• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.841-862
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• 2013

This study analyzed issues in the mathematics curriculum concerning the cognitive development of the vector and inner product concepts in the light of Tall's and Watson's research(Tall, 2004a; Tall, 2004b; Watson et al., 2003; Watson, 2002). Some suggestions in teaching the vector and inner product concepts were elaborated in the terms of these analyses. First, the position vector needs to be represented by an arrow on the coordinate system in order to introduce the component form of a vector represented by a directed line segment. Second, proofs of the vector operation law should be carried out by symbolic manipulations based on the algebraic concept of a vector in the symbolic world. Third, it is appropriate that the inner product is defined as $\vec{a}{\cdot}\vec{b}=a_1b_1+a_2b_2$ (when, $\vec{a}=(a_1,a_2)$, $\vec{b}=(b_1,b_2)$) when it comes to considering the meaning of the inner product relevant to vector space in the formal world. Cognitive growth of concepts of the vector and inner product can be properly induced through revising explanation methods about the concepts in the curriculum in the basis of the above suggestions.

• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Korean Journal of Remote Sensing
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• v.24 no.6
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• pp.641-644
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• 2008

In order to improve a camera rotation calculation based on the bundle adjustment in Chon's camera motion (Chon and Shankar, 2007, 2008), this paper introduces a method calculating the camera rotation. It estimates a unit vector in the optical axis of a camera through the angles between the optical axis and vectors passing a camera position and ground control points (GCP). The camera position is estimated by using the inner product method proposed by Chon. The horizontal and vertical unit vectors of the camera are determined by using Yakimovsky and Cunningham's camera model (CAHV) (1978).

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.177-188
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• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

• Annual Conference on Human and Language Technology
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• 2020.10a
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• pp.427-432
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• 2020

딥러닝(Deep-learning) 기반의 자연어 이해(Natural Language Understanding) 기술들은 최근에 상당한 성과를 성취했다. 하지만 딥러닝 기반의 자연어 이해 기술들은 내적인 동작들과 결정에 대한 근거를 설명하기 어렵다. 본 논문에서는 벡터를 그래프로 변환함으로써 신경망의 내적인 의미 표현들을 설명할 수 있도록 한다. 먼저 인간과 기계 모두가 이해 가능한 표현방법의 하나로 그래프를 주요 표현방법으로 선택하였다. 또한 그래프의 구성요소인 노드(Node) 및 엣지(Edge)의 결정을 위한 Element-Importance Inverse-Semantic-Importance(EI-ISI) 점수와 Element-Element-Correlation(EEC) 점수를 심층신경망의 훈련방법 중 하나인 드랍아웃(Dropout)을 통해 계산하는 방법을 제안한다. 다양한 실험들을 통해, 본 연구에서 제안한 벡터-그래프(Vector2graph) 변환 프레임워크가 성공적으로 벡터의 의미정보를 유지하면서도, 설명 가능한 그래프를 생성함을 보인다. 더불어, 그래프 기반의 새로운 시각화 방법을 소개한다.

• The Transactions of the Korea Information Processing Society
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• v.7 no.12
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• pp.3986-3994
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• 2000

A multiple vector reductive processing occurs during the vector inner product operation ([C] = [A] $\bigodot$,$\square$ [B]) and proceeds at the hardware dyadic pipeline unit. Every scalar result has to be generated with the component merging delay time in the multiple vector reduction($\bigodot$). In this paper we propose a new design method by which the component merging time could be eliminated from the multiple reduction and the scalar results from the reduction($\bigodot$) could be generated nearly in the almost same condensed time as the input components are fel>ded in the dyadic pipeline unitlo) or the output components are drained out of the dyadic pipeline unit($\square$), so called a dedicated chained pipeline unit for only a inner product operation.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.11
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• pp.124-129
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• 2013

This paper proposes a high-performance vector inner product calculation circuit for real-time object recognition based on SVM algorithm. SVM algorithm shows a higher detection rate than other object recognition algorithms. However, it requires a huge amount of computational efforts. Since vector inner product calculation is one of the major operations of SVM algorithm, it is important to implement a high-performance vector inner product calculation circuit for real-time object recognition capability. The proposed circuit adopts the pipeline architecture with six stages to increase the operating speed and makes it possible to recognize objects in real time based on SVM. The proposed circuit was described in Verilog HDL at RTL. For silicon verification, an MPW chip was fabricated using TSMC 180nm standard cell library. The operation of the implemented MPW chip was verified on the test board with test application software developed for the chip verification.

• Korean Journal of Remote Sensing
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• v.23 no.6
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• pp.553-558
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• 2007

The equation based on vector inner product by the angles between pairs of two image rays can independently separate the position and pose of a camera. As our second application, the exterior calibration between a camera and a laser range finder is proposed here through analysis of surfaces created by the equation.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.2
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• pp.129-137
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• 2001

Matching pursuit algorithm was successfully demonstrated useful in low bit-rate video coding, However, one of the practical concerns related to applying the matching pursuit algorithm to application is its massive computation required for finding bases whose weighted sum best approximates the given input image. The main contribution of this paper is that we provide a new method that can drastically reduce the computational load without any degradation of image quality. Its main idea is based on reducing the number of inner product calculation required for finding best bases because the complexity of matching pursuit algorithm is due to the exhaustive local inner product calculation. As the first step, we compute a matrix which is the 1-D inner product of the given motion-compensated error input image with the 1-D vertical Gabor functions using the separable property of Gabor bases. In the second step, we calculate length of each vector in the matrix that corresponds to 1-D horizontal Gabor function, and compare the length with the current maximum absolute inner product value so far. According to the result of this comparison, one can decide whether or not to calculate the inner product. Since most of them do not need to calculate the inner product value, one can significantly reduce the computational load. Experimental results show that proposed method reduces about 70% of inner product calculation compared to the Neff's fast algorithm without any degradation of image quality.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10b
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• pp.592-594
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• 2003

이 논문에서는 wavelet과 sobel filter를 사용하여 영상의 객관적인 평가 점수를 계산하는 새로운 기법을 제안한다. 이 기법은 orthogonal wavelet 변환을 기초로 하고 있으며 원본 영상과 처리된 영상 데이터가 모두 가용하다는 것을 전제로 한다. Wavelet을 이용해 주파수에 따라 분할된 영상 정보를 이용해 각각의 부영역 별 차영상을 획득하고 이 획득된 영상의 에너지를 이용해 화질 평가 수치를 계산한다. 부영역 별로 획득된 영상은 일정한 크기의 블록으로 분할되어 동일한 블록 내에서 가용한 영상의 특징에 관한 정보(contrast, edge 영역의 분포 정도) 벡터와 내적하여 새로운 특징 벡터로 사용되고, 이 특징 벡터의 가중치를 최적화하여 높은 상관도의 화질평가 점수를 산출하게 된다.