• 한국농공학회논문집
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• 제63권1호
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• pp.103-116
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• 2021

Analysis of runoff is substantial for effective water management in the watershed. Runoff occurs by reaction of a watershed to the rainfall and has non-linearity and uncertainty due to the complex relation of weather and watershed factors. ANN (Artificial Neural Network), which learns from the data, is one of the machine learning technique known as a proper model to interpret non-linear data. The performance of ANN is affected by the ANN's structure, the number of hidden layer nodes, learning rate, and activation function. Especially, the activation function has a role to deliver the information entered and decides the way of making output. Therefore, It is important to apply appropriate activation functions according to the problem to solve. In this paper, ANN models were constructed to estimate runoff with different activation functions and each model was compared and evaluated. Sigmoid, Hyperbolic tangent, ReLU (Rectified Linear Unit), ELU (Exponential Linear Unit) functions were applied to the hidden layer, and Identity, ReLU, Softplus functions applied to the output layer. The statistical parameters including coefficient of determination, NSE (Nash and Sutcliffe Efficiency), NSEln (modified NSE), and PBIAS (Percent BIAS) were utilized to evaluate the ANN models. From the result, applications of Hyperbolic tangent function and ELU function to the hidden layer and Identity function to the output layer show competent performance rather than other functions which demonstrated the function selection in the ANN structure can affect the performance of ANN.

• 한국인터넷방송통신학회논문지
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• 제22권6호
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• pp.75-81
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• 2022

주차 공간의 부족함을 획기적으로 해결할 수 있는 자율주행 자동차는 심층 강화 학습을 통해 큰 발전을 이루고 있다. 심층 강화 학습에는 활성화 함수가 사용되는데, 그동안 다양한 활성화 함수가 제안되어 왔으나 적용 환경에 따라 그 성능 편차가 심했다. 따라서 환경에 따라 최적의 활성화 함수를 찾는 것이 효과적인 학습을 위해 중요하다. 본 논문은 자율주행 자동차가 주차를 학습하기 위해 심층 강화 학습을 사용할 때 어떤 활성화 함수를 사용하는 것이 가장 효과적인지 비교 평가하기 위해 강화 학습에 주로 사용되는 12개의 함수를 분석하였다. 이를 위해 성능 평가 환경을 구축하고 각 활성화 함수의 평균 보상을 성공률, 에피소드 길이, 자동차 속도와 비교하였다. 그 결과 가장 높은 보상은 GELU를 사용한 경우였고, ELU는 가장 낮았다. 두 활성화 함수의 보상 차이는 35.2%였다.

• 한국농공학회논문집
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• 제63권1호
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• pp.11-25
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• 2021

The objective of this study was to analyze the impact of activation functions on flood forecasting model based on Artificial neural networks (ANNs). The traditional activation functions, the sigmoid and tanh functions, were compared with the functions which have been recently recommended for deep neural networks; the ReLU, leaky ReLU, and ELU functions. The flood forecasting model based on ANNs was designed to predict real-time runoff for 1 to 6-h lead time using the rainfall and runoff data of the past nine hours. The statistical measures such as R2, Nash-Sutcliffe Efficiency (NSE), Root Mean Squared Error (RMSE), the error of peak time (ETp), and the error of peak discharge (EQp) were used to evaluate the model accuracy. The tanh and ELU functions were most accurate with R2=0.97 and RMSE=30.1 (㎥/s) for 1-h lead time and R2=0.56 and RMSE=124.6~124.8 (㎥/s) for 6-h lead time. We also evaluated the learning speed by using the number of epochs that minimizes errors. The sigmoid function had the slowest learning speed due to the 'vanishing gradient problem' and the limited direction of weight update. The learning speed of the ELU function was 1.2 times faster than the tanh function. As a result, the ELU function most effectively improved the accuracy and speed of the ANNs model, so it was determined to be the best activation function for ANNs-based flood forecasting.

• Journal of Applied and Pure Mathematics
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• 제4권5_6호
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• pp.269-286
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• 2022

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝ^N , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

• 한국인터넷방송통신학회논문지
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• 제19권2호
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• pp.135-141
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• 2019

최근 강화 학습을 통해 게임을 학습하는 인공지능 에이전트를 만드는 연구가 활발히 진행되고 있다. 게임을 에이전트에게 학습 시킬 때 어떠한 딥러닝 활성화 함수를 사용하는지에 따라 그 학습 성능이 달라진다. 본 논문은 2D 슈팅 게임 환경에서 에이전트가 강화 학습을 통해 게임을 학습할 경우 어떤 활성화 함수가 최적의 결과를 얻는지를 비교 평가 한다. 이를 위해 비교 평가에서 사용할 메트릭을 정의하고 각 활성화 함수에 따른 메트릭 값을 학습 시간에 따라 그래프로 나타내었다. 그 결과 ELU (Exponential Linear Unit) 활성화 함수에 1.0으로 파라미터 값을 설정할 경우 게임의 보상 값이 다른 활성화 함수보다 평균적으로 높은 것을 알 수 있었고, 가장 낮은 보상 값을 가졌던 활성화 함수와의 차이는 23.6%였다.

• Communications for Statistical Applications and Methods
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• 제28권3호
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• pp.281-294
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• 2021

In this paper, we propose an adaptive regression method based on the single-layer neural network structure. We adopt a symmetric activation function as units of the structure. The activation function has a flexibility of its form with a parametrization and has a localizing property that is useful to improve the quality of estimation. In order to provide a spatially adaptive estimator, we regularize coefficients of the activation functions via ℓ₁-penalization, through which the activation functions to be regarded as unnecessary are removed. In implementation, an efficient coordinate descent algorithm is applied for the proposed estimator. To obtain the stable results of estimation, we present an initialization scheme suited for our structure. Model selection procedure based on the Akaike information criterion is described. The simulation results show that the proposed estimator performs favorably in relation to existing methods and recovers the local structure of the underlying function based on the sample.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2008년도 하계종합학술대회
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• pp.679-680
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• 2008

When we apply the neural networks to applications, we need to select proper architecture of the network and the activation function of the network is one of most important characteristics. In this research, we propose a method to make a network using multiple activation functions. The performance of the proposed method is investigated through the computer simulations on various regression problems.

• ETRI Journal
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• 제15권2호
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• pp.35-51
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• 1993

This paper presents function approximation based on nonparametric estimation. As an estimation model of function approximation, a three layered network composed of input, hidden and output layers is considered. The input and output layers have linear activation units while the hidden layer has nonlinear activation units or kernel functions which have the characteristics of bounds and locality. Using this type of network, a many-to-one function is synthesized over the domain of the input space by a number of kernel functions. In this network, we have to estimate the necessary number of kernel functions as well as the parameters associated with kernel functions. For this purpose, a new method of parameter estimation in which linear learning rule is applied between hidden and output layers while nonlinear (piecewise-linear) learning rule is applied between input and hidden layers, is considered. The linear learning rule updates the output weights between hidden and output layers based on the Linear Minimization of Mean Square Error (LMMSE) sense in the space of kernel functions while the nonlinear learning rule updates the parameters of kernel functions based on the gradient of the actual output of network with respect to the parameters (especially, the shape) of kernel functions. This approach of parameter adaptation provides near optimal values of the parameters associated with kernel functions in the sense of minimizing mean square error. As a result, the suggested nonparametric estimation provides an efficient way of function approximation from the view point of the number of kernel functions as well as learning speed.

• 한국인터넷방송통신학회논문지
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• 제21권6호
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• pp.117-122
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• 2021

자율주행은 자동차가 사람 없이 운전할 수 있도록 해 주며 최근 인공지능 기술의 발전에 힘입어 매우 활발히 연구되고 있다. 인공지능 기술 중에서도 특히 심층 강화 학습이 가장 효과적으로 사용되는데 이를 위해서는 적절한 활성화 함수를 이용한 신경망 구축이 필수적이다. 여태껏 많은 활성화 함수가 제시됐으나 적용 분야에 따라 서로 다른 성능을 보여주었다. 본 논문은 교차로에서 자율주행을 학습하기 위해 심층 강화 학습을 사용할 때 어떤 활성화 함수를 사용하는 것이 효과적인지 성능을 비교 평가한다. 이를 위해 평가에서 사용할 성능 메트릭을 정의하고 각 활성화 함수에 따른 메트릭의 값을 그래프로 비교하였다. 그 결과 Mish를 사용할 경우 보상이 다른 활성화 함수보다 평균적으로 높은 것을 알 수 있었고 보상이 가장 낮은 활성화 함수와의 차이는 9.8%였다.

• 전자공학회논문지CI
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• 제49권2호
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• pp.115-122
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• 2012

본 논문에서는 CosGauss라고 하는 코사인함수로 모듈화 된 가우시안 활성화함수가 뉴로 네트워크에서 다항식과 계단함수의 근사에 사용될 수 있음을 증명한다. CosGauss 함수는 시그모이드, 하이퍼볼릭 탄젠트, 가우시안 활성화 함수보다 더 많은 범프(bump)를 구성 할 수 있다. 이 함수를 캐스케이드 코릴레이션 뉴로 네트워크 학습에 사용하여 벤치마크 문제인 Tic-Tac-Toe 게임과 아이리스(iris) 식물 문제와 실험하고 여기에서 얻어진 결과를 다른 활성화 함수를 사용한 결과와 비교 분석한다.