• Journal of Practical Engineering Education
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• v.14 no.2
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• pp.305-312
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• 2022

In this paper, we focused on training to create and optimize a basic data prediction model. And we proposed a gradient descent training method of machine learning that is widely used to optimize data prediction models. It visually shows the entire operation process of gradient descent used in the process of optimizing parameter values required for data prediction models by applying the differential method and teaches the effective use of mathematical differentiation in machine learning. In order to visually explain the entire operation process of gradient descent, we implement gradient descent SW in a spreadsheet. In this paper, first, a two-variable gradient descent training method is presented, and the accuracy of the two-variable data prediction model is verified by comparison with the error least squares method. Second, a three-variable gradient descent training method is presented and the accuracy of a three-variable data prediction model is verified. Afterwards, the direction of the optimization practice for gradient descent was presented, and the educational effect of the proposed gradient descent method was analyzed through the results of satisfaction with education for non-majors.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.23-48
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• 2007

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1245-1255
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• 2017

The online learning is a process of obtaining the solution for a given objective function where the data is accumulated in real time or in batch units. The stochastic gradient descent method is one of the most widely used for the online learning. This method is not only easy to implement, but also has good properties of the solution under the assumption that the generating model of data is homogeneous. However, the stochastic gradient method could severely mislead the online-learning when the homogeneity is actually violated. We assume that there are two heterogeneous generating models in the observation, and propose the a new stochastic gradient method that mitigate the problem of the heterogeneous models. We introduce a robust mini-batch optimization method using statistical tests and investigate the convergence radius of the solution in the proposed method. Moreover, the theoretical results are confirmed by the numerical simulations.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.2
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• pp.189-194
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• 2020

This paper analyzes the gradient descent method, which is the one most used for learning neural networks. Learning means updating a parameter so the loss function is at its minimum. The loss function quantifies the difference between actual and predicted values. The gradient descent method uses the slope of the loss function to update the parameter to minimize error, and is currently used in libraries that provide the best deep learning algorithms. However, these algorithms are provided in the form of a black box, making it difficult to identify the advantages and disadvantages of various gradient descent methods. This paper analyzes the characteristics of the stochastic gradient descent method, the momentum method, the AdaGrad method, and the Adadelta method, which are currently used gradient descent methods. The experimental data used a modified National Institute of Standards and Technology (MNIST) data set that is widely used to verify neural networks. The hidden layer consists of two layers: the first with 500 neurons, and the second with 300. The activation function of the output layer is the softmax function, and the rectified linear unit function is used for the remaining input and hidden layers. The loss function uses cross-entropy error.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.10 no.2
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• pp.154-160
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• 2017

In this paper, we studied the Bartlett method to correctly estimate the targets of a unmanned vehicles. The Bartlett method estimates the desired signals by making the gain constant for the received signal incident on the array antenna. In this paper, the weights of the Bartlett method are updated by applying the winner method and steepest descent method in order to estimation the accurate unmanned. The updated weights improve the resolution of the existing Bartlett method by applying optimal weights to all received signals received at the array antenna. Through simulation, we are comparative analysis about the performance of proposed method. From result of simulation, We showed the superior performance of the proposed method relative to the classical method, and Bartlett using steep descent method showed more superior than one using wiener method.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.467-482
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• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.10a
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• pp.143-145
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• 2021

The Sihwa River was first planned to be a fresh water lake, but it failed due to serious environment pollution. During times of destruction and regeneration, changes of ecosystem of Sihwa River was visible, especially the algal ecosystem. It's because many seasonal birds pass through the place. This paper analyzes the changes of algal ecosystem of Sihwa River based on eight ecosystem indices. Moreover, using gradient descent, COD is expressed has a function of three ecosystem indices selected from above which is newly defined as SEI, Sihwa Ecosystem Index. In conclusion, we can observe the current ecosystem more easily without its actual data, but only with informations of the ecosystem.

• The Journal of Engineering Geology
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• v.21 no.1
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• pp.25-34
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• 2011

We applied a slope-stability analysis method, considering infiltration by rainfall, to the construction site where an express highway is being extended. Slope stability analysis that considers infiltration by rainfall can be classified into three methods: a method that considers the downward velocity of the wetting front, a method that considers the upward velocity of the groundwater level, and a method that considers both of these factors. The results of slope stability analysis using $Bishop^{\circ}{\Phi}s$ simplified method indicate that the safety factor due to the downward velocity of the wetting front decreases more rapidly than that due to the upward velocity of the groundwater level. For the third of the above methods, the safety factor decreases more rapidly than for the other two methods. Therefore, slope stability during rainfall should be analyzed with consideration of both the downward velocity of the wetting front and the upward velocity of the groundwater level.

• Journal of Korean Society of Steel Construction
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• v.17 no.2 s.75
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• pp.183-194
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• 2005

In the previous construction method of continuous preflex composite girder bridge, we raised the inner support, and cast slab concrete innegative moment section, then lowered it to introduce compressive force in the slab. There were a few problems in the process such as the time required in raising the support and the bending of the camber. Therefore, this paper represents an improved construction method of continuous preflex composite girder by only moving downward the inner and outer supports to figure out problems in previous construction method. This paper proposes a design formula to find a proper cross section of preflex girder.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.186-186
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• 2022

강수 및 침투 등으로 발생하는 지하수위의 변동을 예측하는 것은 지하수 자원의 활용 및 관리에 필수적이다. 지하수위의 변동은 지하수 자원의 활용 및 관리뿐만이 아닌 홍수 발생과 지반의 응력상태 등에 직접적인 영향을 미치기 때문에 정확한 예측이 필요하다. 본 연구는 인공신경망 중 다층퍼셉트론(Multi Layer Perceptron, MLP)을 이용한 지하수위 예측성능 향상을 위해 MLP의 구조 중 Optimizer를 개량하였다. MLP는 입력자료와 출력자료간 최적의 상관관계(가중치 및 편향)를 찾는 Optimizer와 출력되는 값을 결정하는 활성화 함수의 연산을 반복하여 학습한다. 특히 Optimizer는 신경망의 출력값과 관측값의 오차가 최소가 되는 상관관계를 찾는 연산자로써 MLP의 학습 및 예측성능에 직접적인 영향을 미친다. 기존의 Optimizer는 경사하강법(Gradient Descent, GD)을 기반으로 하는 Optimizer를 사용했다. 하지만 기존의 Optimizer는 미분을 이용하여 상관관계를 찾기 때문에 지역탐색 위주로 진행되며 기존에 생성된 상관관계를 저장하는 구조가 없어 지역 최적해로 수렴할 가능성이 있다는 단점이 있다. 본 연구에서는 기존 Optimizer의 단점을 개선하기 위해 지역탐색과 전역탐색을 동시에 고려할 수 있으며 기존의 해를 저장하는 구조가 있는 메타휴리스틱 최적화 알고리즘을 이용하였다. 메타휴리스틱 최적화 알고리즘 중 구조가 간단한 화음탐색법(Harmony Search, HS)과 GD의 결합모형(HS-GD)을 MLP의 Optimizer로 사용하여 기존 Optimizer의 단점을 개선하였다. HS-GD를 이용한 MLP의 성능검토를 위해 이천시 지하수위 예측을 실시하였으며 예측 결과를 기존의 Optimizer를 이용한 MLP 및 HS를 이용한 MLP의 예측결과와 비교하였다.