L_(1)-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection

Brain tumors come in various types,each with distinct characteristics and treatment approaches,making manual detection a time-consuming and potentially ambiguous process.Brain tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment outcomes.Machine learning models have become key players in automating brain tumor detection.Gradient descent methods are the mainstream algorithms for solving machine learning models.In this paper,we propose a novel distributed proximal stochastic gradient descent approach to solve the L_(1)-Smooth Support Vector Machine(SVM)classifier for brain tumor detection.Firstly,the smooth hinge loss is introduced to be used as the loss function of SVM.It avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent optimization.Secondly,the L_(1) regularization method is employed to sparsify features and enhance the robustness of the model.Finally,adaptive proximal stochastic gradient descent(PGD)with momentum,and distributed adaptive PGDwithmomentum(DPGD)are proposed and applied to the L_(1)-Smooth SVM.Distributed computing is crucial in large-scale data analysis,with its value manifested in extending algorithms to distributed clusters,thus enabling more efficient processing ofmassive amounts of data.The DPGD algorithm leverages Spark,enabling full utilization of the computer’s multi-core resources.Due to its sparsity induced by L_(1) regularization on parameters,it exhibits significantly accelerated convergence speed.From the perspective of loss reduction,DPGD converges faster than PGD.The experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor detection.Frompre-trained models,both the PGD andDPGD outperform other models,boasting an accuracy of 95.21%.

Fractional Gradient Descent RBFNN for Active Fault-Tolerant Control of Plant Protection UAVs

With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.

Rockburst Intensity Grade Prediction Model Based on Batch Gradient Descent and Multi-Scale Residual Deep Neural Network

Rockburst is a phenomenon in which free surfaces are formed during excavation,which subsequently causes the sudden release of energy in the construction of mines and tunnels.Light rockburst only peels off rock slices without ejection,while severe rockburst causes casualties and property loss.The frequency and degree of rockburst damage increases with the excavation depth.Moreover,rockburst is the leading engineering geological hazard in the excavation process,and thus the prediction of its intensity grade is of great significance to the development of geotechnical engineering.Therefore,the prediction of rockburst intensity grade is one problem that needs to be solved urgently.By comprehensively considering the occurrence mechanism of rockburst,this paper selects the stress index(σθ/σc),brittleness index(σ_(c)/σ_(t)),and rock elastic energy index(Wet)as the rockburst evaluation indexes through the Spearman coefficient method.This overcomes the low accuracy problem of a single evaluation index prediction method.Following this,the BGD-MSR-DNN rockburst intensity grade prediction model based on batch gradient descent and a multi-scale residual deep neural network is proposed.The batch gradient descent(BGD)module is used to replace the gradient descent algorithm,which effectively improves the efficiency of the network and reduces the model training time.Moreover,the multi-scale residual(MSR)module solves the problem of network degradation when there are too many hidden layers of the deep neural network(DNN),thus improving the model prediction accuracy.The experimental results reveal the BGDMSR-DNN model accuracy to reach 97.1%,outperforming other comparable models.Finally,actual projects such as Qinling Tunnel and Daxiangling Tunnel,reached an accuracy of 100%.The model can be applied in mines and tunnel engineering to realize the accurate and rapid prediction of rockburst intensity grade.

Efficient and High-quality Recommendations via Momentum-incorporated Parallel Stochastic Gradient Descent-Based Learning

A recommender system(RS)relying on latent factor analysis usually adopts stochastic gradient descent(SGD)as its learning algorithm.However,owing to its serial mechanism,an SGD algorithm suffers from low efficiency and scalability when handling large-scale industrial problems.Aiming at addressing this issue,this study proposes a momentum-incorporated parallel stochastic gradient descent(MPSGD)algorithm,whose main idea is two-fold:a)implementing parallelization via a novel datasplitting strategy,and b)accelerating convergence rate by integrating momentum effects into its training process.With it,an MPSGD-based latent factor(MLF)model is achieved,which is capable of performing efficient and high-quality recommendations.Experimental results on four high-dimensional and sparse matrices generated by industrial RS indicate that owing to an MPSGD algorithm,an MLF model outperforms the existing state-of-the-art ones in both computational efficiency and scalability.

PROJECTED GRADIENT DESCENT BASED ON SOFT THRESHOLDING IN MATRIX COMPLETION

Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.

An Efficient Energy Routing Protocol Based on Gradient Descent Method in WSNs

In a wireless sensor network[1],the operation of a node depends on the battery power it carries.Because of the environmental reasons,the node cannot replace the battery.In order to improve the life cycle of the network,energy becomes one of the key problems in the design of the wireless sensor network(WSN)routing protocol[2].This paper proposes a routing protocol ERGD based on the method of gradient descent that can minimizes the consumption of energy.Within the communication radius of the current node,the distance between the current node and the next hop node is assumed that can generate a projected energy at the distance from the current node to the base station(BS),this projected energy and the remaining energy of the next hop node is the key factor in finding the next hop node.The simulation results show that the proposed protocol effectively extends the life cycle of the network and improves the reliability and fault tolerance of the system.

Gradient Descent Algorithm for Small UAV Parameter Estimation System

A gradient descent algorithm with adjustable parameter for attitude estimation is developed,aiming at the attitude measurement for small unmanned aerial vehicle(UAV)in real-time flight conditions.The accelerometer and magnetometer are introduced to construct an error equation with the gyros,thus the drifting characteristics of gyroscope can be compensated by solving the error equation utilized by the gradient descent algorithm.Performance of the presented algorithm is evaluated using a self-proposed micro-electro-mechanical system(MEMS)based attitude heading reference system which is mounted on a tri-axis turntable.The on-ground,turntable and flight experiments indicate that the estimation attitude has a good accuracy.Also,the presented system is compared with an open-source flight control system which runs extended Kalman filter(EKF),and the results show that the attitude control system using the gradient descent method can estimate the attitudes for UAV effectively.

Designing fuzzy inference system based on improved gradient descent method

The distribution of sampling data influences completeness of rule base so that extrapolating missing rules is very difficult. Based on data mining, a self-learning method is developed for identifying fuzzy model and extrapolating missing rules, by means of confidence measure and the improved gradient descent method. The proposed approach can not only identify fuzzy model, update its parameters and determine optimal output fuzzy sets simultaneously, but also resolve the uncontrollable problem led by the regions that data do not cover. The simulation results show the effectiveness and accuracy of the proposed approach with the classical truck backer-upper control problem verifying.

New Diamond Block Based Gradient Descent Search Algorithm for Motion Estimation in the MPEG- 4 Encoder

Motion estimation is an important part of the MPEG- 4 encoder, due to its significant impact on the bit rate and the output quality of the encoder sequence. Unfortunately this feature takes a significant part of the encoding time especially when the straightforward full search(FS) algorithm is used. In this paper, a new algorithm named diamond block based gradient descent search (DBBGDS) algorithm, which is significantly faster than FS and gives similar quality of the output sequence, is proposed. At the same time, some other algorithms, such as three step search (TSS), improved three step search (ITSS), new three step search (NTSS), four step search (4SS), cellular search (CS) , diamond search (DS) and block based gradient descent search (BBGDS), are adopted and compared with DBBGDS. As the experimental results show, DBBGDS has its own advantages. Although DS has been adopted by the MPEG- 4 VM, its output sequence quality is worse than that of the proposed algorithm while its complexity is similar to the proposed one. Compared with BBGDS, the proposed algorithm can achieve a better output quality.

EFFICIENT GRADIENT DESCENT METHOD OFRBF NEURAL ENTWORKS WITHADAPTIVE LEARNING RATE

A new algorithm to exploit the learning rates of gradient descent method is presented, based on the second-order Taylor expansion of the error energy function with respect to learning rate, at some values decided by "award-punish" strategy. Detailed deduction of the algorithm applied to RBF networks is given. Simulation studies show that this algorithm can increase the rate of convergence and improve the performance of the gradient descent method.

Linear Regression and Gradient Descent Method for Electricity Output Power Prediction

Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method together with regularization is investigated to study the electricity output related to vacuum level and temperature in the turbine. Ninety percent of the data was used to train the regression parameters while the remaining ten percent was used for validation. Final results showed that 99% accuracy could be obtained with this method. This opens a new window for electricity output prediction for power plants.

Pure quantum gradient descent algorithm and full quantum variational eigensolver

Optimization problems are prevalent in various fields,and the gradient-based gradient descent algorithm is a widely adopted optimization method.However,in classical computing,computing the numerical gradient for a function with variables necessitates at least d+1 function evaluations,resulting in a computational complexity of O(d).As the number of variables increases,the classical gradient estimation methods require substantial resources,ultimately surpassing the capabilities of classical computers.Fortunately,leveraging the principles of superposition and entanglement in quantum mechanics,quantum computers can achieve genuine parallel computing,leading to exponential acceleration over classical algorithms in some cases.In this paper,we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function.The complexity of this algorithm is just O(1).Building upon this approach,we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver(VQE),creating a pure quantum variational optimization algorithm.Compared with classical gradient-based optimization algorithm,this quantum optimization algorithm has remarkable complexity advantages,providing an efficient solution to optimization problems.The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms,highlighting the potential of quantum computing in this field.

Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism

In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked.Based on this result,a fractional order iteration approach has been developed by modelling the system with fractional order dynamics.Secondly,to reduce the comsumption of computation,a feedback based event-triggered mechanism has been introduced to the gradient descent method.The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method,and Zeno behavior is proved to be avoided simultaneously.Lastly,the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.

A Stochastic Gradient Descent Method for Computational Design of Random Rough Surfaces in Solar Cells

In this work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar cells.We formulate the design problems as random PDE-constrained optimization problems and seek the optimal statistical parameters for the random surfaces.The optimizations at fixed frequency as well as at multiple frequencies and multiple incident angles are investigated.To evaluate the gradient of the objective function,we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the computation.The stochastic gradient descent method evaluates the gradient of the objective function only at a few samples for each iteration,which reduces the computational cost significantly.Various numerical experiments are conducted to illustrate the efficiency of the method and significant increases of the absorptance for the optimal random structures.We also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions for the random interfaces.

A Gradient Descent Method for Estimating the Markov Chain Choice Model

In this paper,we propose a gradient descent method to estimate the parameters in a Markov chain choice model.Particularly,we derive closed-form formula for the gradient of the log-likelihood function and show the convergence of the algorithm.Numerical experiments verify the efficiency of our approach by comparing with the expectation-maximization algorithm.We show that the similar result can be extended to a more general case that one does not have observation of the no-purchase data.

Stochastic Gradient Compression for Federated Learning over Wireless Network

As a mature distributed machine learning paradigm,federated learning enables wireless edge devices to collaboratively train a shared AI-model by stochastic gradient descent(SGD).However,devices need to upload high-dimensional stochastic gradients to edge server in training,which cause severe communication bottleneck.To address this problem,we compress the communication by sparsifying and quantizing the stochastic gradients of edge devices.We first derive a closed form of the communication compression in terms of sparsification and quantization factors.Then,the convergence rate of this communicationcompressed system is analyzed and several insights are obtained.Finally,we formulate and deal with the quantization resource allocation problem for the goal of minimizing the convergence upper bound,under the constraint of multiple-access channel capacity.Simulations show that the proposed scheme outperforms the benchmarks.

Anderson Acceleration of Gradient Methods with Energy for Optimization Problems

Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experimental results show that the proposed AA-AEGD algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.

Convergence of Stochastic Gradient Descent in Deep Neural Network

Stochastic gradient descent(SGD) is one of the most common optimization algorithms used in pattern recognition and machine learning.This algorithm and its variants are the preferred algorithm while optimizing parameters of deep neural network for their advantages of low storage space requirement and fast computation speed.Previous studies on convergence of these algorithms were based on some traditional assumptions in optimization problems.However,the deep neural network has its unique properties.Some assumptions are inappropriate in the actual optimization process of this kind of model.In this paper,we modify the assumptions to make them more consistent with the actual optimization process of deep neural network.Based on new assumptions,we studied the convergence and convergence rate of SGD and its two common variant algorithms.In addition,we carried out numerical experiments with LeNet-5,a common network framework,on the data set MNIST to verify the rationality of our assumptions.

Convergence analysis of projected gradient descent for Schatten-p nonconvex matrix recovery

The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization(0 < p < 1) problem.Based on the matrix restricted isometry property(M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.