Interweaving Kohonen Maps of Different Dimensions to Handle Measure Zero Constraints on Topological Mappings

The usual Kohonen algorithm uses samples of points in a domain to develop a topological correspondence between a grid of neurons and a continuous domain. Topological means that near points are mapped to near points. However, for many applications there are additional constraints, which are given by sets of measure zero, which are not preserved by this method, because of insufficient sampling. In particular, boundary points do not typically map to boundary points because in general the likelihood of a sample point from a two-dimensional domain falling on the boundary is typically zero for continuous data, and extremely small for numerical data. A specific application, (assigning meshes for the finite element method), was recently solved by interweaving a two-dimensional Kohonen mapping on the entire grid with a one-dimensional Kohonen mapping on the boundary. While the precise method of interweaving was heuristic, the underlying rationale seems widely applicable. This general method is problem independent and suggests a direct generalization to higher dimensions as well.     

混合属性数据集的聚类边界检测技术

为了满足数据分析中获取含有混合属性的数据集聚类的边界需求, 提出一种混合属性数据集的聚类边界检测算法(BERGE). 该算法利用模糊聚类隶属度定义边界因子以识别候选边界集, 然后运用证据积累的思想提取聚类的边界. 在综合数据集和真实数据集上的实验结果表明, BERGE 算法能有效地检测混合属性数据集、数值属性数据集以及分类属性数据集的聚类边界, 与现有同类算法相比具有更高的精度.     

基于统计信息的聚类边界模式检测算法

为有效地检测聚类的边界点,提出基于统计信息的边界模式检测算法。根据数据对象的k距离统计信息设定邻域半径,再利用对象邻域范围内邻居的k距离统计信息寻找边界点。实验结果表明,该算法可以有效地检测出任意形状、不同大小和不同密度聚类的边界点,并可以消除噪声。     

Decision surface estimate of nonlinear system stability domain by Lie series method

The Lie series recursive algorithm for Zubov's partial differential equation is used to generate two sets of points, where one represents the exact asymptotic stability boundary of an equilibrium state of the nonlinear system under consideration and the other is interior to it. Based on these two sets of data as training samples of two classes, a decision hypersurface can be determined such that it is a close approximation of the asymptotic stability boundary.     

一种基于角度的边界点检测算法

针对目前数据挖掘中边界点检测效率低、参数阈值范围不容易确定的问题,提出一种新的边界点检测算法BORAL。该算法基于一个有取值范围的参数阈值,利用在边界点的半径 邻域中边界点与其他点组成的向量夹角中较大的夹角检测边界点,且该夹角邻域内不含有其他点的特征。实验结果表明BORAL能有效检测出边界点、执行效率高,当角度阈值从40°变到57°时,聚类的边界变化不大。     

Measure of circularity for parts of digital boundaries and its fast computation

This paper focuses on the design of an effective method that computes the measure of circularity of a part of a digital boundary. An existing circularity measure of a set of discrete points, which is used in computational metrology, is extended to the case of parts of digital boundaries. From a single digital boundary, two sets of points are extracted so that the circularity measure computed from these sets is representative of the circularity of the digital boundary. Therefore, the computation consists of two steps. First, the inner and outer sets of points are extracted from the input part of a digital boundary using digital geometry tools. Next, the circularity measure of these sets is computed using classical tools of computational geometry. It is proved that the algorithm is linear in time in the case of convex parts thanks to the specificity of digital data, and is in O(nlogn) otherwise. Experiments done on synthetic and real images illustrate the interest of the properties of the circularity measure.     

噪声数据集上的边界点检测算法

为了有效检测聚类的边界点,提出了结合对象的密度及其Eps-邻域中数据的分布特点进行的边界点检测技术和边界点检测算法 ——BOUND。实验结果表明,BOUND能在含有不同形状、大小簇的噪声数据集上有效地检测出聚类的边界点,并且执行效率高。     

基于模型散乱点的三维物体重建

基于三维模型的散乱数据点,通过引入分割平面,对数据集进行划分,将散乱数据划分为n个子集合来重建物体。具体的过程,是通过引入控制参数δ和η,将满足相应条件的3D散乱点划分到相应的子集合中,然后对各个散乱点子集合进行判断,提取其各个子集上的控制点,构造各个子集的控制点构成的边界。最后,对每两个相邻的边界进行相似性评估,对相似的边界之间通过等比例划分,非相似的边界采用全局优化,从而得到重建的三维物体的模型。经过实验证实该方法高效、方便、准确。     

DEM generation from lidar data in wooded mountain areas by cross-section-plane analysis

Ground filtering for airborne lidar data is a challenging task for the generation of digital terrain models (DTMs) in wooded mountain areas. To solve this problem, this article, based on cross-section-plane (CSP) analysis, presents a CSP-based stepwise filtering strategy that can automatically separate terrain from non-terrain points. The filtering strategy consists of four main computing steps: (a) ‘split’ – the raw lidar data are partitioned into 3D cells, in each of which multi-directional CSPs are generated at multiple directions; (b) ‘filter’ – the potential terrain points are selected for each CSP according to lidar data characteristics, such as multi-returns, intensity, and height; (c) ‘detect’ – the initial terrain points are detected for each CSP by exploring distances and slopes between nearby points; and (d) ‘adjust-and-refine’ – the terrain points are extracted from all initial terrain points of all CSPs by a merging-or-intersecting strategy and a five-point refinement. The extensive experiments using three lidar data sets demonstrated that the CSP-based stepwise filtering method is capable of producing reliable DTMs in densely forested mountain areas.     

点云数据压缩中的边界特征检测

点云数据压缩是逆向工程产品建模中必要的数据预处理手段之一。常见的数据压缩算法未考虑点云边界数据点的保留问题，因此在大比例压缩过程中会出现边界数据丢失的情况，从而破坏了数据的完整性。为此，提出了一种利用点云数据小邻域内点的相邻关系来检测边界特征点的算法。该算法能检测出点云数据的内、外边界特征点，同时对边界上的点进行排序，检测出边界特征点中的过渡点，最后构建点云轮廓的边界多边线。该算法不仅能满足在点云数据压缩过程中检测并保留边界特征点的要求，而且生成的边界多边线也为后面的3维模型重建奠定了基础。     

具有聚类功能的边界检测技术的研究

为快速有效地检测聚类的边界点,提出了一种新的基于三角剖分的聚类边界检测算法DTBOUND。该算法通过计算三角剖分图中每个数据点的变异系数将数据集分解成内部点和外部点两部分,然后从每一个未分类的内部点开始进行深度优先遍历,将相连的内部点以及和内部点相连的外部点作为一个聚类;最后从得到的聚类中提取边界点。该算法只有一个参数（变异系数阈值β）,实验结果表明该算法可以快速、有效地识别任意形状、不同大小和不同密度的聚类和聚类的边界点。     

基于局部中心度量的边界点划分密度聚类算法

针对聚类算法在检测任意簇时精确度不高、迭代次数多及效果不佳等缺点,提出了基于局部中心度量的边界点划分密度聚类算法——DBLCM.在局部中心度量的限制下,数据点被划分到核心区域或边界区域.核心区域的点按照互近邻优先成簇的分配方式形成初始簇,边界区域的点参考互近邻中距离最近点所在簇进行分配,从而得到最终簇.为验证算法的有效性,将DBLCM与3个经典算法和3个近几年新提出的优秀算法,在包含任意形状、任意密度的二维数据集和任意维度的多维数据集上进行测试.另外,为了验证DBLCM算法中参数k的敏感性,在所用的数据集上做了k值与簇质量的相关性测试.实验结果表明,DBLCM算法具有识别精度高,检测任意簇效果好和无需迭代等优点,综合性能优于6个对比算法.     

基于变异系数的边界点检测算法

为有效检测聚类的边界点,提出基于变异系数的边界点检测算法.首先计算出数据对象到它的k-距离邻居距离之和的平均值.然后用平均值的倒数作为每个点的密度,通过变异系数刻画数据对象密度分布特征寻找边界点.实验结果表明,该算法可在含有任意形状、不同大小和不同密度的数据集上快速有效检测出聚类的边界点,并可消除噪声.     

基于加权边界度的稀有类检测算法

提出了一种快速的稀有类检测算法——CATION(rare category detection algorithm based on weighted boundary degree).通过使用加权边界度(weighted boundary degree,简称WBD)这一新的稀有类检测标准,该算法可利用反向κ近邻的特性来寻找稀有类的边界点,并选取加权边界度最高的边界点询问其类别标签.实验结果表明,与现有方法相比,该算法避免了现有方法的局限性,大幅度地提高了发现数据集中各个类的效率,并有效地缩短了算法运行所需要的运行时间.     

一种高效的基于联合熵的边界点检测算法

为了快速有效地检测出聚类的边界点,提出一种将网格技术与联合熵相结合的边界点检测算法.该算法中网格技术用于快速查找数据集中聚类边界所在的网格范围,联合熵用于在边界落入的网格范围内准确识别聚类的边界点.实验结果表明.该算法能够在含有噪声点,孤立点的数据集上,有效地检测出聚类的边界,运行效率高.     

基于空间局部偏离因子的离群点检测算法

针对空间数据集的特性,提出一种基于空间局部偏离因子(SLDF)的离群点检测算法。利用SLDF度量空间点对象的离群程度,计算空间数据集中点对象的SLDF值并对其进行排序,将取值较大的前M个点对象作为空间离群点。实验结果表明,该算法能较好地检测空间局部离群点,其有效性与准确性均优于SLZ算法,适用于高维大数据集的空间离群点检测。     

支持k-离群度的边界点检测方法

边界是一种有用的模式,为了有效识别边界,根据边界点周围密度不均匀,提出了一种边界点检测算法——BDKD。该算法用数据对象的k-近邻距离与其邻域内数据对象的平均k-近邻距离之比定义其k-离群度,当k-离群度超过阈值时即确定为边界点。实验结果表明,BDKD算法可以准确检测出各种聚类边界,并能去除噪声,特别是对密度均匀的数据集效果理想。     

Identifying rectangles in laser range data for urban scene reconstruction

In urban scenes, many of the surfaces are planar and bounded by simple shapes. In a laser scan of such a scene, these simple shapes can still be identified. We present a one-parameter algorithm that can identify point sets on a plane for which a rectangle is a fitting boundary. These rectangles have a guaranteed density: no large part of the rectangle is empty of points. We prove that our algorithm identifies all angles for which a rectangle fits the point set of size n in O(nlogn) time. We evaluate our method experimentally on 13 urban data sets and we compare the rectangles found by our algorithm to the α‐shape as a surface boundary.     

融合特征边界信息的不平衡数据过采样方法

针对实际应用中存在的数据集分布不平衡的问题，提出一种融合特征边界数据信息的过采样方法。去除数据集中的噪声点，基于少数类样本点的多类近邻集合，融合特征边界的几何分布信息获得有利于定义最优非线性分类边界的少数类样本点，通过其与所属类簇的结合生成新样本。对不平衡数据集采用多种过采样技术处理后，利用支持向量机进行分类，对比实验表明所提方法有效改善了不平衡数据的分类精度，验证了算法的有效性。