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%.

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.

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.

Thrust Optimization of Flapping Wing via Gradient Descent Technologies

The current work aims at employing a gradient descent algorithm for optimizing the thrust of a flapping wing. An in-house solver has been employed, along with mesh movement methodologies to capture the dynamics of flow around the airfoil. An efficient framework for implementing the coupled solver and optimization in a multicore environment has been implemented for the generation of optimized solutionsmaximizing thrust performance & computational speed.

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.

超椭圆曲线离散对数的Weil Descent代数攻击的分析

本文首先介绍了Galbraith的Weil Descent代数攻击方法,然后对定义在GF(qn)上的形如y2+xy=f(x)的HCDLP能否用Weil Descent代数方法攻击作了详细讨论,作为例子,研究了GF(4)和GF(8)上的这类曲线。得到结论:(1)Weil Descent代数攻击法只能适用于极少部分这类超椭圆曲线;(2)当亏格或基域增大时,Weil Descent方法攻击成功的概率趋向于0。所以说Weil Descent代数攻击法对建立在GF(2n)上的这类超椭圆曲线密码体制并没有太大的威胁。

SPECTRAL MAPPING THEOREM FOR ASCENT,ESSENTIAL ASCENT, DESCENT AND ESSENTIAL DESCENT SPECTRUM OF LINEAR RELATIONS

In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.

Supervised descent method for weld pool boundary extraction during fiber laser welding process

In order to obtain a high-quality weld during the laser welding process, extracting the characteristic parameters of weld pool is an important issue for automated welding. In this paper, the type 304 austenitic stainless steel is welded by a 5 kW high-power fiber laser and a high-speed camera is employed to capture the topside images of weld pools. Then we propose a robust visual-detection approach for the molten pool based on the supervised descent method. It provides an elegant framework for representing the outline of a weld pool and is especially efficient for weld pool detection in the presence of strong uncertainties and disturbances. Finally, welding experimental results verified that the proposed approach can extract the weld pool boundary accurately, which will lay a solid foundation for controlling the weld quality of fiber laser welding process.

A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.

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.

A modified three–term conjugate gradient method with sufficient descent property

A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.

A gradually descent method for discrete global optimization

In this paper, a new method named as the gradually descent method was proposed to solve the discrete global optimization problem. With the aid of an auxiliary function, this method enables to convert the problem of finding one discrete minimizer of the objective function f to that of finding another at each cycle. The auxiliary function can ensure that a point, except a prescribed point, is not its integer stationary point if the value of objective function at the point is greater than the scalar which is chosen properly. This property leads to a better minimizer of f found more easily by some classical local search methods. The computational results show that this algorithm is quite efficient and reliable for solving nonlinear integer programming problems.

Efficient multiuser detector based on box-constrained dichotomous coordinate descent and regularization

The presented iterative multiuser detection technique was based on joint deregularized and box-constrained solution to quadratic optimization with iterations similar to that used in the nonstationary Tikhonov iterated algorithm.The deregularization maximized the energy of the solution,which was opposite to the Tikhonov regularization where the energy was minimized.However,combined with box-constraints,the deregularization forced the solution to be close to the binary set.It further exploited the box-constrained dichotomous coordinate descent algorithm and adapted it to the nonstationary iterative Tikhonov regularization to present an efficient detector.As a result,the worst-case and average complexity are reduced down as K2.8 and K2.5 floating point operation per second,respectively.The development improves the "efficient frontier" in multiuser detection,which is illustrated by simulation results.In addition,most operations in the detector are additions and bit-shifts.This makes the proposed technique attractive for fixed-point hardware implementation.

Comparison of gait properties during level walking and stair ascent and descent with varying loads

This study aimed to compare gait properties during level walking and during stair ascent and descent with varying loads. Fifteen healthy young men (mean age: 22.1 ± 1.6 years) walked while holding four different loads relative to each subject’s body mass (0, 20, 40 and 60% of body mass: BM) on their backs. Stance time, swing time, and double support times were selected as gait parameters. All parameters showed a maximal value during stair ascent and a minimum value during level walking. Stance and double support times increased significan- tly with each load during level walking and during stair ascent and descent. In conclusion, st- air ascent and descent creates more unstable movement than level walking regardless of the weight of the load. The effect of loads on gait increases with the weight of the load and becomes obvious once the load exceeds 60% of BM.

The Convergence of the Steepest Descent Algorithm for D.C.Optimization

Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.

Temperature Prediction Model Identification Using Cyclic Coordinate Descent Based Linear Support Vector Regression

Temperature prediction plays an important role in ring die granulator control,which can influence the quantity and quality of production. Temperature prediction modeling is a complicated problem with its MIMO, nonlinear, and large time-delay characteristics. Support vector machine( SVM) has been successfully based on small data. But its accuracy is not high,in contrast,if the number of data and dimension of feature increase,the training time of model will increase dramatically. In this paper,a linear SVM was applied combing with cyclic coordinate descent( CCD) to solving big data regression. It was mathematically strictly proved and validated by simulation. Meanwhile,real data were conducted to prove the linear SVM model's effect. Compared with other methods for big data in simulation, this algorithm has apparent advantage not only in fast modeling but also in high fitness.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

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.

Ionospheric forecasting model using fuzzy logic-based gradient descent method

Space weather phenomena cause satellite to ground or satellite to aircraft transmission outages over the VHF to L-band frequency range, particularly in the low latitude region. Global Positioning System （GPS） is primarily susceptible to this form of space weather. Faulty GPS signals are attributed to ionospheric error, which is a function of Total Electron Content （TEC）. Importantly, precise forecasts of space weather conditions and appropriate hazard observant cautions required for ionospheric space weather obser- vations are limited. In this paper, a fuzzy logic-based gradient descent method has been proposed to forecast the ionospheric TEC values. In this technique, membership functions have been tuned based on the gradient descent estimated values. The proposed algorithm has been tested with the TEC data of two geomagnetic storms in the low latitude station of KL University, Guntur, India （16.44°N, 80.62°E）. It has been found that the gradient descent method performs well and the predicted TEC values are close to the original TEC measurements.

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.