解线性及二次型规划问题增广的神经网络

本文提出了一个解线性及二次型规划问题的神经网络模型，证明了该网络是全局稳定于平衡点，而平衡点就是线性及二次型规划问题的解，该网络的优点是能够实时获得问题的精确解，且可以同时获得带等式不式约束的对偶问题解，该网络易于电路实现。     

CXFTV2: A Fortran subroutine for the discrete least squares convex approximation

A Fortan subroutine calculates the least squares approximation to n data values containing random errors subject to non-negative second divided differences (convexity). The method employs a dual active set quadratic programming technique that allows several concavities of an iterate to be corrected simultaneously, which is a distinctive feature of this calculation. A B-spline representation of the iterates reduces each active set calculation to an unconstrained minimization with fewer variables that requires only O(n) computer operations. Details in these techniques including the data structure that establishes the implementation of the method are specified. Numerical testing on a variety of data sets indicates that the subroutine is particularly efficient, terminating after a small number of active set changes, the subroutine being suitable for large numbers of data. A numerical example and its output is provided to help the use of the software.     

On formalism and stability of switched systems

In this paper,we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching.Based on known results from the the...     

Quadratic polynomial guided fuzzy C-means and dual attention mechanism for medical image segmentation

Medical image segmentation is the most complex and important task in the field of medical image processing and analysis, as it is linked to disease diagnosis accuracy. However, due to the medical image's high complexity and noise, segmentation performance is limited. We propose a novel quadratic polynomial guided fuzzy C-means and dual attention mechanism composite network model architecture to address the aforementioned issues (QPFC-DA). It has mechanisms for channel and spatial edge attention, which guide the content and edge segmentation branches, respectively. The bi-directional long short-term memory network was added after the two content segmentation branches to better integrate multi-scale features and prevent the loss of important features. Furthermore, the fuzzy C-means algorithm guided by the quadratic polynomial can better distinguish the image's weak edge regions and has a degree of noise resistance, resulting in a membership matrix with less ambiguity and a more reliable segmentation result. We also conducted comparison and ablation experiments on three medical data sets. The experimental results show that this method is superior to several other well-known methods.     

A new hybrid approach for dynamic continuous optimization problems

A new hybrid approach for dynamic optimization problems with continuous search spaces is presented. The proposed approach hybridizes efficient features of the particle swarm optimization in tracking dynamic changes with a new evolutionary procedure. In the proposed dynamic hybrid PSO (DHPSO) algorithm, the swarm size is varied in a self-regulatory manner. Inspired from the microbial life, the particles can reproduce infants and the old ones die. The infants are especially reproduced by high potential particles and located near the local optimum points, using the quadratic interpolation method. The algorithm is adapted to perform in continuous search spaces, utilizing continuous movement of the particles and using Euclidian norm to define the neighborhood in the reproduction procedure. The performance of the new proposed approach is tested against various benchmark problems and compared with those of some other heuristic optimization algorithms. In this regard, different types of dynamic environments including periodic, linear and random changes are taken with different performance metrics such as real-time error, offline performance and offline error. The results indicate a desirable better efficiency of the new algorithm over the existing ones.     

Quadratic optimization fine tuning for the Support Vector Machines learning phase

This work presents a comparative analysis of specific, rather than general, mathematical programming implementation techniques of the quadratic optimization problem (QP) based on Support Vector Machines (SVM) learning process. Considering the Karush–Kuhn–Tucker (KKT) optimality conditions, we present a strategy of implementation of the SVM-QP following three classical approaches: (i) active set, also divided in primal and dual spaces, methods, (ii) interior point methods and (iii) linearization strategies. We also present the general extension to treat large-scale applications consisting in a general decomposition of the QP problem into smaller ones, conserving the exact solution approach. In the same manner, we propose a set of heuristics to take into account for a better than a random selection process for the initialization of the decomposition strategy. We compare the performances of the optimization strategies using some well-known benchmark databases.     

Multi-label core vector machine with a zero label

Multi-label core vector machine (Rank-CVM) is an efficient and effective algorithm for multi-label classification. But there still exist two aspects to be improved: reducing training and testing computational costs further, and detecting relevant labels effectively. In this paper, we extend Rank-CVM via adding a zero label to construct its variant with a zero label, i.e., Rank-CVMz, which is formulated as the same quadratic programming form with a unit simplex constraint and non-negative ones as Rank-CVM, and then is solved by Frank–Wolfe method efficiently. Attractively, our Rank-CVMz has fewer variables to be solved than Rank-CVM, which speeds up training procedure dramatically. Further, the relevant labels are effectively detected by the zero label. Experimental results on 12 benchmark data sets demonstrate that our method achieves a competitive performance, compared with six existing multi-label algorithms according to six indicative instance-based measures. Moreover, on the average, our Rank-CVMz runs 83 times faster and has slightly fewer support vectors than its origin Rank-CVM.     

On-line identification of interacting two-tank system

In order to demonstrate the effectiveness of the process identification algorithm, on-line parameter estimator is evaluated experimentally by using two-tank system with interaction. On-line parameter estimator used in this paper is based on a recursive parameter estimation algorithm. MIMO linear, bilinear and quadratic models based on ARMA model are used to identify two-tank system. A quadratic model for two-tank system with interaction is developed to confirm the propriety of MIMO quadratic model used in identification of two-tank system. The results of on-line identification experiments on the two-tank system show that the estimated parameters of each model converge and the output tracking errors are bounded by disturbance bound. But, the quadratic model showed the best convergence.     

基于边缘敏感的SLIC和二次密度聚类的GGO分割

针对磨玻璃肺结节(Ground Glass Opacity,GGO)边界对比度低、大小各异和灰度不均匀等造成分割准确率低的问题,提出一种基于边缘敏感的SLIC和二次密度聚类相结合的分割算法。将图像边缘检测结果与SLIC超像素算法相结合,并将其中含有边缘的超像素块用区域质心代替其原始聚类中心,改善SLIC边界黏连性较差的问题;针对密度聚类不能完整分割GGO的问题,提出二次密度聚类的方法,对密度聚类定位到的簇及其邻域簇进行二次密度聚类。实验结果表明,该算法分割GGO的平均准确率达90.17%,灵敏度达84%。