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.     

脑电Laplacian空域滤波的改进算法

Laplacian空域滤波通过被关注的通道与相邻通道信号转换,能有效地提高脑电信号的信噪比,经典的Laplacian空域滤波矩阵由通道之间的距离确定.该方法依赖于相应通道定位的准确性,实际应用中不能保证电极精准安放并存在个体差异,影响了该方法的应用效果.为了提高该算法的通用性,采用高斯模型改进经典Laplacian空域滤波算法,根据用户调试数据确定模型相关参数,进而确定空域滤波矩阵.采用国际脑机接口竞赛BCI competition 2005 Ⅳ数据集验证滤波后的效果,总体比经典Laplacian方法识别准确度提高10个百分比,采用改进方法滤波后不同类间距离增大、同类间距离减小,提高了信号的信噪比.     

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。     

改进拉普拉斯金字塔模型的高动态图像色调映射方法

高动态图像的色调映射是图像处理的研究热点,用于解决常规色调范围显示设备无法有效显示高动态图像的问题.针对当前色调映射不能精准地显示出图像内容(如丢失细节、模糊弱边缘)的问题,提出一种改进拉普拉斯金字塔模型的高动态图像色调映射方法.首先基于滤波和下采样处理计算出对输入图像进行了简单去噪的高斯金字塔;然后通过约束强边缘数量分离出高斯金字塔中每层图像的强?弱边缘和细节;再针对每层图像构造其分层映射函数,通过增强细节、弱边缘的对比度以及保持强边缘对每层图像进行逐点映射,并据此计算描述每层对比度变化的拉普拉斯金字塔;最后根据拉普拉斯金字塔自底向上重构出目标图像.与已有的多种色调映射方法相比,根据客观评价和主观评价的结果表明,文中方法能增强细节和弱边缘、避免强边缘处梯度反转,更清晰、准确地显示出高动态图像内容.     

改进型LOG算子在偏振片绝对角度中的应用

光学成像系统自身通常都具有一定的偏振效应,严重影响仪器偏振测量精度,而提高仪器中偏振片绝对角度精度能提高偏振定标精度,对校正光学系统自身的偏振特性具有重要的意义。对偏振片直线透光轴Raw图像高精度边缘定位和直线检测是偏振片绝对角度计算的关键步骤。针对传统LOG算子各向同性及虚假边缘与边缘定位精度相矛盾的缺陷,提出改进型一阶导阈值旋转式椭圆对称LOG算子。该算子不仅保留了经典LOG算子的优点,还具有对不同角度的边缘更加有效地进行检测,在保持边缘定位精度下,减少虚假边缘的特点。在处理得到的边缘二值图像上,进行直线检测求出偏振片绝对角度,通过对比分析最小二乘法线性拟合和霍夫变换的直线检测效果,得出霍夫变换能精确计算出偏振片绝对角度。实验证明改进型LOG算子与霍夫变换相结合提高了偏振片绝对角度测量精度,对偏振定标精度具有很大的提高。     

条件生成对抗遥感图像时空融合

目的 卫星遥感技术在硬件方面的局限导致获取的遥感图像在时间与空间分辨率之间存在矛盾,而时空融合提供了一种高效、低成本的方式来融合具有时空互补性的两类遥感图像数据（典型代表是Landsat和MODIS （moderate-resolution imaging spectroradiometer）图像）,生成同时具有高时空分辨率的融合数据,解决该问题。方法 提出了一种基于条件生成对抗网络的时空融合方法,可高效处理实际应用中的大量遥感数据。与现有的学习模型相比,该模型具有以下优点：1）通过学习一个非线性映射关系来显式地关联MODIS图像和Landsat图像;2）自动学习有效的图像特征;3）将特征提取、非线性映射和图像重建统一到一个框架下进行优化。在训练阶段,使用条件生成对抗网络建立降采样Landsat和MODIS图像之间的非线性映射,然后在原始Landsat和降采样Landsat之间训练多尺度超分条件生成对抗网络。预测过程包含两层：每层均包括基于条件生成对抗网络的预测和融合模型。分别实现从MODIS到降采样Landsat数据之间的非线性映射以及降采样Landsat与原始Landsat之间的超分辨率首建。结果 在基准数据集CIA （coleam bally irrigation area）和LGC （lower Gwydir catchment）上的结果表明,条件生成对抗网络的方法在4种评测指标上均达到领先结果,例如在CIA数据集上,RMSE （root mean squared error）、SAM （spectral angle mapper）、SSIM （structural similarity）和ERGAS （erreur relative global adimensionnelle desynthese）分别平均提高了0.001、0.15、0.008和0.065;在LGC数据集上分别平均提高了0.001 2、0.7、0.018和0.008 9。明显优于现有基于稀疏表示的方法与基于卷积神经网络的方法。结论 本文提出的条件生成对抗融合模型,能够充分学习Landsat和MODIS图像之间复杂的非线性映射,产生更加准确的融合结果。     

基于SLIC和区域生长的目标分割算法

传统区域生长算法的分割结果依赖于种子点的选取,且图像自身的噪声以及灰度值不均匀等问题易在分割目标过程中形成分割空洞,针对以上问题提出了基于超像素的改进区域生长算法。采用拉普拉斯锐化,增强待分割目标边界,之后根据像素灰度相似的特征采用SLIC（简单线性迭代聚类算法）超像素分割将原始图像分割成若干不规则区域,建立不规则区域间的无向加权图,选取种子区域,根据无向加权图以分割好的不规则区域为单位进行区域生长,最后在分割目标边缘处以像素为单位做区域生长,细化边界。对比于传统区域生长算法,改进后的算法在分割结果上受种子点选取影响较小,且能有效地解决分割空洞等问题。对比于聚类分割,Otsu（最大类间方差）阈值分割法等典型算法,该算法在分割精度上具有明显优势。     

双向通信无人机集群领航顶点选取方法

领航顶点选取是关系到领航-跟随模式无人机集群等多智能体系统可控性的重要问题。以具有几十架个体的无人机集群为研究对象,针对领航顶点选取问题,基于Laplace矩阵的特征向量,提出关键集概念。从理论上证明2关键集、3关键集以及独立关键集的图特征。在此基础上,给出求无向网络最小关键集的CSA算法,通过数值仿真实验获得了不同规模、不同通信半径条件下无人机集群最小领航集的数值特征。