A globally convergent BFGS method for pseudo-monotone variational inequality problems

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.     

The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making

The Pythagorean fuzzy set (PFS) is characterized by two functions expressing the degree of membership and the degree of nonmembership, which square sum of them is equal or less than 1. It was proposed as a generalization of a fuzzy set to deal with indeterminate and inconsistent information. In this study, we shall present some novel Dice similarity measures of PFSs and the generalized Dice similarity measures of PFSs and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision-making models with Pythagorean fuzzy information. Then, we apply the generalized Dice similarity measures between PFSs to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.     

Graph-based video fingerprinting using double optimal projection

A double optimal projection method that involves projections for intra-cluster and inter-cluster dimensionality reduction are proposed for video fingerprinting. The video is initially set as a graph with frames as its vertices in a high-dimensional space. A similarity measure that can compute the weights of the edges is then proposed. Subsequently, the video frames are partitioned into different clusters based on the graph model. Double optimal projection is used to explore the optimal mapping points in a low-dimensional space to reduce the video dimensions. The statistics and geometrical fingerprints are generated to determine whether a query video is copied from one of the videos in the database. During matching, the video can be roughly matched by utilizing the statistics fingerprint. Further matching is thereafter performed in the corresponding group using geometrical fingerprints. Experimental results show the good performance of the proposed video fingerprinting method in robustness and discrimination.     

Thermodynamic description of the Cu-Ge-Pb system: Experiment and modeling

Decades of scientific work dedicated to the investigation of phase diagrams gave significant benefit to industry and science. After all those years of phase diagram investigation still there is missing information about phase diagram of some ternary systems. One of those systems is Cu-Ge-Pb. It is known importance of Cu-based alloys and Ge-based alloys in electro industry. Since such combination is not tested before this work will provide information about phase diagram of ternary Cu-Ge-Pb system. In this work ternary Cu-Ge-Pb system has been tested experimentally and analytically by using Calphad model. Two isothermal sections at 600 and 400 °C and three vertical sections are experimentally tested and results were compared with calculated corresponding phase diagrams. None of the ternary compound and large solubility of third element in binary compound is not confirmed. Liquidus projection, invariant reaction and scheme of invariant reaction are presented. Scheil and Lever simulation of solid phases for Cu₈₀Ge₁₀Pb₁₀ alloy were calculated.     

结构化加权稀疏低秩恢复算法在人脸识别中的应用

针对训练样本或测试样本存在污损的情况，提出一种结构化加权稀疏低秩恢复算法（structured and weighted-sparse low rank representation，SWLRR）。SWLRR对低秩表示进行加权稀疏约束和结构化约束，使得低秩表示系数更加趋近于块对角结构，进而可获得具有判别性的低秩表示。SWLRR将训练样本恢复成干净训练样本后，再根据原始训练样本和恢复后的训练样本学习到低秩投影矩阵，把测试样本投影到相应的低秩子空间，即可有效地去除测试样本中的污损部分。在几个人脸数据库上的实验结果验证了SWLRR在不同情况下的有效性和鲁棒性。     

基于普吕克直线的多线结构光视觉传感器标定方法

针对多线结构光系统的快速标定,提出了一种基于普吕克直线的标定方法。传统的线结构光标定方法大多以单点的形式进行提取和坐标系转换,从而获得平面方程。然而单点数量较多会导致操作复杂,不适用于多线结构光的标定。为了解决这个问题,提出了一种新的标定方法,该方法在标定过程中全部采用普吕克矩阵的形式,而不是直接使用点特征。该方法有利于在摄像机坐标系下快速准确地获得光平面方程。同时设计了一种与该方法相对应的用于标定多线结构光的平面标定靶标。为了将一般直线转换为普吕克直线,将图像平面维度延展,定义了一个新的图像空间。为了对普吕克直线的坐标系进行转换,重新表达了基于普吕克直线的透视投影模型。基于普吕克空间中直线与平面的性质,对多条结构光线的普吕克矩阵进行合并即可高效地构造出线性的矩阵方程,从而进一步拟合出结构光平面方程。实验验证了所提方法并证明了校准精度的显著提高,当测试距离为1.8 m时,测量得到的三维点的RMS误差在0.08 mm之内。