基于NMF分组策略的人脸识别

提出一种运用非负矩阵分解（NMF）分组策略进行人脸识别的方法。将训练图像分组,分别对每组图像作NMF,获取每组图像的基图像构成的非负特征子空间,将训练图像和测试图像分别向各个特征子空间进行投影,将每组图像提取出的特征系数混合,根据最近邻原则进行识别。基于ORL人脸数据库上的实验证明了该方法的有效性。     

一种基于受限约束范围标签传播的半监督学习算法

提出一种基于受限约束范围标签传播的半监督学习算法。首先利用相似性矩阵计算得出概率转移矩阵,进而通过概率转移矩阵得出受限约束范围。然后在约束范围内利用半监督学习框架下的标签传播算法计算基于路径的相似性,路径相似性决定了标签传播的重要路径。由于只使用几条重要的传播路径使得算法中省去计算每一条路径的相似度,计算复杂度大大减少。最终使得标签在带标签数据与未标签数据之间通过几条重要的路径之间传播。实验已经证明此算法的有效性。     

基于矩阵完整化的分块整合推荐算法

传统的推荐系统往往是通过使用协同过滤或基于内容的方式来实现的,而文中将矩阵完整化的方法应用到推荐系统中。由于数据的稀疏性,直接使用矩阵完整化的方法会给推荐结果带来不小的误差。考虑到使用用户中存在一些活跃用户,挖掘出这些特殊用户,由他们组成的数据会降低稀疏性,而且对活跃用户提高 推荐质量,会产生更大的商业价值。提出了一种分块整合推荐的方法,实验结果表明该方法能够提升推荐精度。     

Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants

Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-linearized approach. This method is applied for developing two block-oriented algorithms based on diagonal Padé approximants. MATLAB versions of the above algorithms are developed, comparing, under equal conditions, accuracy and computational costs with other piecewise-linearized algorithms implemented by the authors. Experimental results show the advantages of solving stiff or non-stiff DMREs by the implemented algorithms.     

Constrained motion planning of nonholonomic systems

This paper addresses the constrained motion planning problem for nonholonomic systems represented by driftless control systems with output. The problem consists in defining a control function driving the system output to a desirable point at a given time instant, whereas state and control variables remain over the control horizon within prescribed bounds. The state and control constraints are handled by extending the control system with a pair of state equations driven by the violation of constraints, and adding regularizing perturbations. For the regularized system a Jacobian motion planning algorithm is designed, called imbalanced. Solutions of example constrained motion planning problems for the rolling ball illustrate the theoretical concepts.     

Dynamic normal forms and dynamic characteristic polynomial

We present the first fully dynamic algorithm for computing the characteristic polynomial of a matrix. In the generic symmetric case, our algorithm supports rank-one updates in O(n²logn) randomized time and queries in constant time, whereas in the general case the algorithm works in O(n²klogn) randomized time, where k is the number of invariant factors of the matrix. The algorithm is based on the first dynamic algorithm for computing normal forms of a matrix such as the Frobenius normal form or the tridiagonal symmetric form. The algorithm can be extended to solve the matrix eigenproblem with relative error 2^−b in additional O(nlog²nlogb) time. Furthermore, it can be used to dynamically maintain the singular value decomposition (SVD) of a generic matrix. Together with the algorithm, the hardness of the problem is studied. For the symmetric case, we present an Ω(n²) lower bound for rank-one updates and an Ω(n) lower bound for element updates.     

A Proof-Planning Framework with explicit Abstractions based on Indexed Formulas

A major motivation of proof-planning is to bridge the gap between high-level, cognitively adequate reasoning for specific domains, and calculus-level reasoning to ensure soundness. For high reasoning levels the cognitive adequacy of representation and reasoning techniques is a major issue, while for lower reasoning levels the adequacy wrt. the modelled domain is important. Furthermore, proof construction is an engineering task and there is a need to support the design and application of proof-search engineering methods. To this end we present a framework to explicitly support different reasoning levels. To structure reasoning levels the framework allows for an explicit representation of abstractions and proof-search refinement techniques. In order to ensure soundness within a reasoning level, we use techniques developed in the context of matrix characterisation relying on the notion of indexed formulas. Furthermore, we introduce a uniform concept for contextual reasoning, and sketch basic tacticals for the definition of tactics to organise the overall proof-search inside and across different reasoning levels.     

Efficient Solution of A, x ( k )?= b ( k ) Using A ?1

In this work, we consider the problem of solving , , where b ^(k+1) = f(x ^(k)). We show that when A is a full matrix and , where depends on the specific software and hardware setup, it is faster to solve for by explicitly evaluating the inverse matrix A ⁻¹ rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A.     

三维图形引擎中骨骼蒙皮动画的一种实现方法*

提出了三维图形引擎中骨骼蒙皮动画的一种实现方法,即将现有的关节动画与单一网格动画相结合,利用骨架的继承变换和顶点混合技术使骨骼蒙皮动画平滑逼真。实验表明该方法有良好的显示效果,并具有较好的实时性,且占用的存储空间不大,能够满足当前三维图形引擎对动画技术的要求。