scholarly journals Efficient 3D Shape Registration by Using Distance Maps and Stochastic Gradient Descent Method

2020 ◽  
Vol 75 (1) ◽  
pp. 81-102
Author(s):  
Polycarp Omondi Okock ◽  
Jozef Urbán ◽  
Karol Mikula
Keyword(s):  
Level Sets ◽  
Gradient Descent ◽  
Descent Method ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Gradient Descent Method ◽  
3D Shape ◽  
Shape Registration ◽  
Gradient Descent Methods ◽  
Speed Up

AbstractThis paper presents an efficient 3D shape registration by using distance maps and stochastic gradient descent method. The proposed algorithm aims to find the optimal affine transformation parameters (translation, scaling and rotation) that maps two distance maps to each other. These distance maps represent the shapes as an interface and we apply level sets methods to calculate the signed distance to these interfaces. To maximize the similarity between the two distance maps, we apply sum of squared difference (SSD) optimization and gradient descent methods to minimize it. To address the shortcomings of the standard gradient descent method, i.e., many iterations to compute the minimum, we implemented the stochastic gradient descent method. The outcome of these two methods are compared to show the advantages of using stochastic gradient descent method. In addition, we implement computational optimization’s such as parallelization to speed up the registration process.

scholarly journals Hyperparameter-free optimizer of stochastic gradient descent that incorporates unit correction and moment estimation

2018 ◽  
Author(s):  
Kazunori D Yamada
Keyword(s):  
Deep Learning ◽  
Gradient Descent ◽  
Mathematical Optimization ◽  
Descent Method ◽  
Learning Rate ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Gradient Descent Method ◽  
Moment Estimation ◽  
Estimation System

ABSTRACTIn the deep learning era, stochastic gradient descent is the most common method used for optimizing neural network parameters. Among the various mathematical optimization methods, the gradient descent method is the most naive. Adjustment of learning rate is necessary for quick convergence, which is normally done manually with gradient descent. Many optimizers have been developed to control the learning rate and increase convergence speed. Generally, these optimizers adjust the learning rate automatically in response to learning status. These optimizers were gradually improved by incorporating the effective aspects of earlier methods. In this study, we developed a new optimizer: YamAdam. Our optimizer is based on Adam, which utilizes the first and second moments of previous gradients. In addition to the moment estimation system, we incorporated an advantageous part of AdaDelta, namely a unit correction system, into YamAdam. According to benchmark tests on some common datasets, our optimizer showed similar or faster convergent performance compared to the existing methods. YamAdam is an option as an alternative optimizer for deep learning.

scholarly journals SSGD: A Safe and Efficient Method of Gradient Descent

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jinhuan Duan ◽  
Xianxian Li ◽  
Shiqi Gao ◽  
Zili Zhong ◽  
Jinyan Wang
Keyword(s):  
Gradient Descent ◽  
Large Scale ◽  
Optimization Problems ◽  
Unit Vector ◽  
Descent Method ◽  
Stochastic Gradient ◽  
Learning System ◽  
Training Data ◽  
Stochastic Gradient Descent ◽  
Gradient Descent Method

With the vigorous development of artificial intelligence technology, various engineering technology applications have been implemented one after another. The gradient descent method plays an important role in solving various optimization problems, due to its simple structure, good stability, and easy implementation. However, in multinode machine learning system, the gradients usually need to be shared, which will cause privacy leakage, because attackers can infer training data with the gradient information. In this paper, to prevent gradient leakage while keeping the accuracy of the model, we propose the super stochastic gradient descent approach to update parameters by concealing the modulus length of gradient vectors and converting it or them into a unit vector. Furthermore, we analyze the security of super stochastic gradient descent approach and demonstrate that our algorithm can defend against the attacks on the gradient. Experiment results show that our approach is obviously superior to prevalent gradient descent approaches in terms of accuracy, robustness, and adaptability to large-scale batches. Interestingly, our algorithm can also resist model poisoning attacks to a certain extent.

scholarly journals Implicit Stochastic Gradient Descent Method for Cross-Domain Recommendation System

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2510
Author(s):  
Nam D. Vo ◽  
Minsung Hong ◽  
Jason J. Jung
Keyword(s):  
Gradient Descent ◽  
Recommendation System ◽  
Computation Time ◽  
Descent Method ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Gradient Descent Method ◽  
Target Domain ◽  
Cross Domain ◽  
Gradient Descent Algorithm

The previous recommendation system applied the matrix factorization collaborative filtering (MFCF) technique to only single domains. Due to data sparsity, this approach has a limitation in overcoming the cold-start problem. Thus, in this study, we focus on discovering latent features from domains to understand the relationships between domains (called domain coherence). This approach uses potential knowledge of the source domain to improve the quality of the target domain recommendation. In this paper, we consider applying MFCF to multiple domains. Mainly, by adopting the implicit stochastic gradient descent algorithm to optimize the objective function for prediction, multiple matrices from different domains are consolidated inside the cross-domain recommendation system (CDRS). Additionally, we design a conceptual framework for CDRS, which applies to different industrial scenarios for recommenders across domains. Moreover, an experiment is devised to validate the proposed method. By using a real-world dataset gathered from Amazon Food and MovieLens, experimental results show that the proposed method improves 15.2% and 19.7% in terms of computation time and MSE over other methods on a utility matrix. Notably, a much lower convergence value of the loss function has been obtained from the experiment. Furthermore, a critical analysis of the obtained results shows that there is a dynamic balance between prediction accuracy and computational complexity.

Sign in / Sign up

Export Citation Format

Share Document