非均匀节点情形下的一类三角B样条曲线

给出一类在非均匀节点情形下带参数的三角B样条基函数,讨论了这类基函数的性质以及在重节点情形时的变化,并利用这类基函数构造了相应的三角B样条曲线,这类曲线具有与二次非均匀B样条曲线相似的性质。在控制顶点不变的情况下,可以通过改变形状参数取值来调节曲线的形状。此外,它还能精确表示圆、椭圆等曲线。     

一类超越曲线的有理表示

基于类Bcrnstein三角基函数和有理Berastcin基函数之间的关系，利用三角多项式空间规范B基的性质，得到将该空间基函数转换为有理Bernstein基函数的方法，给出了该空间中超越曲线有理表示的有效算法．     

5阶三角多项式空间中的拟Bézier基在三角域上的推广

为了进一步研究非多项式空间的拟B啨zier基,完善其关于三角域部分的理论,将5阶三角多项式空间G=span{1,sint,cost,sin2t,cos2t}上的基推广到三角域上,构造出满足正性、权性、对称性、边界性质和线性无关性的拟B啨zier基,使得相应的三角曲面不用有理形式就可以表示球面片.实例结果表明,使用这组基可以精确地造型出整球面.     

基于基函数展开的双隐层过程神经元网络及其应用

提出一类基于基函数展开的双隐层过程神经元网络模型．过程神经元隐层完成对输入信息过程模式特征的提取和对时间的聚合运算，非时变一般神经元隐层用于提高网络对系统输入输出之间复杂关系的映射能力．在输入空问中引入一组函数正交基，将输入函数和网络权函数表示为该组正交基的展开形式，利用基函数的正交性简化过程神经元聚合运算．以旋转机械故障诊断和油藏开发过程采收率的模拟为例，验证了模型和算法的有效性。     

T—Bezier曲线及G^1拼接条件

针对目前NURBS模型的局限性问题，在对T—Bezier基函数压曲线端点特性分析的基础上。提出了k次T—Bezier基函数的表达式，通过重新参数化使其参数区间范围规范为【0，1】，给出了椭圆弧和心脏线的T-Bezier表示，并给出T-Bezier曲线间G^1拼接的几何条件，所得结论具有明确的几何意义，能够较好地应用于曲面造型中。     

基于三角和代数多项式的T-Bézier曲线

该文从Γn=span{ 1,t,t2 ,t3 ,… ,tn -4,sint,cost,sin2t,cos2t}中提取出名为T B啨ｚｉｅｒ的一组基 ,分析了该组基的性质 ,并由该组基定义了T B啨ｚｉｅｒ曲线 ,同时证明了许多有实际应用价值的曲线 (如代数曲线和超越曲线 )可以用T B啨ｚｉｅｒ曲线的形式精确表示 .     

带形状参数的三角多项式均匀B样条

该文给出了n阶带形状参数的三角多项式均匀B样条基函数．由带形状参数的三角多项式均匀B样条基组成的样条曲线可通过改变形状参数的取值而调整曲线的形状,并且可以精确表示圆、椭圆、螺旋线等曲线．随着阶数的升高,形状参数的取值范围将扩大．     

改进的非负稀疏编码图像基学习算法

图像基学习是图像特征提取与表示的重要方法之一。非负稀疏编码不仅具有标准稀疏编码算法的自适应性、空间的局部性、方向性和频域的带通性,而且更能反应哺乳动物的视觉机制。本文在非负稀疏编码的基础上,利用经验模态分解技术加入了图像的结构信息,提出了结合经验模态分解的非负稀疏编码算法,保证了系数矩阵的稀疏性与所提取图像特征的结构性。学习得到的图像基不仅具有非负稀疏编码的特征,而且更好地表示出图像的结构信息。     

带形状参数的双曲多项式均匀B样条

给出了n阶带形状参数的双曲多项式均匀B样条基函数.由带形状参数的双曲多项式均匀B样条基组成的样条曲线可通过改变形状参数的取值调整曲线的形状,并且可以精确表示双曲线.随着阶数的升高,形状参数的取值范围将扩大.     

均匀B样条基与DP-NTP基之间的转换与应用

B样条基以其标准全正性和局部支柱性的长处,在曲线曲面构造中被广泛应用.而作为其特殊情况的均匀B样条,又因其操作简便等长处,对其的研究在工业造型设计方面也十分有意义.2003年,Delgado和Pe?a提出了另一类用标准全正基(DP-NTP基)构造的新曲线表示形式,这种曲线在求值运算中具有线性时间复杂度的明显优势,同时像B样条曲线那样具有模拟或保持控制多边形形状的保形性质,但没有形状局部可调性.为了使它们实现优势互补,并在不同的造型系统之间进行数据的交换和传递,给出了均匀B样条曲线与DP-NTP曲线的相互转换.实例表明,其结果可在CAD系统中,尤其在曲线曲面需要快速求值或形状局部可调的场合得到相当广泛的应用.     

基于新约束图模型的布图规划和布局算法

布图规划和布局构形的表示是基于随机优化方法的布图规划和布局算法的核心问题.针对Non-slicing结构的布图规划和布局,提出了一种新的基于约束图表示的模型.基于该模型及其性质,可以得到近似O(n)时间复杂度的有效的布局算法.通过引入变形网格的假设,得到了一种新的更加精确的Non-Slicing结构的表示模型:梯形网格模型.其空间复杂度为n(3+lg[n]),时间复杂度为O(n),解空间规模为n!2^3n-7.已经证明,梯形网格模型可以表示所有的Slicing结构的布局,同时又可以有效地表示Non-Slicing结构的布局,而时间复杂度与Slicing表示相同.实验结果表明,该表示优于刚刚发表的O-tree模型.梯形网格模型是一种拓扑模型,而O-tree的表示依赖于模块的尺寸,因而梯形网格能更有效地处理含有软模块的的布图规划问题.     

基于表示学习的开放域中文知识推理

知识库通常以网络的形式被组织起来,网络中每个节点代表实体,而每条连边则代表实体间的关系。为了利用这种网状知识库中的知识,往往需要设计专门的、复杂度较高的图算法。然而这些算法并不能很好适用于知识推理,尤其是随着知识库的知识规模不断扩大,基于网状结构知识库的推理很难较好地满足实时计算的需求。该文使用基于TransE模型的知识表示学习进行知识推理,包括对实体关系三元组中关系指示词以及尾实体的推理,其中关系指示词推理的实验取得了较好的结果,且推理过程无需设计复杂的算法,仅涉及向量的简单运算。另外,该文对原始TransE模型的代价函数进行改进,以更好地适用于开放域中文知识库表示学习。     

Image representation using Laplacian regularized nonnegative tensor factorization

Tensor provides a better representation for image space by avoiding information loss in vectorization. Nonnegative tensor factorization (NTF), whose objective is to express an n-way tensor as a sum of k rank-1 tensors under nonnegative constraints, has recently attracted a lot of attentions for its efficient and meaningful representation. However, NTF only sees Euclidean structures in data space and is not optimized for image representation as image space is believed to be a sub-manifold embedded in high-dimensional ambient space. To avoid the limitation of NTF, we propose a novel Laplacian regularized nonnegative tensor factorization (LRNTF) method for image representation and clustering in this paper. In LRNTF, the image space is represented as a 3-way tensor and we explicitly consider the manifold structure of the image space in factorization. That is, two data points that are close to each other in the intrinsic geometry of image space shall also be close to each other under the factorized basis. To evaluate the performance of LRNTF in image representation and clustering, we compare our algorithm with NMF, NTF, NCut and GNMF methods on three standard image databases. Experimental results demonstrate that LRNTF achieves better image clustering performance, while being more insensitive to noise.     

扩展的DBNS椭圆曲线标量乘算法

椭圆曲线密码体制的快速实现取决于标量乘算法的运算效率。在传统的（2,3）-双基数标量乘算法的基础上,提出了一种新的（2,5）-双基数标量乘算法。实验数据表明,该算法不仅继承了双基数标量乘算法的优点,同时还改进了传统双基数标量乘算法的不足,如预计算时间长和存储空间要求大等问题,使其应用于存储空间较小的领域如智能卡等成为可能。     

Time-space trade-offs for compressed suffix arrays

Given a binary string of length n, we give a representation of its suffix array that takes O(nt(lgn)^1/t) bits of space such that given i,1?i?n, the ith entry in the suffix array of the string can be retrieved in O(t) time, for any parameter 1?t?lglgn. For t=lglgn, this gives a compressed suffix array representation of Grossi and Vitter [Proc. Symp. on Theory Comput., 2000, pp. 397-406]. For t=O(1/ε), this gives the best known (in terms of space) compressed suffix array representation with constant query time. From this representation one can construct a suffix tree structure for a text of length n, that uses o(nlgn) bits of space which can be used to find all the k occurrences of a given pattern of length m in O(m/lgn+k) time. No such structure was known earlier.     

SPN分组密码中最优扩散层的构造与验证

SPN结构中的扩散层往往是矢量空间GF(2m)n上的线性变换,它与n阶矩阵在确定基 下一一对应。分支数B=n+1的扩散层是最优的,其充分必要条件是:对应矩阵的任意k阶子阵均 为非奇异。设计了构造最优SPN线性层的算法,并给出了线性变换最优扩散特性的验证算法。最 后,给出GF(28)8上一个最优线性变换及其验证结果的示例。     

Modelling and estimating the pose of a human arm

Pose estimation of 3-D objects based on monocular computer vision is an ill-posed problem. To ease matters a model-based approach can be applied. Such an approach usually relies on iterating when matching the model and the image data. In this paper we estimate the 3-D pose of a human arm from a monocular image. To avoid the inherent problems when iterating, we apply an exhaustive matching strategy. To make this plausible, we reduce the size of the solution space through a very compact model representation of the arm and prune the solution space. The model is developed through a detailed investigation of the functionality and structure of the arm and the shoulder complex. The model consists of just two parameters and is based on the screw-axis representation together with image measurements. The pruning is achieved through kinematic constraints and it turns out that the solution space of the compact model can be pruned , on average. Altogether, the compact representation and the constraints reduce the solution space significantly and, therefore, allow for an exhaustive matching procedure. The approach is tested in a model-based silhouette framework, and tests show promising results.Published online: 8 August 2003Correspondence to: Thomas B. Moeslund     

Dimensionality reduction via kernel sparse representation

Dimensionality reduction (DR) methods based on sparse representation as one of the hottest research topics have achieved remarkable performance in many applications in recent years. However, it’s a challenge for existing sparse representation based methods to solve nonlinear problem due to the limitations of seeking sparse representation of data in the original space. Motivated by kernel tricks, we proposed a new framework called empirical kernel sparse representation (EKSR) to solve nonlinear problem. In this framework, nonlinear separable data are mapped into kernel space in which the nonlinear similarity can be captured, and then the data in kernel space is reconstructed by sparse representation to preserve the sparse structure, which is obtained by minimizing a ?1 regularization-related objective function. EKSR provides new insights into dimensionality reduction and extends two models: 1) empirical kernel sparsity preserving projection (EKSPP), which is a feature extraction method based on sparsity preserving projection (SPP); 2) empirical kernel sparsity score (EKSS), which is a feature selection method based on sparsity score (SS). Both of the two methods can choose neighborhood automatically as the natural discriminative power of sparse representation. Compared with several existing approaches, the proposed framework can reduce computational complexity and be more convenient in practice.     

基于改进FP-tree的最大频繁项目集挖掘算法

针对已有算法为了减少PF-tree中路径被重复遍历的次数,需要保存FP-tree中所有频繁1-项集的条件模式基的问题,对FP-tree的数据结构进行修改,使得只需要保存FP-tree中每个叶子节点的父节点到根节点路径上项目组成的条件模式基,降低了保存条件模式基的存储空间开销。在分析最大频繁项目集挖掘算法中搜索空间以及数据表示方法的基础上,通过理论分析和证明,设计了剪枝策略和压缩策略,缩小了算法搜索空间,压缩了FP-tree的规模,提高了算法的执行效率。最后将新算法分别与NHTFPG算法、FpMAX算法进行对比,验证算法的正确性和有效性。实验结果表明,新算法保存FP-tree条件模式基所需要的存储空间不到NHTFPG算法的50%,执行效率比FpMAX算法提高了2~3倍。