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

• Proceedings of the KIEE Conference
• /
• 1987.07b
• /
• pp.1595-1597
• /
• 1987

Two gradient methods, steepest descent method and conjugate gradient descent method, are compar ed through application to vector linear predictors. It is found that the convergence rate of the conju-gate gradient descent method is much faster than that of the steepest descent method.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.15 no.12
• /
• pp.7277-7282
• /
• 2014

In this study, the gradient descent algorithm was used for FLC analysis and the algorithm was used to represent the effects of nonlinear parameters, which alter the antecedent and consequence fuzzy variables of FLC. The controller parameters choose the control variable by iteration for gradient descent algorithm. The FLC consists of 7 membership functions, 49 rules and a two inputs - one output system. The system adopted the Min-Max inference method and triangle type membership function with a 13 quantization level.

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

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

• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.701-716
• /
• 1998

In this paper we develop algorithms in programming lan-guage SCHEME for implementation of the main first order gradient techniques for unconstrained optimization. Implementation of the de-scent techniques which use non-optimal descent steps as well as imple-mentation of the optimal descent techniques are described. Also we investigate implementation of the global problem called optimization along a line. Developed programs are effective and simpler with re-spect to the corresponding in the procedural programming languages. Several numerical examples are reported.

• Journal of Biomedical Engineering Research
• /
• v.28 no.6
• /
• pp.817-824
• /
• 2007

Tractography using Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvector in the white matter of the brain. However, the fiber tracking methods suffer from the noise included in the diffusion tensor images that affects the determination of the principal eigenvector. As the fiber tracking progresses, the accumulated error creates a large deviation between the calculated fiber and the real fiber. This problem of the DT-MRI tractography is known mathematically as the ill-posed problem which means that tractography is very sensitive to perturbations by noise. To reduce the noise in DT-MRI measurements, a tensor-valued median filter which is reported to be denoising and structure-preserving in fiber tracking, is applied in the tractography. In this paper, we proposed the modified gradient descent method which converges fast and accurately to the optimal tensor-valued median filter by changing the step size. In addition, the performance of the modified gradient descent method is compared with others. We used the synthetic image which consists of 45 degree principal eigenvectors and the corticospinal tract. For the synthetic image, the proposed method achieved 4.66%, 16.66% and 15.08% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively. For the corticospinal tract, at iteration number ten the proposed method achieved 3.78%, 25.71 % and 11.54% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively.

• Journal of Korea Water Resources Association
• /
• v.55 no.11
• /
• pp.903-911
• /
• 2022

Groundwater, one of the resources for supplying water, fluctuates in water level due to various natural factors. Recently, research has been conducted to predict fluctuations in groundwater levels using Artificial Neural Network (ANN). Previously, among operators in ANN, Gradient Descent (GD)-based Optimizers were used as Optimizer that affect learning. GD-based Optimizers have disadvantages of initial correlation dependence and absence of solution comparison and storage structure. This study developed Gradient Descent combined with Harmony Search (GDHS), a new Optimizer that combined GD and Harmony Search (HS) to improve the shortcomings of GD-based Optimizers. To evaluate the performance of GDHS, groundwater level at Icheon Yullhyeon observation station were learned and predicted using Multi Layer Perceptron (MLP). Mean Squared Error (MSE) and Mean Absolute Error (MAE) were used to compare the performance of MLP using GD and GDHS. Comparing the learning results, GDHS had lower maximum, minimum, average and Standard Deviation (SD) of MSE than GD. Comparing the prediction results, GDHS was evaluated to have a lower error in all of the evaluation index than GD.

• Genomics & Informatics
• /
• v.5 no.3
• /
• pp.95-101
• /
• 2007

In this paper, we consider the variable selection methods in the Cox model when a large number of gene expression levels are involved with survival time. Deciding which genes are associated with survival time has been a challenging problem because of the large number of genes and relatively small sample size (n<

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.38 no.1
• /
• pp.1-6
• /
• 2001

In this paper we reanalyze Kohonen‘s learning vector quantizing (LVQ) Learning rule which is based on Hcbb’s learning rule with a view to a gradient descent method. Kohonen's LVQ can be classified into two algorithms according to 6learning mode: unsupervised LVQ(ULVQ) and supervised LVQ(SLVQ). These two algorithms can be represented as gradient descent methods, if target values of output neurons are generated properly. As a result, we see that the LVQ learning method is a special case of a gradient descent method and also that LVQ is represented by a generalized percetron-like LVQ(PLVQ).