基于样本加权的格拉斯曼平均算法

格拉斯曼平均子空间对应着高斯数据的主成分,解决了PCA的扩展性问题,但算法假定样本的贡献取决于样本的长度,这可能导致离群点对算法的干扰较强。为此,利用无监督学习数据的局部特性或监督学习中样本的类别信息建立样本的权重,从而提出一种基于样本加权的格拉斯曼平均的算法,在UCI数据集和ORL人脸数据库上的实验结果表明,新算法有好的鲁棒性并且其识别率比已有方法提高1%~2%。     

Computing with graphs and graph transformations

Many software applications require the construction and manipulation of graphs. In standard programming languages, this is accomplished using low‐level mechanisms such as pointer manipulation or array indexing. In contrast, graph productions are a convenient high‐level visual notation for coding graph modifications. A graph production replaces one subgraph by another subgraph. Graph productions can define a graph grammar and graph language, or can directly transform an input graph into an output graph. Graph transformation has been applied in many areas, including the definition of visual languages and their tools, the construction of software development environments, the definition of constraint programming algorithms, the modeling of distributed systems, and the construction of neural networks. One application is presented in detail: the interpretation of mathematical notation in scanned document images. The graph models the set of mathematical symbols, and their spatial and logical relationships. This graph is transformed by productions written in the PROGRES language. Copyright © 1999 John Wiley & Sons, Ltd.     

An efficient method for decomposition of regular structures using graph products

In this paper an efficient method is presented for calculating the eigenvalues of regular structural models. A structural model is called regular if they can be viewed as the direct or strong Cartesian product of some simple graphs known as their generators. The eigenvalues of the adjacency and Laplacian matrices for a regular graph model are easily obtained by the evaluation of eigenvalues of its generators. The second eigenvalue of the Laplacian of a graph is also obtained using a much faster and much simple approach than the existing methods. Copyright © 2004 John Wiley & Sons, Ltd.     

标题位置等因素对表图使用绩效的影响

考察表、图标题位置、数据复杂度和问题难度对表、图使用绩效的影响。49名大学生随机分为表格组和图形组。结果表明:(1)从表中提取信息更快、更准确,但对图中信息的回忆正确率更高;(2)标题位于上方时提取信息更快更准,回忆正确率也更高;(3)数据复杂度主要影响反应正确率;(4)对简单问题的反应既快又准,但回忆正确率较低。     

Factorization for efficient solution of eigenproblems of adjacency and Laplacian matrices for graph products

Many structural models can be generated as the graph products of two or three subgraphs known as their generators. The main types of graph products consist of Cartesian, strong Cartesian, direct, and lexicographic products. In this paper, a general method is presented for the factorization of these graph products, such that the eigenvalues of the entire graph are obtained as the union of the eigenvalues of the weighted subgraphs defined here. The adjacency and Laplacian matrices for each graph product are studied separately. For graphs with missing elements (cut‐outs), the eigenvalues are calculated with the additional use of the Rayleigh quotient approach. The main idea stems from the rules recently developed by the authors for block diagonalization of matrices. These products have many applications in computational mechanics, such as ordering, graph partitioning, dynamic analysis, and stability analysis of structures. Some of these applications are addressed in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Sequence comparison on the connection machine

We give two parallel algorithms for sequence comparison on the Connection Machine 2 (CM-2). The specific comparison measure we compute is the edit distance: given a finite alphabet ∑ and two input sequences X ϵ ∑⁺ and Y ϵ ∑⁺ the edit distance d(X,Y) is the minimum cost of transforming X into Y via a series of weighted insertions, deletions and substitutions of characters. The edit distance comparison measure is equivalent to or subsumes a broad range of well known sequence comparison measures. The CM-2 is very fast at performing parallel prefix operations. Our contribution consists of casting the problem in terms of these operations. Our first algorithm computes d(X,Y) using N processors and O(M S) time units, where M = min(|X|,||Y|) + 1, N = max(|X|,|Y|) + 1 and S is the time required for a parallel prefix operation. The second algorithm computes d(X,Y) using NM processors and O((log N log M)(S + R)) time units, where R is the time for a ‘router’ communication step—one in which each processor is able to read data, in parallel, from the memory of any other processor. Our algorithms can also be applied to several variants of the problem, such as subsequence comparisons, and one—many and many-many comparisons on 'sequence databases'.     

基于Hopfield网络的图的同构算法

本文应用Hopfield网络,系统地研究了图的同构问題,通过建立相应的数学理论,改进并简化了前人所提出的能量函数,从而简化了网络的复杂性,提高了网络的收敛速度。最后给出了实验研究的结果。     

任意图的同构判定算法:特征向量法

在构建有效描述任意图邻接矩阵的基础上,分别计算2个矩阵的特征值所对应的特征向量,并依据它们的极大无关组寻找可能的同构对应关系.通过逐一考查全体特征值,实现图同构的判定并确定同构图的顶点对应关系.随着判定规模增大及图对称性增强,与已有方法相比,文中方法具有更高的同构判定效率.实验结果表明,在多数情况下该方法是快捷有效的.     

进化设计中拓扑搜索和参数的协同优化算法

为了解决基于遗传编程(GP)的动态系统进化设计过程中拓扑和参数协同优化的问题,讨论了基于GP的进化设计种群拓扑多样性保存策略,提出了一种拓扑适应值共享-拥挤协同搜索算法。该算法避免计算小生境半径、通过自适应适应度函数来惩罚拓扑子群,保证了拓扑多样性和阻止局部收敛的发生。实验结果表明,该算法保证了动态系统进化设计中拓扑和参数同步搜索的平衡,有效地克服了局部收敛,能确保获得理想的设计结果。     

基于实值RBM的深度生成网络研究

受限玻尔兹曼机（restricted Boltzmann machine,简称RBM）是一种概率无向图,传统的RBM模型假设隐藏层单元是二值的,二值单元的优势在于计算过程和采样过程相对简单,然而二值化会对基于隐藏层单元的特征提取和数据重构过程带来信息损失.因此,将RBM的可见层单元和隐藏层单元实值化并保持模型训练的有效性,是目前RBM理论研究的重点问题.为了解决这个问题,将二值单元拓展为实值单元,利用实值单元建模数据并提取特征.具体而言,在可见层单元和隐藏层单元之间增加辅助单元,然后将图正则化项引入到能量函数中,基于二值辅助单元和图正则化项,流形上的数据有更高的概率被映射为参数化的截断高斯分布;同时,远离流形的数据有更高的概率被映射为高斯噪声.由此,模型的隐层单元可以被表示为参数化截断高斯分布或高斯噪声的采样实值.该模型称为基于辅助单元的受限玻尔兹曼机（restricted Boltzmann machine with auxiliary units,简称ARBM）.在理论上分析了模型的有效性,然后构建了相应的深度模型,并通过实验验证模型在图像重构任务和图像生成任务中的有效性.