Recursive decomposition and bounds of the lattice of Moore co-families

A collection of sets on a ground set U _n (U _n ?=?{1,2,...,n}) closed under intersection and containing U _n is known as a Moore family. The set of Moore families for a fixed n is in bijection with the set of Moore co-families (union-closed families containing the empty set) denoted $\mathbb{M}_n$ . In this paper, we propose a recursive definition of the set of Moore co-families on U _n . Then we apply this decomposition result to compute a lower bound on $|\mathbb M_n|$ as a function of $|\mathbb M_{n-1}|$ , the Dedekind numbers and the binomial coefficients. These results follow the work carried out in [1] to enumerate the number of Moore families on U ₇.     

Recursive partitioning clustering tree algorithm

Clustering analysis elicits the natural groupings of a dataset without requiring information about the sample class and has been widely used in various fields. Although numerous clustering algorithms have been proposed and proven to perform reasonably well, no consensus exists about which one performs best in real situations. In this study, we propose a nonparametric clustering method based on recursive binary partitioning that was implemented in a classification and regression tree model. The proposed clustering algorithm has two key advantages: (1) users do not have to specify any parameters before running it; (2) the final clustering result is represented by a set of if–then rules, thereby facilitating analysis of the clustering results. Experiments with the simulations and real datasets demonstrate the effectiveness and usefulness of the proposed algorithm.     

A top-down algorithm for generating the Hasse tree of a fuzzy preorder closure

This paper describes a new top-down algorithm for the stepwise generation of the different levels or Hasse diagrams of the Hasse tree associated to the fuzzy preorder closure (min-transitive closure) of a given reflexive binary fuzzy relation. The algorithm is based upon a recently established weight-driven method for computing the min-transitive closure of a reflexive binary fuzzy relation. The way in which this method gradually establishes the fuzzy preorder closure implies that for the generation of a specific level of the Hasse tree, the newly proposed algorithm does not require the complete computation of this closure.     

Designing a decompositional rule extraction algorithm for neural networks with bound decomposition tree

The neural networks are successfully applied to many applications in different domains. However, due to the results made by the neural networks are difficult to explain the decision process of neural networks is supposed as a black box. The explanation of reasoning is important to some applications such like credit approval application and medical diagnosing software. Therefore, the rule extraction algorithm is becoming more and more important in explaining the extracted rules from the neural networks. In this paper, a decompositional algorithm is analyzed and designed to extract rules from neural networks. The algorithm is simple but efficient; can reduce the extracted rules but improve the efficiency of the algorithm at the same time. Moreover, the algorithm is compared to the other two algorithms, M-of-N and Garcez, by solving the MONK’s problem.     

基于LDLT分解求实对称矩阵特征值的递归算法

基于线性代数与矩阵理论,给出利用LDLT分解计算实对称矩阵特征值的递归算法。该算法可求出实对称矩阵在给定区间内的特征值的个数,并可计算满足精度要求的特征值。理论分析和实际测试证明该算法是有效的。     

基于Cube的数据展现结构的研究

为了为用户提供合适的OLAP可视化工具,研究了OLAP可视化技术的范围和概念,并研究了OLAP可视化技术的研究现状。重点研究了分解树技术的内容以及拓展,根据分解树的优点和缺点提出了新的OLAP可视化技术:多角度增强分解树。该技术可从两个方面对OLAP数据进行钻取,其中提出的多角度钻取,通过不同的角度来对比观察数据,提高了模式发现能力。针对该技术,设计了系统架构,确定了系统流程,完成了系统的开发。最后对OLAP可视化研究的前景进行了总结。     

基于正交分解的递推子空间闭环辨识方法

为实现闭环系统在线辨识,提出递推正交分解闭环子空间辨识方法(RORT)。首先,根据闭环系统状态空间模型和数据间投影关系,构建确定-随机模型,并利用GIVENS变换实现投影向量的递推QR分解;然后,引入带遗忘因子的辨识算法,构建广义能观测矩阵的递推更新形式,以减少子空间辨识算法中QR分解和SVD分解的计算量;最后,针对某型号陀螺仪闭环系统进行实验。实验结果表明, RORT法的辨识拟合度高于91%,能够对陀螺仪闭环系统模型参数进行在线监测。     

A refinement of a spherical decomposition algorithm

A refinement is suggested to the O'Rourke-Badler spherical decomposition algorithm which reduces its complexity from 0(n3) to 0(n2)     

Comments on "Recursive filtering algorithm for a two-dimensional system"

General comments on quarter-plane causal 2-D filters are proffered, and logical errors in the derivation of a recent algorithm of this ilk are discussed.     

Hammerstein-Wiener系统的递推贝叶斯参数辨识算法

为了辨识一类非线性Hammerstein-Wiener系统,基于递推贝叶斯算法和奇异值分解,提出了一种两阶段在线辨识算法。该算法首先利用递推贝叶斯算法估计乘积项参数,然后利用奇异值分解得到待估计参数。仿真结果表明,所提算法可以以较小的计算量获得精度较高的参数估计值。     

矩阵的Doolittle递归分解算法及符号程序设计

将矩阵An×n的Doolittle分解推广到Am×n上，并在常规的迭代算法上加以创新，给出了递归的分解算法．在实现算法的过程中，对数据进行了巧妙处理，使中间数据及最终计算结果都具有分数形式，提高了结果的精确度，而且更符合人们阅读的习惯．经过运行测试，算法设计合理，程序运行高效准确．程序是对MathSoft公司的交互式的数学文字软件Mathcad的矩阵分解的数值计算扩充到符号运算．     

Object recognition algorithm using a vocabulary tree and a pre-matching array

A vocabulary tree algorithm builds a tree structure with the off-line learning method using a large training image dataset. After constructing the tree structure, we can retrieve a query image class very quickly by searching it. This algorithm has come into the spotlight recently because of the great reduction in computation time. In this article, we suggest a method which improves the classification accuracy by searching a vocabulary tree many times for each test dataset. The information which is given by the pre-matching array determines how the tree is visited. Using our new algorithm, we can reduce the miss-classification rate considerably. On the other hand, losses in computation time and memory allocation are negligible with respect to real-time recognition.     

A parallel algorithm for constructing a labeled tree

A tree T is labeled when the n vertices are distinguished from one another by names such as v₁, v₂…v_n . Two labeled trees are considered to be distinct if they have different vertex labels even though they might be isomorphic. According to Cayley's tree formula, there are n^n-2 labeled trees on n vertices. Prufer used a simple way to prove this formula and demonstrated that there exists a mapping between a labeled tree and a number sequence. From his proof, we can find a naive sequential algorithm which transfers a labeled tree to a number sequence and vice versa. However, it is hard to parallelize. In this paper, we shall propose an O(log n) time parallel algorithm for constructing a labeled tree by using O(n) processors and O(n log n) space on the EREW PRAM computational model     

The tree MVA algorithm

A new algorithm to solve product form queueing networks, especially those with large numbers of centers and chains, is presented. This algorithm is a Tree version of Mean Value Analysis (MVA). Tree MVA is analogous to the Tree version of Convolution developed by Lam and Lien. Like Tree Convolution, Tree MVA allows exact solution of large networks which are intractable with previous sequential algorithms. As with the sequential versions of Convolution and MVA, Tree MVA has better numerical properties than Tree Convolution. Further, Tree MVA avoids the computational complexity of sequential MVA in networks with several queue dependent centers. Thus, we consider Tree MVA to be the best algorithm for general product form networks.     

Hierarchical matrix techniques for a domain decomposition algorithm

Summary In this paper, we investigate the effectiveness of hierarchical matrix techniques when used as the linear solver in a certain domain decomposition algorithm. In particular, we provide a direct performance comparison between an algebraic multigrid solver and a hierarchical matrix solver which is based on nested dissection clustering within the software package PLTMG.      

Recursive parameter identification algorithm stability analysis via pi-sharing

Pi-sharing is introduced as an extension of the application of passivity and hyperstability concepts for discrete-time systems, providing connections between input-output and state-space stability notions. Using tools developed within the pi-sharing framework, new stability results for the output error class identification algorithm are derived. This approach offers a clear interpretation of the role of the SPR condition in the work of Landau and Silveira and its absence in the work of Tomizuka and Altay.     

一种政策语篇拟合度递归下降评估算法

在分析和研究国内外基于向量空间模型的文本拟合度计算方法的基础上,提出了一种递归下降的政策文本拟合度计算方法。该方法基于政策文本预处理和递归下降等技术给出了政策子句拟合度计算方法和政策语篇拟合度计算方法。该方法不直接建立一般经典算法都要涉及的词频向量,而是将相同词汇进行合并。然后利用递归下降的方法,从政策子句、段落和语篇三个不同的层次分析政策语篇的一致性问题,降低拟合度计算的空间复杂度。实验结果表明,该方法与现有的一些拟合度计算方法相比,有效地提高了一致性验证的效率和准确率。     

Recursive algorithm for the two-stage EFOP estimation method

A recursive algorithm for the two-stage empirical frequency-domain optimal parameter （EFOP） estimation method was proposed. The EFOP method was a novel system identification method for Black-box models that combines time-domain estimation and frequency-domain estimation. It has improved anti-disturbance performance, and could precisely identify models with fewer sample numbers. The two- stage EFOP method based on the boot-strap technique was generally suitable for Black-box models, but it was an iterative method and takes too much computation work so that it did not work well online. A recursive algorithm was proposed for dis- turbed stochastic systems. Some simulation examples are included to demonstrate the validity of the new method.     

An algorithm for hierarchical reduction and decomposition of a directed graph

With the algorithm described, it is possible to decompose a directed graph without loops and cycles into subgraphs which have one and only one source, one and only one sink and no other connections to the complement of the subgraph. The algorithm delivers all subgraphs with this property and the hierarchical structure of these subgraphs. Examples and some experiences on computing time are given.