Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be...Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be recognized as data living on mani- fold surfaces. So interpolation and approximation for these data are of general interest. This paper presents two approaches for mani- fold data interpolation and approximation through the properties of Laplace-Beltrami operator （Laplace operator defined on a mani- fold surface）. The first one is to use Laplace operator minimizing the membrane energy of a scalar function defined on a manifold. The second one is to use bi-Laplace operator minimizing the thin plate energy of a scalar function defined on a manifold. These two approaches can process data living on high genus meshed surfaces. The approach based on Laplace operator is more suitable for manifold data approximation and can be applied manifold data smoothing, while the one based on bi-Laplace operator is more suit- able for manifold data interpolation and can be applied image extremal envelope computation. All the application examples demon- strate that our procedures are robust and efficient.展开更多
为有效识别和剔除风电机组实测数据中的异常数据,通过分析风电机组实测数据的高维特征,提出一种基于流形学习的异常数据识别算法。首先,采用k-近邻互信息算法实现风电机组特征变量选择;随后,使用将样本间距离度量替换为欧几里得度量和...为有效识别和剔除风电机组实测数据中的异常数据,通过分析风电机组实测数据的高维特征,提出一种基于流形学习的异常数据识别算法。首先,采用k-近邻互信息算法实现风电机组特征变量选择;随后,使用将样本间距离度量替换为欧几里得度量和局部主成分分析(local principal component analysis,LPCA)差别加权和的优化t-分布随机近邻嵌入(t-distributed stochastic neighbor embedding,t-SNE)算法挖掘出高维流形数据中具有内在规律的低维特征,使得具有不同分布特征的数据在可视化二维空间中显著分离;最后,采用基于密度的噪声空间聚类(density-based spatial clustering of applications with noise,DBSCAN)算法对二维空间中的数据进行聚类。结果表明,与主成分分析(principal component analysis,PCA)算法、局部线性嵌入(locally linear embedding,LLE)算法和原t-SNE算法相比,所提方法能够对各种复杂工况数据进行可视化分离聚类,并对异常数据进行识别和剔除。展开更多
流形数据由一些弧线状或环状的类簇组成,其特点是同一类簇的样本间距离差距较大。密度峰值聚类算法不能有效识别流形类簇的类簇中心且分配剩余样本时易引发样本的连续误分配问题。为此,本文提出面向流形数据的共享近邻密度峰值聚类(dens...流形数据由一些弧线状或环状的类簇组成,其特点是同一类簇的样本间距离差距较大。密度峰值聚类算法不能有效识别流形类簇的类簇中心且分配剩余样本时易引发样本的连续误分配问题。为此,本文提出面向流形数据的共享近邻密度峰值聚类(density peaks clustering based on shared nearest neighbor for manifold datasets,DPC-SNN)算法。提出了一种基于共享近邻的样本相似度定义方式,使得同一流形类簇样本间的相似度尽可能高;基于上述相似度定义局部密度,不忽略距类簇中心较远样本的密度贡献,能更好地区分出流形类簇的类簇中心与其他样本;根据样本的相似度分配剩余样本,避免了样本的连续误分配。DPC-SNN算法与DPC、FKNNDPC、FNDPC、DPCSA及IDPC-FA算法的对比实验结果表明,DPC-SNN算法能够有效发现流形数据的类簇中心并准确完成聚类,对真实以及人脸数据集也有不错的聚类效果。展开更多
基金Supported by National Natural Science Foundation of China (No.61202261,No.61173102)NSFC Guangdong Joint Fund(No.U0935004)Opening Foundation of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education of China(No.93K172012K02)
文摘Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be recognized as data living on mani- fold surfaces. So interpolation and approximation for these data are of general interest. This paper presents two approaches for mani- fold data interpolation and approximation through the properties of Laplace-Beltrami operator （Laplace operator defined on a mani- fold surface）. The first one is to use Laplace operator minimizing the membrane energy of a scalar function defined on a manifold. The second one is to use bi-Laplace operator minimizing the thin plate energy of a scalar function defined on a manifold. These two approaches can process data living on high genus meshed surfaces. The approach based on Laplace operator is more suitable for manifold data approximation and can be applied manifold data smoothing, while the one based on bi-Laplace operator is more suit- able for manifold data interpolation and can be applied image extremal envelope computation. All the application examples demon- strate that our procedures are robust and efficient.
文摘为有效识别和剔除风电机组实测数据中的异常数据,通过分析风电机组实测数据的高维特征,提出一种基于流形学习的异常数据识别算法。首先,采用k-近邻互信息算法实现风电机组特征变量选择;随后,使用将样本间距离度量替换为欧几里得度量和局部主成分分析(local principal component analysis,LPCA)差别加权和的优化t-分布随机近邻嵌入(t-distributed stochastic neighbor embedding,t-SNE)算法挖掘出高维流形数据中具有内在规律的低维特征,使得具有不同分布特征的数据在可视化二维空间中显著分离;最后,采用基于密度的噪声空间聚类(density-based spatial clustering of applications with noise,DBSCAN)算法对二维空间中的数据进行聚类。结果表明,与主成分分析(principal component analysis,PCA)算法、局部线性嵌入(locally linear embedding,LLE)算法和原t-SNE算法相比,所提方法能够对各种复杂工况数据进行可视化分离聚类,并对异常数据进行识别和剔除。
文摘流形数据由一些弧线状或环状的类簇组成,其特点是同一类簇的样本间距离差距较大。密度峰值聚类算法不能有效识别流形类簇的类簇中心且分配剩余样本时易引发样本的连续误分配问题。为此,本文提出面向流形数据的共享近邻密度峰值聚类(density peaks clustering based on shared nearest neighbor for manifold datasets,DPC-SNN)算法。提出了一种基于共享近邻的样本相似度定义方式,使得同一流形类簇样本间的相似度尽可能高;基于上述相似度定义局部密度,不忽略距类簇中心较远样本的密度贡献,能更好地区分出流形类簇的类簇中心与其他样本;根据样本的相似度分配剩余样本,避免了样本的连续误分配。DPC-SNN算法与DPC、FKNNDPC、FNDPC、DPCSA及IDPC-FA算法的对比实验结果表明,DPC-SNN算法能够有效发现流形数据的类簇中心并准确完成聚类,对真实以及人脸数据集也有不错的聚类效果。
