基于Hessian图正则稀疏NMF的高光谱解混

基于非负矩阵分解(Nonnegative Matrix Factorization, NMF)的高光谱解混(Hyperspectral Unmixing,HU)方法引起了大家的关注,因为可以将一个非负高光谱图像(Hyperspectral Imagery, HSI)数据矩阵分解为两个非负矩阵的乘积,分别对应于端元矩阵和丰度系数矩阵。目前,图约束的NMF算法已经被证明对高光谱解混是有效的,因为它们可以捕获HSI的几何特性。为了挖掘数据在混合过程中的几何结构和稀疏性,提出了一种稀疏的Hessian图正则化NMF(SHGNMF)算法。SHGNMF算法是将丰度矩阵的L1/2正则化器和Hessian图正则化项都添加到每个NMF模型中,同时采用乘法更新规则。最后用模拟数据和真实数据进行实验,验证了所提出的SHGNMF算法相对于其他NMF算法的优越性。     

基于 GA-BRBPNN 的航空自耦变压整流器 故障诊断方法

航空自耦变压整流器(auto-transformer rectifier unit, ATRU)是飞机高压直流电网关键电能变换装置,在运行过程中受高 温、机械应力、荷载波动等因素持续影响,其内部元件可能出现相应故障,进而威胁飞机可靠运行及持续适航。 针对 ATRU 整流 部分故障信号频谱难以区分、诊断准确率不高问题,提出一种遗传算法(genetic algorithm,GA)与贝叶斯正则化反向传播神经网 络(Bayesian regularisation back propagation neural network,BRBPNN)相结合的故障诊断识别方法。 首先,实现 ATRU 故障仿真, 以时频分析方式处理所得信号,从而挖掘不同故障状态的特征信息;随后采用 GA 算法优化 BRBPNN 初始权阈值并建立最优 GA-BRBNPNN 诊断模型,将特征样本输入诊断模型进行故障分类识别,测试模型性能;最后,搭建故障模拟实验平台对实测数 据进行模型验证。 实验结果分析可知,对于仿真故障,该模型诊断准确率可达 99. 46%,对于实测故障,该模型可全部诊断识别 待测样本;由此表明提出的 GA-BRBPNN 优化模型诊断效果好,具有较高实用价值。     

基于约束空间光谱联合的亚像素定位方法北大核心CSCD

针对高光谱遥感图像,提出了一种约束空间光谱的亚像素定位方法。传统的亚像素定位方法以解混的结果作为输入,可能无法充分利用高光谱图像丰富的光谱信息。本文所提出的基于约束空间光谱联合的亚像素定位方法(constraint spatial-spectral subpixel mapping,CSSSM),利用下采样将像素丰度与亚像素丰度显式联系起来,代入线性解混模型得到亚像素丰度求解的新模型。在求解过程中,通过添加稀疏性约束与平滑性约束,以限制亚像素丰度的解空间,亚像素丰度求解更精确。其中,针对亚像素丰度稀疏性先验采用重加权1范数作为新的约束,并自适应地更新权重;针对亚像素丰度空间先验信息则采用全变分(total variational,TV)正则化作为约束,然后使用乘法迭代算法求解亚像素丰度,最后利用赢者通吃的策略进行类别确定。在两个合成数据集上进行了实验,结果表明,本方法能够进一步提高亚像素定位的精度。     

Cold-Start Link Prediction via Weighted Symmetric Nonnegative Matrix Factorization with Graph Regularization

Link prediction has attracted wide attention among interdisciplinary researchers as an important issue in complex network. It aims to predict the missing links in current networks and new links that will appear in future networks. Despite the presence of missing links in the target network of link prediction studies, the network it processes remains macroscopically as a large connected graph. However, the complexity of the real world makes the complex networks abstracted from real systems often contain many isolated nodes. This phenomenon leads to existing link prediction methods not to efficiently implement the prediction of missing edges on isolated nodes. Therefore, the cold-start link prediction is favored as one of the most valuable subproblems of traditional link prediction. However, due to the loss of many links in the observation network, the topological information available for completing the link prediction task is extremely scarce. This presents a severe challenge for the study of cold-start link prediction. Therefore, how to mine and fuse more available non-topological information from observed network becomes the key point to solve the problem of cold-start link prediction. In this paper, we propose a framework for solving the cold-start link prediction problem, a joint-weighted symmetric nonnegative matrix factorization model fusing graph regularization information, based on low-rank approximation algorithms in the field of machine learning. First, the nonlinear features in high-dimensional space of node attributes are captured by the designed graph regularization term. Second, using a weighted matrix, we associate the attribute similarity and first order structure information of nodes and constrain each other. Finally, a unified framework for implementing cold-start link prediction is constructed by using a symmetric nonnegative matrix factorization model to integrate the multiple information extracted together. Extensive experimental validation on five real networks with attributes shows that the proposed model has very good predictive performance when predicting missing edges of isolated nodes.     

Optimal parameters identification and sensitivity study for abrasive waterjet milling model

In this paper we present the work related to the parameters identification for abrasive waterjet milling (AWJM) model that appears as an ill-posed inverse problem. The necessity of studying this problem comes from the industrial milling applications where the possibility to predict and model the final surface with high accuracy is one of the primary tasks in the absence of any knowledge of the model parameters that should be used. The adjoint approach based on corresponding Lagrangian gives the opportunity to find out the unknowns of the AWJM model and their optimal values that could be used to reproduce the required trench profile. Due to the complexity of the nonlinear problem and the large number of the model parameters, we use an automatic differentiation software tool. This approach also gives us the ability to distribute the research on more complex cases and consider different types of model errors and 3D time dependent model with variations of the jet feed speed. This approach gives us a good opportunity to identify the optimal model parameters and predict the surface profile both with self-generated data and measurements obtained from the real production. Considering different types of model errors allows us to receive the results acceptable in manufacturing and to expect the proper identification of unknowns.     

A Study of a Convex Variational Diffusion Approach for Image Segmentation and Feature Extraction

We analyze a variational approach to image segmentation that is based on a strictly convex non-quadratic cost functional. The smoothness term combines a standard first-order measure for image regions with a total-variation based measure for signal transitions. Accordingly, the costs associated with discontinuities are given by the length of level lines and local image contrast. For real images, this provides a reasonable approximation of the variational model of Mumford and Shah that has been suggested as a generic approach to image segmentation.The global properties of the convex variational model are favorable to applications: Uniqueness of the solution, continuous dependence of the solution on both data and parameters, consistent and efficient numerical approximation of the solution with the FEM-method.Various global and local properties of the convex variational model are analyzed and illustrated with numerical examples. Apart from the favorable global properties, the approach is shown to provide a sound mathematical model of a useful locally adaptive smoothing process. A comparison is carried out with results of a region-growing technique related to the Mumford-Shah model.     

Direct Visible Surface Interpolation

The computation of visible surfaces is usually formulated in a regularization framework based on thin-plate and membrane splines. When discretized, this formulation leads to large sparse linear systems. Most surface interpolation methods solve these sparse systems with iterative methods. Here we explore the use of direct methods. Through a careful analysis of the regularization operator, we derive direct methods that efficiently make use of all zeros in the sparse discretization of the operator. Experimental results show that, compared with iterative interpolation methods, the direct methods we present are competitive in general, and they provide significant speed-ups for problems involving discontinuities. In addition to their use in visible-surface interpolation, the presented methods also support very efficient time integration for deformable surfaces.     

Weighted and extended total variation for image restoration and decomposition

In various information processing tasks obtaining regularized versions of a noisy or corrupted image data is often a prerequisite for successful use of classical image analysis algorithms. Image restoration and decomposition methods need to be robust if they are to be useful in practice. In particular, this property has to be verified in engineering and scientific applications. By robustness, we mean that the performance of an algorithm should not be affected significantly by small deviations from the assumed model. In image processing, total variation (TV) is a powerful tool to increase robustness. In this paper, we define several concepts that are useful in robust restoration and robust decomposition. We propose two extended total variation models, weighted total variation (WTV) and extended total variation (ETV). We state generic approaches. The idea is to replace the TV penalty term with more general terms. The motivation is to increase the robustness of ROF (Rudin, Osher, Fatemi) model and to prevent the staircasing effect due to this method. Moreover, rewriting the non-convex sublinear regularizing terms as WTV, we provide a new approach to perform minimization via the well-known Chambolle's algorithm. The implementation is then more straightforward than the half-quadratic algorithm. The behavior of image decomposition methods is also a challenging problem, which is closely related to anisotropic diffusion. ETV leads to an anisotropic decomposition close to edges improving the robustness. It allows to respect desired geometric properties during the restoration, and to control more precisely the regularization process. We also discuss why compression algorithms can be an objective method to evaluate the image decomposition quality.     

一维热传导问题时变边界上热通量重构问题

具有Neumann边界条件的抛物方程的初边值问题是偏微分方程研究领域的一类经典问题.正问题是由已知的边界条件和初始条件来求区域温度场的问题.如果边界条件不足,但给出了区域内部的一些额外信息,这样便构成了一类热通量重构的反问题.本文讨论了一维热传导问题时动边界上的热通量重构问题,借助于位势理论方法,引入密度函数,将反问题本质上转化为一类关于密度函数的具有弱奇性核的第一类Volterra积分方程,采用了Tikhonov正则化,在正则化参数的选取上采用了后验的模型函数方法,数值结果验证了反演方法的有效性.