The essential order of approximation for nearly exponential type neural networks

1 Introduction Artificial neural networks have been extensively applied in various fields of science and engineering. Why is so is mainly because the feedforward neural networks (FNNs) have the universal approximation capability[1-9]. A typical example of…     

Truth-value transmittal fuzzy reasoning interpolator

Fuzzy reasoning and interpolation were used independently as two methods of ex- pression functional relationship approximately in the past. The relevancy behind them was discussed firstly in refs. [1―3]. In ref. [1], fuzzy reasoning algorithms used com- monly at present were approximated to some interpolation algorithms. Based on the analysis of rationality of such approximation, the author of ref. [4] put forward the con- cept of the fuzzy reasoning interpolator. In this paper, we keep on re…     

Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.     

Approximation algorithm for weighted weak vertex cover

The problem of efficiently monitoring the network flow is regarded as the problem to find out the minimum weighted weak vertex cover set for a given graph G = (V, E). In this paper, we give an approximation algorithm to solve it, which has the approximation ratio ln d 1, where d is the maximum degree of the vertex in graph G, and improve the previous work.     

The essential order of approximation for neural networks

There have been various studies on approximation ability of feedforward neural networks (FNNs). Most of the existing studies are, however, only concerned with density or upper bound estimation on how a multivariate function can be approximated by an FNN, and consequently, the essential approximation ability of an FNN cannot be revealed. In this paper, by establishing both upper and lower bound estimations on approximation order, the essential approximation ability (namely, the essential approximation order) of a class of FNNs is clarified in terms of the modulus of smoothness of functions to be approximated. The involved FNNs can not only approximate any continuous or integrable functions defined on a compact set arbitrarily well, but also provide an explicit lower bound on the number of hidden units required. By making use of multivariate approximation tools, it is shown that when the functions to be approximated are Lipschitzian with order up to 2, the approximation speed of the FNNs is uniquely deter     

Quadrature Kalman Filter （QKF） and Reduced Quadrature Kalman Filter （R-QKF） in Ballistic Target Tracking

Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncation errors due to linearization can be compensated. These filters include the unscented Kalman filter （UKF）, the central difference filter （CDF） and the divided difference filter （DDF）, and they are also called Sigma Point Filters （SPFs） in a unified way. For higher order approximation of the nonlinear function. Ito and Xiong introduced an algorithm called the Gauss Hermite Filter, which is revisited in [5]. The Gauss Hermite Filter gives better approximation at the expense of higher computation burden, although it＇s less than the particle filter. The Gauss Hermite Filter is used as introduced in [5] with additional pruning step by adding threshold for the weights to reduce the quadrature points.     

On Constrained Facility Location Problems

Given m facilities each with an opening cost, n demands, and distance between every demand and facility, the Facility Location problem finds a solution which opens some facilities to connect every demand to an opened facility such that the total cost of the solution is minimized. The k-Facility Location problem further requires that the number of opened facilities is at most k, where k is a parameter given in the instance of the problem. We consider the Facility Location problems satisfying that for every demand the ratio of the longest distance to facilities and the shortest distance to facilities is at most ω, where ω is a predefined constant. Using the local search approach with scaling technique and error control technique, for any arbitrarily small constant > 0, we give a polynomial-time approximation algorithm for the ω-constrained Facility Location problem with approximation ratio 1 + ω + 1 + ε, which significantly improves the previous best known ratio (ω + 1)/α for some 1≤α≤2, and a polynomial-time approximation algorithm for the ω-constrained k- Facility Location problem with approximation ratio ω+1+ε. On the aspect of approximation hardness, we prove that unless NP■DTIME(nO(loglogn)), the ω-constrained Facility Location problem cannot be approximated within 1 + lnω - 1, which slightly improves the previous best known hardness result 1.243 + 0.316ln(ω - 1). The experimental results on the standard test instances of Facility Location problem show that our algorithm also has good performance in practice.     

Approximation Algorithms for 3D Orthogonal Knapsack

We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is either forbidden or permitted, and we wish to maximize the total profit. Since this optimization problem is NP-hard, we focus on approximation algorithms. We obtain fast and simple algorithms for the non-rotational scenario with approximation ratios 9 ε and 8 ε , as well as an algorithm with approximation ratio 7 ε that uses more sophisticated techniques; these are the smallest approximation ratios known for this problem. Furthermore, we show how the used techniques can be adapted to the case where rotation by 90° either around the z-axis or around all axes is permitted, where we obtain algorithms with approximation ratios 6 ε and 5 ε , respectively. Finally our methods yield a 3D generalization of a packability criterion and a strip packing algorithm with absolute approximation ratio 29/4, improving the previously best known result of 45/4.     

A practical algorithm for the minimum rectilinear steiner tree

An O(n^2) time approximation algorithm for the minimum rectilinear Steiner tree is proposed.The approximation ratio of the algorithm is strictly less than 1.5.The computing performances show the costs of the spanning trees produced by the algorithm are only 0.8% away from the optimal ones.     

A Quotient Space Approximation Model of Multiresolution Signal Analysis

In this paper, we present a quotient space approximation model of multiresolution signal analysis and discuss the properties and characteristics of the model. Then the comparison between wavelet transform and the quotient space approximation is made. First, when wavelet transform is viewed from the new quotient space approximation perspective,it may help us to gain an insight into the essence of multiresolution signal analysis. Second, from the similarity between wavelet and quotient space approximations, it is possible to transfer the rich wavelet techniques into the latter so that a new way for multiresolution analysis may be found.     

基于流形距离的人工免疫无监督分类与识别算法

将一种新的流形距离作为相似性度量测度, 提出了一种用于无监督分类与识别的人工免疫系统方法. 通过基于流形距离的相似性度量, 有效利用样本集固有的全局一致性信息, 充分挖掘无类属样本的空间分布信息, 对样本进行类别划分. 新方法将免疫响应过程建模为一个四元组 AIR=(G,I,R,A) , 其中 G 为引发免疫响应的外界刺激, 即抗原; I 为所有可能抗体的集合; R 为抗体间相互作用的规则集合; A 为支配抗体反应、指导抗体进化的动态算法. 针对无监督分类问题, 将抗体编码为代表各类别的典型样本序号的排列, 利用动态算法 A 搜索能代表各类别的典型样本的最佳组合. 将新方法与标准的 K-均值算法、基于流形距离的进化聚类算法以及 Maulik 等人提出的基于遗传算法的聚类算法进行了性能比较. 对 6 个人工数据集及手写体数字识别问题的仿真实验结果显示, 新方法对样本空间分布复杂的无监督分类问题和实际的模式识别问题具有较高的准确率和较好的鲁棒性.     

人工免疫算法及其应用研究

为了有效地解决病态的约束优化问题,提出了一种模拟生物免疫系统自我调节功能的人工免疫算法,介绍了算法的基本步骤,构造了几种人工免疫算子,分析了算法的收敛性.人工免疫算法继承了遗传算法“优胜劣汰”的自我淘汰机制,但新抗体的产生方法比遗传算法中新个体的产生方法灵活得多.在进行抗体选择时若能确保当时的最优抗体可以进入下一代抗体群,则人工免疫算法是全局收敛的.100个城市TSP问题的仿真实例显示人工免疫算法比遗传算法具有更强的全局搜索能力和收敛速度.     

Symbiotic artificial immune system

Artificial Immune System algorithms use antibodies that fully specify the solution of an optimization, learning, or pattern recognition problem. By being restricted to fully specified antibodies, an AIS algorithm cannot make use of schemata or classes of partial solutions, while sub solutions can help a lot in faster emergence of a totally good solution in many problems. To exploit schemata in artificial immune systems, this paper presents a novel algorithm that combines traditional artificial immune systems and symbiotic combination operator. The algorithm starts searching with partially specified antibodies and gradually builds more and more specified solutions till it finds complete answers. The algorithm is compared with CLONALG algorithm on several multimodal function optimization and combinatorial optimization problems and it is shown that it is faster than CLONALG on most problems and can find solutions in problems that CLONALG totally fails.     

面向存储安全系统的新型人工免疫算法

提出了新型人工免疫算法,用于研究高效的存储安全系统.首先给出了基于免疫存储安全系统的结构和相关定义.在分析人工免疫算法中已有匹配规则的基础上,为提高安全系统的效率,提出了任意r连续位匹配规则,提高检测器识别非自体的能力,减少存储安全系统识别非自体所需的成熟检测器数量;为了使存储安全系统能适应不同的自体集,自动优化检测效率和准确性,避免检测存储安全系统的失效,本文提出了自适应匹配阈值机制.分析了使用不同匹配规则时检测器能识别的最大非法访问请求数量,以及对不同自体集采用静态匹配阈值和自适应匹配阅值机制时存储安全系统的检测效率和准确性.使用新型人工免疫算法实现安全原型系统,验证了算法的性能.最后通过修改开源存储区域网系统Lustre中智能磁盘部分的源代码,实现了基于免疫安全磁盘的原型系统,测试增加存储安全系统前后Lustre系统的I/O性能,结果表明新型人工免疫算法能高效地保护存储系统的安全.     

基于混沌和免疫应答的增量聚类新算法

受免疫应答原理的启发, 提出了一种适用于增量数据聚类的人工免疫系统框架, 以及在此框架上的结合混沌的自组织增量聚类新算法, 称为免疫应答算法(Immune response algorithm, IRA). 新算法利用Logistic混沌序列生成初始抗体种群, 利用其多样性识别新增的不属于任何已知簇的数据, 该过程模拟了初次免疫应答. 同时, 初次免疫应答形成的记忆抗体可用于二次免疫应答, 即识别新增的属于已知簇的数据. 为了减少数据冗余, 算法用中心点和代表点表示已知簇并动态更新其识别区域, 这样算法不但能动态、自组织地形成聚类, 而且实现了数据特征的提取. 模拟实验充分显示出该算法无论在聚类质量上还是数据特征的提取上, 都具有一定优势, 且具有参数数量少、速度快、对数据输入次序不敏感的优点, 在实际问题中有一定应用价值.     

Baldwinian learning in clonal selection algorithm for optimization

Artificial immune systems are a kind of new computational intelligence methods which draw inspiration from the human immune system. Most immune system inspired optimization algorithms are based on the applications of clonal selection and hypermutation, and known as clonal selection algorithms. These clonal selection algorithms simulate the immune response process based on principles of Darwinian evolution by using various forms of hypermutation as variation operators. The generation of new individuals is a form of the trial and error process. It seems very wasteful not to make use of the Baldwin effect in immune system to direct the genotypic changes. In this paper, based on the Baldwin effect, an improved clonal selection algorithm, Baldwinian Clonal Selection Algorithm, termed as BCSA, is proposed to deal with optimization problems. BCSA evolves and improves antibody population by four operators, clonal proliferation, Baldwinian learning, hypermutation, and clonal selection. It is the first time to introduce the Baldwinian learning into artificial immune systems. The Baldwinian learning operator simulates the learning mechanism in immune system by employing information from within the antibody population to alter the search space. It makes use of the exploration performed by the phenotype to facilitate the evolutionary search for good genotypes. In order to validate the effectiveness of BCSA, eight benchmark functions, six rotated functions, six composition functions and a real-world problem, optimal approximation of linear systems are solved by BCSA, successively. Experimental results indicate that BCSA performs very well in solving most of the test problems and is an effective and robust algorithm for optimization.     

结合免疫优化和LS-SVRM观测器的非线性系统自适应鲁棒控制

针对一类单输入单输出不确定非线性控制系统提出了一种自适应鲁棒控制算法. 由于最小均方支持向量回归机(LS-SVRM)的最终解可以化为一个具有线性约束的二次规划问题, 不存在局部极小, 所以该算法在不要求假设系统的状态向量是可测的条件下通过设计基于LS-SVRM的观测器来估计系统的状态向量; 同时在算法中假设LS-SVRM的最优逼近参数向量和标称参数向量之差的范数和逼近误差的界限是未知的, 因此可通过对未知界限估计的调节来提高系统的鲁棒性. 考虑到LS-SVRM本身参数对LS-SVRM性能的影响, 本文应用一种新的免疫优化算法对LS-SVRM的参数进行优化, 从而提高LS-SVRM的逼近能力. 理论研究和仿真例子证实了所提方法的可行性和有效性.     

基于自适应人工免疫网络算法的数据挖掘

基于人工免疫网络(Artificial Immune Network:aiNet),提出了一种自适应的人工免疫网络聚类算法。在该算法中,网络抗体间的抑制阀值、抗体的克隆数目、抗体的选择和再选择数目、抗体的变异大小都随网络进化而自适应变化,使最终网络结构更符合原始数据的内在结构,降低了算法对决策者的先验知识的依赖,也提高了算法的泛化能力,很好地解决了算法与问题的相关性。仿真实验结果表明了该算法的有效性和实用性。     

基于免疫应答原理的多目标优化免疫算法及其应用

基于免疫应答原理，合理地构建免疫算子及引入一种新的小生境技术, 提出一种 解决多目标优化问题的免疫算法. 在此算法中，将优化问题的可行解对应抗体及Pareto最优个体对应抗原，这种抗原存于抗原群中,并应用新的聚类算法不断更新抗原群中的抗原, 进而获大量的Pareto最优解, 这些解能很好地分布在Pareto面（此指由Pareto最优解构成）上. 理论证明了该算法能获Pareto最优解. 最后，将该文的算法与文献\[3\]的算法SPEA进行仿真比较, 获该算法的有效性, 此表明免疫算法解决多目标优化问题具有广阔的前景.     

基于人工免疫网络的盲均衡算法

针对传统常模盲均衡算法存在的收敛到局部极小值点问题,提出一种基于人工免疫网络的盲均衡算法,把均衡器系数向量作为抗体,经过一系列抗体克隆、变异和抑制等操作,搜索到适应度值最高的抗体,即均衡器的最优系数。仿真实验结果表明,该算法是有效的。