We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-function...We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.展开更多
离群点检测任务是指检测与正常数据在特征属性上存在显著差异的异常数据。大多数基于聚类的离群点检测方法主要从全局角度对数据集中的离群点进行检测,而对局部离群点的检测性能较弱。基于此,本文通过引入快速搜索和发现密度峰值方法改...离群点检测任务是指检测与正常数据在特征属性上存在显著差异的异常数据。大多数基于聚类的离群点检测方法主要从全局角度对数据集中的离群点进行检测,而对局部离群点的检测性能较弱。基于此,本文通过引入快速搜索和发现密度峰值方法改进K-means聚类算法,提出了一种名为KLOD(local outlier detection based on improved K-means and least-squares methods)的局部离群点检测方法,以实现对局部离群点的精确检测。首先,利用快速搜索和发现密度峰值方法计算数据点的局部密度和相对距离,并将二者相乘得到γ值。其次,将γ值降序排序,利用肘部法则选择γ值最大的k个数据点作为K-means聚类算法的初始聚类中心。然后,通过K-means聚类算法将数据集聚类成k个簇,计算数据点在每个维度上的目标函数值并进行升序排列。接着,确定数据点的每个维度的离散程度并选择适当的拟合函数和拟合点,通过最小二乘法对升序排列的每个簇的每1维目标函数值进行函数拟合并求导,以获取变化率。最后,结合信息熵,将每个数据点的每个维度目标函数值乘以相应的变化率进行加权,得到最终的异常得分,并将异常值得分较高的top-n个数据点视为离群点。通过人工数据集和UCI数据集,对KLOD、LOF和KNN方法在准确度上进行仿真实验对比。结果表明KLOD方法相较于KNN和LOF方法具有更高的准确度。本文提出的KLOD方法能够有效改善K-means聚类算法的聚类效果,并且在局部离群点检测方面具有较好的精度和性能。展开更多
An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces gener...An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>（R）w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>（S）, 1≤P≤∞, we obtain a new equivalence expression.展开更多
文摘We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.
文摘离群点检测任务是指检测与正常数据在特征属性上存在显著差异的异常数据。大多数基于聚类的离群点检测方法主要从全局角度对数据集中的离群点进行检测,而对局部离群点的检测性能较弱。基于此,本文通过引入快速搜索和发现密度峰值方法改进K-means聚类算法,提出了一种名为KLOD(local outlier detection based on improved K-means and least-squares methods)的局部离群点检测方法,以实现对局部离群点的精确检测。首先,利用快速搜索和发现密度峰值方法计算数据点的局部密度和相对距离,并将二者相乘得到γ值。其次,将γ值降序排序,利用肘部法则选择γ值最大的k个数据点作为K-means聚类算法的初始聚类中心。然后,通过K-means聚类算法将数据集聚类成k个簇,计算数据点在每个维度上的目标函数值并进行升序排列。接着,确定数据点的每个维度的离散程度并选择适当的拟合函数和拟合点,通过最小二乘法对升序排列的每个簇的每1维目标函数值进行函数拟合并求导,以获取变化率。最后,结合信息熵,将每个数据点的每个维度目标函数值乘以相应的变化率进行加权,得到最终的异常得分,并将异常值得分较高的top-n个数据点视为离群点。通过人工数据集和UCI数据集,对KLOD、LOF和KNN方法在准确度上进行仿真实验对比。结果表明KLOD方法相较于KNN和LOF方法具有更高的准确度。本文提出的KLOD方法能够有效改善K-means聚类算法的聚类效果,并且在局部离群点检测方面具有较好的精度和性能。
文摘An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>（R）w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>（S）, 1≤P≤∞, we obtain a new equivalence expression.
