Ridge Polynomial神经网络带动量项异步梯度算法的收敛性

将动量项引入到Ridge Polynomial神经网络异步梯度训练算法的误差函数中,有效地改善了算法的收敛效率,并从理论上分析了Ridge Polynomial神经网络的带动量项的异步梯度算法的收敛性,给出了算法的单调性和收敛性(包括强收敛性和弱收敛性)。算法的这些收敛性质对于如何选取学习率和初始权值来进行高效的网络训练是非常重要的。最后通过计算机仿真实验验证了带动量项的异步梯度算法的高效性和理论分析的正确性。     

Credit rating with a monotonicity-constrained support vector machine model

Deciding whether borrowers can fulfill their obligations is a major issue for financial institutions, and while various credit rating models have been developed to help achieve this, they cannot reflect the domain knowledge of human experts. This paper proposes a new rating model based on a support vector machine with monotonicity constraints derived from the prior knowledge of financial experts. Experiments conducted on real-world data sets show that the proposed method, not only data driven but also domain knowledge oriented, can help correct the loss of monotonicity in data occurring during the collecting process, and performs better than the conventional counterpart.     

基于单调性分析与符号处理技术的套筒滚子链优化设计通用解

本文利用单调性分析和计算机符号处理技术对套筒滚子链进行优化设计，求出了通用形式的最优解，这一最优解适用于具有各种参数的同一类模型，对于具体问题，只要将已知参数值代入就可得到最优解之值，同时这一方法不需进行数值优化中的迭代。     

The monotone convergence of a class of parallel nonlinear relaxation methods for nonlinear complementarity problems

We set up a class of parallel nonlinear multisplitting AOR methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems. The different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods, as well as a lot of new relaxed parallel nonlinear multisplitting methods for solving the nonlinear complementarity problems. The two-sided approximation properties and the influences on the convergence rates from the relaxation parameters about our new methods are shown, and sufficient conditions guaranteeing the methods to converge globally are discussed. Finally, a lot of numerical results show that our new methods are feasible and efficient.     

微分方程初──边值问题近似解的双侧逼近

本文给出了微分方程初──边值问题的现代数学规划配点法的近似解法。特别对残差关于解不具有一致强单调性的微分方程问题，找到了最优近似解法。它使现代数学规划加权残值法的应用范围进一步拓宽。     

Graph searching with advice

Fraigniaud et al. [L. Blin, P. Fraigniaud, N. Nisse, S. Vial, Distributing chasing of network intruders, in: 13th Colloquium on Structural Information and Communication Complexity, SIROCCO, in: LNCS, vol. 4056, Springer-Verlag, 2006, pp. 70–84] introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice   of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching problem in a distributed setting. In this variant of the problem, all searchers are initially placed at a particular node of the network. The aim of the team of searchers is to clear a contaminated graph in a monotone connected way, i.e., the cleared part of the graph is permanently connected, and never decreases while the search strategy is executed. Moreover, the clearing of the graph must be performed using the optimal number of searchers, i.e. the minimum number of searchers sufficient to clear the graph in a monotone connected way in a centralized setting. We show that the minimum number of bits of advice permitting the monotone connected and optimal clearing of a network in a distributed setting is Θ(nlogn)$\Theta (nlogn)$, where n$n$ is the number of nodes of the network. More precisely, we first provide a labelling of the vertices of any graph G$G$, using a total of O(nlogn)$O(nlogn)$ bits, and a protocol using this labelling that enables the optimal number of searchers to clear G$G$ in a monotone connected distributed way. Then, we show that this number of bits of advice is optimal: any distributed protocol requires Ω(nlogn)$\Omega (nlogn)$ bits of advice to clear a network in a monotone connected way, using an optimal number of searchers.     

Incremental Beam search

Beam search is a heuristic search algorithm that explores a state-space graph by expanding w most promising nodes at each level (depth) of the graph, where w is called the beam-width which is taken as input from the user. The quality of the solution produced by beam search does not always monotonically improve with the increase in beam-width making it difficult to choose an appropriate beam-width for effective use. We present an algorithm called Incremental Beam Search (IncB) which guarantees monotonicity, and is also anytime in nature. Experimental results on the sliding-tile puzzle, the traveling salesman, and the single-machine scheduling problems show that IncB significantly outperforms basic monotonic methods such as iterative widening beam search as well as some of the state-of-the-art anytime heuristic search algorithms in terms of the quality of the solution produced at the end as well as the anytime performance.     

量化粗糙集的单调性属性约简方法

单调性在经典粗糙集属性约简过程中发挥着重要的作用。然而,在一些泛化模型(如量化粗糙集模型)中该性质并不存在。针对该问题,提出了量化粗糙集模型中下近似单调约简的定义,并给出了求得该约简的启发式方法。实验结果表明,相较于下近似保持约简算法,下近似单调约简算法不仅耗时短,而且增加了由正域和边界域表示的确定性,同时降低了由边界域带来的不确定性。     

Sequential covering rule induction algorithm for variable consistency rough set approaches

We present a general rule induction algorithm based on sequential covering, suitable for variable consistency rough set approaches. This algorithm, called VC-DomLEM, can be used for both ordered and non-ordered data. In the case of ordered data, the rough set model employs dominance relation, and in the case of non-ordered data, it employs indiscernibility relation. VC-DomLEM generates a minimal set of decision rules. These rules are characterized by a satisfactory value of the chosen consistency measure. We analyze properties of induced decision rules, and discuss conditions of correct rule induction. Moreover, we show how to improve rule induction efficiency due to application of consistency measures with desirable monotonicity properties.     

一种求解工程问题规律性知识的方法

设计规律性知识的获取是智能设计要解决的基本问题之一。本文根据工程问题符号表达的优化设计模型的特点，提出了一种求解符号优化模型的方法，利用该方法可求出一类问题的最优解的用非线性代数系统的标准基（Ｇｒｏｅｂｎｅｒ基）来描述的解析表达式，从而得出有规律性的知识和指导设计。