scholarly journals Constrained stochastic gradient descent for large-scale least squares problem

2013 ◽  
Author(s):  
Yang Mu ◽  
Wei Ding ◽  
Tianyi Zhou ◽  
Dacheng Tao
Keyword(s):  
Least Squares ◽  
Gradient Descent ◽  
Large Scale ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Least Squares Problem

scholarly journals Stochastic Subgradient for Large-Scale Support Vector Machine Using the Generalized Pinball Loss Function

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1652
Author(s):  
Wanida Panup ◽  
Rabian Wangkeeree
Keyword(s):  
Support Vector Machine ◽  
Loss Function ◽  
Gradient Descent ◽  
Large Scale ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Support Vector ◽  
Hinge Loss ◽  
Gradient Descent Algorithm ◽  
Pinball Loss

In this paper, we propose a stochastic gradient descent algorithm, called stochastic gradient descent method-based generalized pinball support vector machine (SG-GPSVM), to solve data classification problems. This approach was developed by replacing the hinge loss function in the conventional support vector machine (SVM) with a generalized pinball loss function. We show that SG-GPSVM is convergent and that it approximates the conventional generalized pinball support vector machine (GPSVM). Further, the symmetric kernel method was adopted to evaluate the performance of SG-GPSVM as a nonlinear classifier. Our suggested algorithm surpasses existing methods in terms of noise insensitivity, resampling stability, and accuracy for large-scale data scenarios, according to the experimental results.

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 On the Convergence Properties of a K-step Averaging Stochastic Gradient Descent Algorithm for Nonconvex Optimization

2018 ◽  
Author(s):  
Fan Zhou ◽  
Guojing Cong
Keyword(s):  
Gradient Descent ◽  
Large Scale ◽  
Stochastic Gradient ◽  
Learning Problems ◽  
Stochastic Gradient Descent ◽  
Convergence Properties ◽  
Descent Algorithm ◽  
Convergence Results ◽  
Gradient Descent Algorithm ◽  
Parallel Stochastic Gradient Descent

We adopt and analyze a synchronous K-step averaging stochastic gradient descent algorithm which we call K-AVG  for solving large scale machine learning problems. We establish the convergence results of K-AVG for nonconvex objectives. Our analysis of K-AVG applies to many existing variants of synchronous SGD.  We explain why the K-step delay is necessary and leads to better performance than traditional parallel stochastic gradient descent which is equivalent to K-AVG with $K=1$. We also show that K-AVG scales better with the number of learners than asynchronous stochastic gradient descent (ASGD). Another advantage of K-AVG over ASGD is that it allows larger stepsizes and facilitates faster convergence. On a cluster of $128$ GPUs, K-AVG is faster than ASGD implementations and achieves better accuracies and faster convergence for training with the CIFAR-10 dataset.

Stochastic Gradient Descent Based K-Means Algorithm on Large Scale Data Clustering

2014 ◽  
Vol 687-691 ◽  
pp. 1342-1345 ◽  
Author(s):  
Jie Ding ◽  
Li Peng Zhu ◽  
Bin Hu ◽  
Ren Long Hang ◽  
Yu Bao Sun
Keyword(s):  
Gradient Descent ◽  
Large Scale ◽  
Clustering Algorithm ◽  
Distance Matrix ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Data Sets ◽  
Human Beings ◽  
Large Scale Data ◽  
Scale Data

With the rapid advance of data collection and storage technique, it is easy to acquire tens of millions or even billions of data sets. How to explore and exploit the useful or interesting information for human beings from these data sets has become an urgent issue. Traditional k-means clustering algorithm has been widely used in data mining community. First, randomly initialize k clustering centres. Then, all instances are classified into k different classes according to their distances to clustering centres. Lastly, update the clustering centres by the mean of its corresponding constituent instances. This whole process will be iterated until convergence. Obviously, at each iteration, distance matrix from all instances to k clustering centres must be calculated which will cost so much time when encounter large scale data sets. To address this issue, in this paper, we proposed a fast optimization algorithm based on stochastic gradient descent (SGD). At each iteration, randomly choose an instance, search its corresponding clustering centre and then update it immediately. Experimental results show that our proposed method achieves a competitive clustering results with less time cost.

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