Stable local dimensionality reduction approaches

Dimensionality reduction is a big challenge in many areas. A large number of local approaches, stemming from statistics or geometry, have been developed. However, in practice these local approaches are often in lack of robustness, since in contrast to maximum variance unfolding (MVU), which explicitly unfolds the manifold, they merely characterize local geometry structure. Moreover, the eigenproblems that they encounter, are hard to solve. We propose a unified framework that explicitly unfolds the manifold and reformulate local approaches as the semi-definite programs instead of the above-mentioned eigenproblems. Three well-known algorithms, locally linear embedding (LLE), laplacian eigenmaps (LE) and local tangent space alignment (LTSA) are reinterpreted and improved within this framework. Several experiments are presented to demonstrate the potential of our framework and the improvements of these local algorithms.     

常用边缘检测方法分析与比较

论文对几种常用的图像边缘检测算法进行了分析,实际上这几种方法都在我们的生活生产乃至国防中得到了广泛的应用。论文在分析的基础上,进一步进行了比对说明,指出了它们各自的特点。     

Gaussian-Hermite moment-based depth estimation from single still image for stereo vision

Depth information of objects plays a significant role in image-based rendering. Traditional depth estimation techniques use different visual cues including the disparity, motion, geometry, and defocus of objects. This paper presents a novel approach of focus cue-based depth estimation for still images using the Gaussian-Hermite moments (GHMs) of local neighboring pixels. The GHMs are chosen due to their superior reconstruction ability and invariance properties to intensity and geometric distortions of objects as compared to other moments. Since depths of local neighboring pixels are significantly correlated, the Laplacian matting is employed to obtain final depth map from the moment-based focus map. Experiments are conducted on images of indoor and outdoor scenes having objects with varying natures of resolution, edge, occlusion, and blur contents. Experimental results reveal that the depth estimated from GHMs can provide anaglyph images with stereo quality better than that provided by existing methods using traditional visual cues.     

三维块匹配波域调和滤波图像去噪

针对当前图像去噪算法缺乏对整体结构的分析以及运算量过大的不足,提出了一种利用波域调和滤波扩散模型改进BM3 D去噪技术的新算法.首先,利用传统的欧氏距离法将相似二维图像块合并,得到三维数组,再将联合滤波后的三维数组进行逆变换,得到图像的预估计数据.其次,通过小波分解变换提取预估计图像中的高频部分进行滤波,为避免边缘模糊...     

具有最小距离拉普拉斯谱半径的双圈图（英）

一个连通图的距离拉普拉斯矩阵的最大特征值称为这个图的距离拉普拉斯谱半径．本文中,我们先得到距离拉普拉斯谱半径的一个好的下界,然后利用这个下界确定了单圈图中具有最小距离拉普拉斯谱半径的唯一极图．最后,再次利用这个下界,并结合距离拉普拉斯矩阵的特征多项式确定出了双圈图中具有最小距离拉普拉斯谱半径的极图．     

基于拉普拉斯特征映射学习的隐匿FDI攻击检测

智能电网中的隐匿虚假数据入侵(False data injection, FDI)攻击能够绕过坏数据检测机制, 导致控制中心做出错误的状态估计, 进而干扰电力系统的正常运行. 由于电网系统具有复杂的拓扑结构, 故基于传统机器学习的攻击信号检测方法存在维度过高带来的过拟合问题, 而深度学习检测方法则存在训练时间长、占用大量计算资源的问题. 为此, 针对智能电网中的隐匿FDI攻击信号, 提出了基于拉普拉斯特征映射降维的神经网络检测学习算法, 不仅降低了陷入过拟合的风险, 同时也提高了隐匿FDI攻击检测学习算法的泛化能力. 最后, 在IEEE57-Bus电力系统模型中验证了所提方法的优点和有效性.     

用概率推导和加权迭代L1范数实现信号重构

在对信号稀疏性统计分析的基础上,将具有稀疏描述能力的拉普拉斯分布用于描述信号的先验分布,基于贝叶斯法,利用信号采样值、拉普拉斯先验分布和高斯似然模型,推导信号的后验概率密度估计;最后将最大后验概率(MAP)估计过程转化为加权迭代L1范数的最小化问题。在求解过程中,与非加权的L1范数法进行对比表明,信号重构性能明显提高;通过实验计算,详细讨论了其中一些参数的取值原则和范围;针对稀疏度不同的信号,随着信号非零点数的增加,本文算法重构结果明显优于基追踪(BP)和(OMP)法;与同类的IRL1算法相比较,本文算法更具普遍性和理论意义。     

基于拉普拉斯特征映射的仿射传播聚类

仿射传播方法难以处理具有流形结构的数据集。为此,提出一种基于拉普拉斯特征映射的仿射传播聚类算法(APPLE),在标准仿射传播的基础上增强流形学习的能力。使用测地距离计算数据点间相似度,采用拉普拉斯特征映射对数据集进行降维及特征提取。对图像聚类应用的实验结果证明了APPLE的聚类效果优于标准仿射传播方法。