• Journal of the Korean School Mathematics Society
• /
• v.7 no.2
• /
• pp.81-97
• /
• 2004

This paper is a study on the understanding process of「Matrix and Graph」on discrete mathematics using TI-92 calculator. For this purpose, we investigated the understanding process of two middle school students learning the concepts of matrix and graph using TI-92 calculator. In this process, we collected qualitative data using recorder and video camera. Then we categorized these data as follows: students' attitude related to using technology, understanding process of meaning, expression and operation of matrix and graph, mathematical communication, etc. From this, we have the following conclusions: First, students inquired out the meaning and role of matrix by themselves using calculator. We could see that calculator can do the role of good learning partner to them. Second, students realized their own mistakes when they used calculator on the process of learning matrix. So we found that calculator could form the self-leading learning circumstance on learning matrix. Third, calculators reinforce the mathematical communication in learning matrix and graph. That is, calculator could be a good mediator to reinforce mathematical communication between teacher and students, among students on learning matrix and graph.

• Proceedings of the Korea Multimedia Society Conference
• /
• 2003.05b
• /
• pp.138-141
• /
• 2003

본 연구에서는 뉴우턴법의 고정점 알고리즘에 학습파라미터를 추가한 새로운 고정점 알고리즘의 신경망 기반 독립성분분석기법을 제안하였다. 이는 목적함수의 1차 미분을 이용하는 뉴우턴법에서 역혼합행렬의 경신을 빠르게 하기 위함이고, 모멘트는 접선을 구하는 과정에서 함수의 기울기변화에 따른 발진을 줄여 좀 더욱 더 빠른 학습을 하기 위함이다. 제안된 기법을 512×512 픽셀의 5개 영상으로부터 임의의 혼합행렬에 따라 발생되는 영상들을 각각 대상으로 시뮬레이션 한 결과, 기존의 고정점 알고리즘은 학습파리미터에 영향을 받으며, 적절한 파라미터값의 설정(학습율 1, 모멘트 0.0001)은 보다 우수한 분리성능과 빠른 분리속도를 얻을 수 있음을 확인하였다.

• Proceedings of the Korea Multimedia Society Conference
• /
• 2002.05c
• /
• pp.320-324
• /
• 2002

본 연구에서는 모멘트와 뉴우턴법 및 모멘트와 할선법에 각각 기초한 고정점 알고리즘의 신경망 기반 독립성분분석 기법을 제안하였다. 여기서 뉴우턴법과 할선법은 각각 엔트로피에 기초한 목적함수의 근을 구하는 근사화 방법으로 빠른 경신을 위함이고, 모멘트는 근사화에 의한 역혼합행렬의 경신과정에서 발생하는 발진을 줄여 좀 더 빠른 학습을 위함이다. 제안된 기법을 256×256 픽셀(pixel)의 8개 지문영상으로부터 임의의 혼합행렬에 따라 발생되는 영상들을 각각 대상으로 시뮬레이션 한 결과, 모멘트와 할선법에 기초한 알고리즘이 모멘트와 뉴우턴에 기초한 알고리즘보다 우수한 분리성능과 빠른 학습속도가 있음을 확인하였다.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.26 no.11
• /
• pp.1623-1629
• /
• 2022

Matrix multiplication is a fundamental operation widely used in science and engineering. There is an approximate matrix multiplication method as a way to reduce the amount of computation of matrix multiplication. Approximate matrix multiplication determines an appropriate probability distribution for selecting columns and rows of matrices, and performs approximate matrix multiplication by selecting columns and rows of matrices according to this distribution. Probability distributions are generated by considering both matrices A and B participating in matrix multiplication. In this paper, we propose a method to generate a probability distribution that selects columns and rows of matrices to be used for approximate matrix multiplication, targeting only matrix A. Approximate matrix multiplication was performed on 1000×1000 ~ 5000×5000 matrices using existing and proposed methods. The approximate matrix multiplication applying the proposed method compared to the conventional method has been shown to be closer to the original matrix multiplication result, averaging 0.02% to 2.34%.

• Proceedings of the Korean Information Science Society Conference
• /
• 2006.06a
• /
• pp.391-393
• /
• 2006

인터넷의 급속한 확산과 대량 정보의 이동은 문서의 요약을 더욱 필요로 하고 있다. 본 논문은 비음수 행렬 인수분해로(NMF, non-negative matrix factorization) 얻어진 비음수 의미 가변 행렬(NSVM, non-negative semantic variable matrix)을 이용하여 자동으로 포괄적 문서요약 하는 새로운 방범을 제안하였다. 제안된 방법은 인간의 인식 과정과 유사한 비음수 제약을 사용한다. 이 결과 잠재의미색인에 비해 더욱 의미 있는 문장을 선택하여 문서를 요약할 수 있다. 또한, 비지도 학습에 의한 문서요약으로 사전 전문가에 의한 학습문장이 필요 없으며, 적은 계산비용을 통하여 쉽게 문장을 추출할 수 있는 장점을 갖는다.

• Communications of Mathematical Education
• /
• v.37 no.3
• /
• pp.443-465
• /
• 2023

This study examines the content of vectors and matrices in Artificial Intelligence Mathematics textbooks (AIMTs) from the 2015 revised mathematics curriculum. We analyzed the implementation of foundational mathematical concepts, specifically definitions and related sub-concepts of vectors and matrices, in these textbooks, given their importance for understanding AI. The findings reveal significant variations in the presentation of vector-related concepts, definitions, sub-concepts, and levels of contextual information and descriptions such as vector size, distance between vectors, and mathematical interpretation. While there are few discrepancies in the presentation of fundamental matrix concepts, differences emerge in the subtypes of matrices used and the matrix operations applied in image data processing across textbooks. There is also variation in how textbooks emphasize the interconnectedness of mathematics for explaining vector-related concepts versus the textbooks place more emphasis on AI-related knowledge than on mathematical concepts and principles. The implications for future curriculum development and textbook design are discussed, providing insights into improving AI mathematics education.

• Journal of Advanced Navigation Technology
• /
• v.12 no.4
• /
• pp.372-377
• /
• 2008

This paper proposes a new query-based document summarization method using the semantic feature matrix and the semantic variable matrix. The proposed method doesn't need the training phase using training data comprising queries and query specific documents. And it exactly summarizes documents for the given query by using semantic features and semantic variables that is better at identifying sub-topics of document. Because the NMF have a great power to naturally extract semantic features representing the inherent structure of a document. The experimental results show that the proposed method achieves better performance than other methods.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.54 no.3
• /
• pp.55-62
• /
• 2017

Non-negative matrix factorization (NMF) is one of the typical parts-based representation in which images are expressed as a linear combination of basis vectors that show the lcoal features or objects in the images. In this paper, we represent face images using various NMF methods and recognize their face identities based on extracted features using a learning vector quantization. We analyzed the various NMF methods by comparing extracted basis vectors. Also we confirmed the availability of NMF to the face recognition by verification of recognition rate of the various NMF methods.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.33 no.3
• /
• pp.39-46
• /
• 2005

In this paper, adaptive higher harmonic control technique using Neural Networks (NN) is proposed. First, linear transfer function is estimated to relate the input harmonics and output harmonics, then NN which has the universal function approximation property is applied to expand application range of the transfer function. Optimal control gain matrix computed from the transfer function is used to train NN weights. Online weight adaptation laws are derived from Lyapunov's direct method to guarantee internal stability. Results of the simulation of 6-input 2-output nonlinear system show that adaptive HHC is applicable to the system with uncertain transfer function.

• Journal of Digital Contents Society
• /
• v.16 no.4
• /
• pp.605-613
• /
• 2015

This paper addresses the problem to make sparse the projection matrix in pattern recognition method. Recently, the size of computer program is often restricted in embedded systems. It is very often that developed programs include some constant data. For example, many pattern recognition programs use the projection matrix for dimension reduction. To improve the recognition performance, very high dimensional feature vectors are often extracted. In this case, the projection matrix can be very big. Recently, RSR(roated sparse regression) method[1] was proposed. This method has been proved one of the best algorithm that obtains the sparse matrix. We propose three methods to improve the RSR; outlier removal, sampling and elastic net RSR(E-RSR) in which the penalty term in RSR optimization function is replaced by that of the elastic net regression. The experimental results show that the proposed methods are very effective and improve the sparsity rate dramatically without sacrificing the recognition rate compared to the original RSR method.