Eigensolution of specially structured matrices with hyper‐symmetry

Recently, four canonical forms have been developed and applied to the dynamics and stability analysis of symmetric frames. In this paper, hyper‐symmetric matrices and specially structured matrices are defined and efficient methods are proposed for the eigensolution of such matrices. Applications are extended to hyper‐graphs and specially structured graphs. Simple methods are developed for calculating the eigenvalues of the Laplacian matrices of such graphs. The developments presented in this paper can also be considered as generalization of Form II and Form III symmetry, previously defined by the authors. Copyright © 2006 John Wiley & Sons, Ltd.     

Laplacian group sparse modeling of human actions

Recently, many local-feature based methods have been proposed for feature learning to obtain a better high-level representation of human behavior. Most of the previous research ignores the structural information existing among local features in the same video sequences, while it is an important clue to distinguish ambiguous actions. To address this issue, we propose a Laplacian group sparse coding for human behavior representation. Unlike traditional methods such as sparse coding, our approach prefers to encode a group of relevant features simultaneously and meanwhile allow as less atoms as possible to participate in the approximation so that video-level sparsity is guaranteed. By incorporating Laplacian regularization the method is capable to ensure the similar approximation of closely related local features and the structural information is successfully preserved. Thus, a compact but discriminative human behavior representation is achieved. Besides, the objective of our model is solved with a closed-form solution, which reduces the computational cost significantly. Promising results on several popular benchmark datasets prove the efficiency and effectiveness of our approach.     

Sentiment visualization and classification via semi-supervised nonlinear dimensionality reduction

Sentiment analysis, which detects the subjectivity or polarity of documents, is one of the fundamental tasks in text data analytics. Recently, the number of documents available online and offline is increasing dramatically, and preprocessed text data have more features. This development makes analysis more complex to be analyzed effectively. This paper proposes a novel semi-supervised Laplacian eigenmap (SS-LE). The SS-LE removes redundant features effectively by decreasing detection errors of sentiments. Moreover, it enables visualization of documents in perceptible low dimensional embedded space to provide a useful tool for text analytics. The proposed method is evaluated using multi-domain review data set in sentiment visualization and classification by comparing other dimensionality reduction methods. SS-LE provides a better similarity measure in the visualization result by separating positive and negative documents properly. Sentiment classification models trained over reduced data by SS-LE show higher accuracy. Overall, experimental results suggest that SS-LE has the potential to be used to visualize documents for the ease of analysis and to train a predictive model in sentiment analysis. SS-LE can also be applied to any other partially annotated text data sets.     

基于拉普拉斯方向的差值线性判别分析

标准的LDA方法通常有3个问题:1)为了确保类内散度矩阵的非奇异性,必须首先通过PCA进行维数约简,这限制了对更多维数空间的使用;2)当每人只有单个训练样本时,类内散度矩阵必然奇异,此时LDA无法工作;3)缺乏对像素间的局部相关性的考虑。为了解决这些问题,提出一种基于拉普拉斯方向的差值线性判别分析方法。该方法通过拉普拉斯方向实现更鲁棒的图像相异性测度,通过引入差值散度矩阵来避免类内散度矩阵的奇异性。实验结果显示,该算法对表情变化、光照改变及不同遮挡情况获得了更高的识别率,尤其针对光照变化,效果更加显著。     

基于特征保持的三维模型四面体化及优化

三维模型四面体化是一种重要的有限元网格生成技术.介绍了一种特征保持的四面体网格生成及优化算法.首先使用三维模型主成分分析进行预处理,然后用体心立方构建初始四面体,接着通过拉普拉斯坐标改变模型边界切点的移动方式保持模型的局部特征,最后构造改进的密度能量误差函数优化四面体网格质量.实验结果表明,该方法可行、有效,且能很好地保持模型特征.     

基于量子力学和拉普拉斯金字塔的图像融合方法

针对数字图像的融合问题,研究一种基于量子力学理论的图像分解方法,并将其结合拉普拉斯金字塔变换,提出一种新的图像融合方法.先把2幅灰度图像表示成量子比特的形式,然后把每幅图像分解成4幅特征子图,根据分解后特征子图的不同含义,使用不同的融合策略分别对子图进行融合.其中一幅子图使用拉普拉斯金字塔变换进行融合,另外3幅子图使用区域梯度取大法进行融合,最后通过重构得到融合图像.仿真实验表明该方法融合效果较好,在主观视觉感受和客观评价指标上均优于传统的图像融合方法.     

带 2细分结构的四边形化

在Morse函数理论的基础上,提出一种新的从三角网格中建立四边形网格多分辨率表示的方法．先由人工指定或从拉普拉斯矩阵的特征函数中提取临界点,计算带约束的拉普拉斯方程得到光滑的Morse函数．函数的临界点（极大、极小和鞍点）有规律地分布在模型表面,在三角网格表面梯度场的引导下, 生成临界点间流线,得到临界点间的拓扑关系．通过临界点交换规则,同样是采用流线的方法,得到更精细的四边形网格。 最终可实现无需参数化而仅用流线方法来建立不同多分辨率表示的四边形网格。     

Stabilization of symmetric formations to motion around convex loops

We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms.     

无人机的追逃对抗仿真研究

代数图论方法较之微分对策建立的无人机追逃对抗模型更易仿真求解,利用梯度方法改变Laplacian矩阵的非零特征值给出了对抗双方的控制输入,仿真证明了该方法的可行性.利用边界权值函数考虑无人机通信或感知能力的变化.然后,针对仿真过程中遇到的问题提出根据实际情况构造不同的性能指标.仿真表明逃逸者为迷惑追击者不时交叉逃逸;而追击者也会更换追击目标:相对距离不断变化.     

基于球面参数化的点模型渐变

为了获得光滑自然的点模型渐变效果,基于球面参数化,提出了一种鲁棒的渐变算法。该算法首先对源和目标模型进行球面参数化,使得参数化后的模型嵌入到单位球面上;然后在球面上自适应地对齐模型间的相应特征点,并将球面映射到矩形参数域上,基于该域建立模型间各采样点的对应关系;接着在渐变过程中,采用拉普拉斯算子计算出中间点模型的几何位置,以保持模型的细节;最后利用移动最小二乘曲面进行动态上采样,以消除中间模型的裂缝。实验结果表明,该算法具有良好匹配的采样点对应和光滑的渐变过程。