The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from t...The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from the geometric point of view, and present a new method of determining knots. This method replaces the chord length, which is closer to the arc length of the mini- mum-area ellipse with arc length, and avoids the occurrence of ＇oscillation＇ and ＇loops＇. We compare the new method with the uni- form method, chord length method and the centripetal method. The comparison is performed on the quality of cubic spline curves using these methods. In most cases, the result of our method is better than others.展开更多
为解决因排查效率低、数据更新不及时等因素导致低压配电网户变关系连接形式与实际不符的问题,提出一种基于角度分段线性近似(anglepiecewiselinearrepresentation,APLR)和改进密度峰值聚类(improved clustering by fast search find of...为解决因排查效率低、数据更新不及时等因素导致低压配电网户变关系连接形式与实际不符的问题,提出一种基于角度分段线性近似(anglepiecewiselinearrepresentation,APLR)和改进密度峰值聚类(improved clustering by fast search find of density peaks,ICFSFDP)相结合的户变关系识别方法。首先,根据电压曲线中相邻线段的角度变化量提取曲线的转折点,利用APLR对曲线进行自适应降维重构;随后,使用ICFSFDP算法对降维数据组展开聚类分析,在决策图中由拟合函数与坐标轴围成面积的最小值得到最优类簇数目,进而得到聚类和非聚类中心用户;最后,使用动态时间弯曲(dynamic time warping,DTW)距离计算聚类和非聚类中心用户之间的距离相似度,进而得到户变关系。将所提方法应用于模拟和真实数据中,均可证实所提方法的有效性。算例分析结果表明:该方法能够对时间间隔不同、不等维的序列进行分析,且不需要人为设定聚类算法的参数,户变关系识别准确率高。展开更多
基金Supported by the National Research Foundation for the Doctoral Program of Higher Education of China(20110131130004)Independent Innovation Foundation of Shandong University,IIFSDU(2012TB013)Ji’nan Science and Technology Development Project(No.201202015)
文摘The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from the geometric point of view, and present a new method of determining knots. This method replaces the chord length, which is closer to the arc length of the mini- mum-area ellipse with arc length, and avoids the occurrence of ＇oscillation＇ and ＇loops＇. We compare the new method with the uni- form method, chord length method and the centripetal method. The comparison is performed on the quality of cubic spline curves using these methods. In most cases, the result of our method is better than others.
文摘为解决因排查效率低、数据更新不及时等因素导致低压配电网户变关系连接形式与实际不符的问题,提出一种基于角度分段线性近似(anglepiecewiselinearrepresentation,APLR)和改进密度峰值聚类(improved clustering by fast search find of density peaks,ICFSFDP)相结合的户变关系识别方法。首先,根据电压曲线中相邻线段的角度变化量提取曲线的转折点,利用APLR对曲线进行自适应降维重构;随后,使用ICFSFDP算法对降维数据组展开聚类分析,在决策图中由拟合函数与坐标轴围成面积的最小值得到最优类簇数目,进而得到聚类和非聚类中心用户;最后,使用动态时间弯曲(dynamic time warping,DTW)距离计算聚类和非聚类中心用户之间的距离相似度,进而得到户变关系。将所提方法应用于模拟和真实数据中,均可证实所提方法的有效性。算例分析结果表明:该方法能够对时间间隔不同、不等维的序列进行分析,且不需要人为设定聚类算法的参数,户变关系识别准确率高。
