基于目前最优化方法理论教学与实验教学脱节的现状,设计了一套实验课程,包括基本算法和课程项目两大模块,分别覆盖了经典的最速下降法、Newton法、拟Newton法、共轭梯度法、惩罚函数法和近年来广泛使用的随机梯度下降法、支持向量机算法等.该实验课程能有效衔接最优化方法的理论与实验教学,有助于学生深入理解最优化理论及思想、掌握最优化算法设计技巧、提升创新能力和工程实践能力.

In this paper, we obtain a sinc discretization method for solving the boundary value problems of differential-algebraic equations (DAEs) and prove that the discrete solutions converge to the true solutions of the DAEs exponentially. In the process of presenting the solution, we find that the discrete solution is determined by a large and ill-conditioned linear system. To efficiently solve the linear system, we construct block-tridiagonal preconditioners for the iterative methods. Moreover, we derive the bounds for the eigenvalues of the preconditioned matrices. Numerical experiments are given to illustrate the effective performance and applicability of our method.

地表温度作为衡量地球表面水热平衡的关键参数,具有两大时空分布特征:第一,空间分布一致性,即属性相近的像元地表温度与其地表亮温间的相关关系相对稳定;第二,时间序列周期性,且同一地区时间越接近地表温度值越相似.基于这两大特征将空间统计模型与时间序列滤波相结合,提出了用于云下像元地表温度重建的时空联合算法.以2008年MODIS地表温度产品为研究对象,采用Landsat TM数据和AMSR E地表亮温数据重建中国9个省份的地表温度值,并与基于MODIS地表分类产品的多通道统计模型重建结果进行对比.实验结果表明,所提算法实用性强,能有效实现大面积复杂下垫面区域的地表温度重建;平均重建误差约为1.2K,相较于基于下垫面分类的多通道统计模型下降了76％,算法精度明显提高.

地震发生前普遍存在的热红外辐射异常现象,是当前评估区域发震危险性的重要参数之一.然而,并非所有的地表红外异常都与构造活动或地震有关,如何排除非构造因素对地表热红外辐射的影响,从强噪声背景中提取微弱信号,是当前利用热红外遥感技术研究构造活动的难点.地表温度(LST)背景场是热异常提取的基础,而以往研究中所建立的背景场不能有效反映当年气候变化对其的影响,造成热异常提取精度受限.为此,文中在提取热异常的过程中对背景场进行了改进,结合地表温度时间序列的周期性特征,引入谐波分析,采用傅里叶逼近的方法拟合地表温度离散时序,从中提取其年趋势,建立1个动态的、同时包含局地信息和年际特征的、更加可靠的地表温度背景场;将其引入RST模型,基于“kσ”准则识别地震热异常信息;最终采用异常方向、异常强度和距离指数这3个指标对异常结果进行分析,验证算法的有效性.利用MODIS地表温度产品,基于所提算法对2008年汶川地震进行了再研究,结果表明:1)汶川地震前存在明显的热异常,沿龙门山断裂呈带状分布,持续时间较长;2)发震期无明显的异常现象;3)震后热异常的发生具有循环往复性,但异常幅度和影响范围明显缩小.与传统的空间温度均值RST算法异常提取结果相比,文中方法所提取的热异常在空间分布上与活动断裂带更为吻合,对异常的产生消散过程刻画更加细致,表明以地表温度年趋势作为地震构造热异常提取的背景场更加可靠.

针对当前基于被动微波遥感重建地表温度的统计方法难以实现大面积复杂下垫面区域数值重建的问题,提出了基于统计模型与滤波算法联合的地表温度重建方法.从时间序列角度探索地表温度与地表亮温的相关性,建立二者之间的统计模型,不需要进行地物分类,能有效避免下垫面复杂度对重建精度的影响;遍历像元,实现对大面积区域的数值重建.此外,采用滤波算法对基于统计模型的结果进行改正,利用地表温度时间序列的周期性进一步控制反演误差.针对MODIS地表温度产品重建的实验结果表明:所提算法精度明显提高,可用于各类下垫面覆盖区域的地表温度重建.

By taking MODIS daily land surface temperature (LST) data and AMSR-E brightness temperature (BT) data from 2007 to 2008 as the input, combining with the land cover type data, the statistics and analysis of the relativity between MODIS_LST and AMSR-E_BT in different land cover types, channels and polarization ways are produced. Based on the International Geosphere-Bio-sphere Program (IGBP) vegetation classification scheme, land cover data is re-classified into seven types, including water, forest land, grass land, farmland, urban land, desert land and other land cover types. The statistical result shows that the correlation is ap-parent between MODIS_LST and AMSR-E_BT in 18.7 GHz, 23.8 GHz and 36.5 GHz channel, and it reveals a higher correlation in the vertical channel compared to the horizontal channel. Moreover, this paper finds out that the microwave channel of AMSR-E_BT, which has the highest relativity with MODIS-LST, is different with respect to different land cover types. In addition, by con-sidering the impact of mixed pixel, this paper analyzes the correlation between MODIS_LST and AMSR-E_BT for 25 types of land cover type combinations. It is inferred that the correlation declines as the quantity of land cover types in the single mixed pixel in-creases. Finally, according to different land cover type combinations, the inversion model is established by adopting the multivariate linear regression method, and this model has been applied to inverse MODIS_LST in a part of the study area. Inversion results re-veal that the error is limited in ± 3.15 K in average, and the inversion accuracy is raised by 1.5 K successfully in comparison with the inversion model without considering land cover type combination. However, there are some problems with MODIS land surface temperature inversion by using AMSR-E brightness temperature, such as the space resolution variation between MODIS LST and AMSR-E_BT, changes of land cover type with changing seasons and the influence of relative humidity of land cover on the retriev-al accuracy. Therefore, selecting land surface bright temperature with a high quality and space resolution, considering season varia-tions and classification accuracy of land cover type factors are future research directions.

地震预测是地震科学研究的主要领域之一.震前热异常现象(地表温度异常升高)普遍存在并且与地震三要素有复杂的非线性关系.文中结合神经网络的优点,提出将热异常信息作为地震预测的信息源,通过构建神经网络,进行地震预测的思路,并进行了试验.基于8d合成的1km分辨率的MODIS数据,利用RST算法提取震前热异常信息,在分析震前热异常信息时空变化的基础上,确定出BP神经网络的结构,利用该网络对中国及周边100个5级以上震例,以及70个随机无震样本进行训练和仿真.试验结果表明,通过RST算法提取的震前热异常指数值,用于BP神经网络地震预测是可行的,其预测的试验结果刻画出了地震要素与热异常值间的非线性相关性.未来预测区域范围的选取以及神经网络中隐层神经元的数量将对地震预测效果产生较大的影响.

In this paper, the deterministic convergence of the batch back-propagation algorithm with penalty (BPAP) is proved under certain relaxed conditions for the activation function, the learning rate and the stationary point set of the error function. Both weak and strong convergence results are established. The boundedness of the weights in the training procedure is also proved in a simple and clear way. As a result, the usual requirements on the boundedness of the weights to guarantee the convergence are removed. Simulation results for an approximation problem are presented to support our theoretical findings.

L1/2正则子比L2正则子更具稀疏性,有更强的剪枝能力;但其非凸、非光滑以及不满足Lipschitz条件的函数性质,使神经网络训练过程易于出现数值振荡现象,并且给收敛性分析带来理论困难.用光滑函数逼近L1/2正则子在克服数值振荡的同时可以保证目标函数具有良好的连续可微性质.针对提出的带光滑L1/2正则化项的逆向迭代神经网络模型,证明了误差函数的单调递减性质及算法的确定型收敛性:弱收敛和强收敛.数值实验表明,新的逆向迭代学习算法较已有算法保证了输入向量序列在训练过程中的稳定性及稀疏性,并有较好的泛化能力.

The momentum method is a commonly used method to accelerate the learning of neural networks. In this paper, a new adaptive momentum algorithm is proposed for split-complex recurrent neural networks training. Different from other momentum methods, this new algorithm uses a variable gain factor and a variable learning rate to speed up the convergence and smooth the weight trace. The global convergence of the new algorithm is proved under mild conditions. Numerical results show that the algorithm is efficient for the given test problems.

In this paper, we study the convergence of an online gradient method with inner-product penalty and adaptive momentum for feedforward neural networks, assuming that the training samples are permuted stochastically in each cycle of iteration. Both two-layer and three-layer neural network models are considered, and two convergence theorems are established. Sufficient conditions are proposed to prove weak and strong convergence results. The algorithm is applied to the classical two-spiral problem and identification of Gabor function problem to support these theoretical findings.

In this paper, a batch gradient algorithm with adaptive momentum is considered and a convergence theorem is presented when it is used for two-layer feedforward neural networks training. Simple but necessary sufficient conditions are offered to guarantee both weak and strong convergence. Compared with existing general requirements, we do not restrict the error function to be quadratic or uniformly convex. A numerical example is supplied to illustrate the performance of the algorithm and support our theoretical finding.

In this paper, the deterministic convergence of an online gradient method with penalty and momentum is investigated for training two-layer feedforward neural networks. The monotonicity of the new error function with the penalty term in the training iteration is firstly proved. Under this conclusion, we show that the weights are uniformly bounded during the training process and the algorithm is deterministically convergent. Sufficient conditions are also provided for both weak and strong convergence results.

In this paper, the convergence of a new back-propagation algorithm with adaptive momentum is analyzed when it is used for training feedforward neural networks with a hidden layer. A convergence theorem is presented and sufficient conditions are offered to guarantee both weak and strong convergence result. Compared with existing results, our convergence result is of deterministic nature and we do not require the error function to be quadratic or uniformly convex.

A general updating rule for learning rates was presented and the convergence of the corresponding batch gradient algorithms with variable learning rates for training feedforward neural networks was proved.The monotonicity of the error function in the training iteration was also proved.

In this paper, a Bayesian classifier for modeling consumer response to direct marketing is constructed based on a novel genetic algorithm (GA). To evaluate the performance of this model, we test it with a large amount of validation data of direct marketing and compare the results with other benchmark methods, including recency-frequency-monetary (RFM) analysis, Chi-Square automatic interaction detector (CHAID), logistic regression (LR) and so on. The results demonstrate the superiority of this model over the others in terms of accuracy of prediction and interpretable of results. Recently, it has been adopted by a credit card company to effectively handle business problems.

In this paper a squared penalty term is added to the conventional error function to improve the generalization of neural networks. A weight boundedness theorem and two convergence theorems are proved for the gradient learning algorithm with penalty when it is used for training a two-layer feedforward neural network. To illustrate above theoretical findings, numerical experiments are conducted based on a linearly separable problem and simulation results are presented. The abstract goes here.

In this paper, a new back propagation (BP) algorithm with adaptive momentum is proposed, where the momentum coefficient is adjusted iteratively based on the current descent direction and the weight increment in the last iteration. A convergence result of the algorithm is presented when it is used for training feed forward neural networks (FNNs) with a hidden layer. Simulation results have shown that this new algorithm has a distinct superiority in fast convergence and smoothing oscillation over the conventional BP method. Moreover, the range for the learning rate has been widened after the inclusion of such an adaptable momentum while maintaining the stability of networks.

In this paper, a novel Bayesian classifier model is constructed based on genetic algorithms (GA) for the prediction of customer churn. Experiment results have shown that it not only matches potential churning customers well from the large amount of validation data but also shows higher classifying precision compared with the other three Bayesian classifier models. Recently, the model has been adopted by a Japanese enterprise to successfully handle some business problems of potential churning customers prediction.

A continuous recurrent neural network model is presented for computing the largest and smallest generalized eigenvalue of a symmetric positive pair (A,B). Convergence properties to the extremum eigenvalues based upon Liapunov functional with the help of the generalized eigen-decomposition theorem is obtained. Compared with other existing models, this model is also suitable for computing the smallest generalized eigenvalue simply by replacing A by -A as well as maintaining invariant norm property. Numerical simulation further shows the effectiveness of the proposed model.