etc. We designed and developed web-based virtual learning contents contained in the proposed system based on Mathematia, webMathematica and phpMath taking advantages of rapid computation and visualization. The virtual learning system for discrete math provides movie lectures and 'practice mode' authored with phpMath in order to enhance conceptual understanding of each movie lesson. In particular, matrix learning is facilitated with conceptual diagram that provides interactive quizzes. Once the quiz results are submitted, Bayesian inference network diagnoses strong and weak parts of learning nodes for generating diagnostic reports to facilitate personalized learning. As part of formative evaluation, the overall responses were collected for future revision of the system with 10 university students.

• Proceedings of the Korean Information Science Society Conference
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• 2006.06a
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• pp.52-54
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• 2006

특정한 기능을 하는 DNA 조각은 특정한 염기 서열들을 가진다. 이를 이용하여 특정 조각의 DNA 서열을 위치 점수 행렬을 이용하여 표현할 수 있다. 하지만 찾고자 하는 DNA 부분들이 완전히 밝혀진 것이 아닐 수 있다. 따라서 현재 밝혀진 정보만을 이용하여 위치 점수 행렬을 만들 경우, 실제 서얼 패턴이 아닌 편중된 정보가 얻어질 수 있다. 따라서 본 논문에서는 위치 점수 행렬의 혼합 모델을 이용하여, 각각의 특정 군집들을 대표할 수 있는 행렬들을 구분하여 구성하였다. 본 논문에서는 약 22개의 염기로 구성된 microRNA 서열 중, 초반부의 8개의 염기 서열정보를 이용하여, 이들 위치의 서열상의 특성을 확인해 보고자 하였다. miRNA 서열을 대표하기 위한 위치 점수 행렬들은 구분하여 만들고, EM 알고리즘을 이용하여 학습한다. 학습 결과 얻어진 혼합 모델과 은닉 변수를 통해 microRNA들을 군집화하고, 각각의 군집에 속한 microRNA 서열의 특성을 확인한다.

• Journal for History of Mathematics
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• v.23 no.2
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• pp.89-99
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• 2010

Today linear algebra is one of compulsory courses for university mathematics by virtue of its theoretical fundamentals and fruitful applications. Vector theory and matrix theory constitute of main topics in linear algebra. In the present paper we consider the question which of the two topics is prior in teaching of linear algebra. We suggest that vector theory should be prior to matrix theory contrary to the historical order of them.

• Proceedings of the Korea Multimedia Society Conference
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• 2003.05b
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• pp.210-213
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• 2003

본 연구에서는 뉴우턴법의 고정점 알고리즘에 적응 조정이 가능한 학습파라미터를 이용한 신경망 기반 독립성분분석기법을 제안하였다. 이는 고정점 알고리즘의 1차 미분을 이용하는 뉴우턴법에서 역혼합행렬의 경신 상태에 따라 학습율과 모멘트가 적응조정되도록 함으로써 분리속도와 분리성능을 개선시키기 위함이다. 제안된 기법을 512$\times$512 픽셀의 10개 영상으로부터 임의의 혼합행렬에 따라 발생되는 영상들의 분리에 적용한 결과, 기존의 고정점 알고리즘에 의한 결과보다 우수한 분리성능과 빠른 분리속도가 있음을 확인하였다.

• The Mathematical Education
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• v.62 no.2
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• pp.269-287
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• 2023

Matrix theory is widely used not only in mathematics, natural sciences, and engineering, but also in social sciences and artificial intelligence. In the 2009 revised mathematics curriculum, matrices were removed from high school math education to reduce the burden on students, but in anticipation of the age of artificial intelligence, they will be reintegrated into the 2022 revised education curriculum. Therefore, there is a need to analyze the matrix content covered in other countries to suggest a meaningful direction for matrix education and to derive implications for textbook composition. In this study, we analyzed the German mathematics curriculum and standard education curriculum, as well as the matrix units in the German Hesse state mathematics curriculum and textbook, and identified the characteristics of their content elements and development methods. As a result of our analysis, it was found that the German textbooks cover matrices in three categories: matrices for solving linear equations, matrices for explaining linear transformations, and matrices for explaining transition processes. It was also found that the emphasis was on mathematical reasoning and modeling when learning matrices. Based on these findings, we suggest that if matrices are to be reintegrated into school mathematics, the curriculum should focus on deep conceptual understanding, mathematical reasoning, and mathematical modeling in textbook composition.

• Journal of Korean Society of Transportation
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• v.18 no.4
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• pp.75-85
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• 2000

The Purpose of this study is to analyze wether the composition of training sample have a relation with the Predictive ability and the learning results of ANNs(Artificial Neural Networks) fur predicting one cycle ahead of the queue length(veh.) in a signalized intersection. In this study, ANNs\` training sample is classified into the assumption of two cases. The first is to utilize time-series(Per cycle) data of queue length which would be detected by one detector (loop or video) The second is to use time-space correlated data(such as: a upstream feed-in flow, a link travel time, a approach maximum stationary queue length, a departure volume) which would be detected by a integrative vehicle detection systems (loop detector, video detector, RFIDs) which would be installed between the upstream node(intersection) and downstream node. The major findings from this paper is In Daechi Intersection(GangNamGu, Seoul), in the case of ANNs\` training sample constructed by time-space correlated data between the upstream node(intersection) and downstream node, the pattern recognition ability of an interrupted traffic flow is better.

• Journal of the Korean Institute of Telematics and Electronics T
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• v.35T no.1
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• pp.33-39
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• 1998

This paper discusses approximation modelling of discrete-time linear time-varying system(LTVS). The wavelet transform is considered as a tool for representing and approximating a LTVS. The joint time-frequency properties of wave analysis are appropriate for describing the LTVS. Simulation results is included to illustrate the potential application of the technique.