Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give ...Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).展开更多
Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the est...Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the estimators βn* and gn*forβ and g are obtained by using class K and the least square methods. It is shown that βn* is asymptotically normal and gn* achieves the convergent rate O(n-1/3).展开更多
In this paper,a new multiclass classification algorithm is proposed based on the idea of Locally Linear Embedding(LLE),to avoid the defect of traditional manifold learning algorithms,which can not deal with new sample...In this paper,a new multiclass classification algorithm is proposed based on the idea of Locally Linear Embedding(LLE),to avoid the defect of traditional manifold learning algorithms,which can not deal with new sample points.The algorithm defines an error as a criterion by computing a sample's reconstruction weight using LLE.Furthermore,the existence and characteristics of low dimensional manifold in range-profile time-frequency information are explored using manifold learning algorithm,aiming at the problem of target recognition about high range resolution MilliMeter-Wave(MMW) radar.The new algorithm is applied to radar target recognition.The experiment results show the algorithm is efficient.Compared with other classification algorithms,our method improves the recognition precision and the result is not sensitive to input parameters.展开更多
在复杂产品的制造过程中,轮廓(profile)数据是一类广泛存在的质量数据类型。为了能够尽快监测出线性轮廓内自相关过程中的异常,针对质量数据仅存在正常样本的情况,提出了基于一类支持向量机(one-class Support Vector Machine,OCSVM)的...在复杂产品的制造过程中,轮廓(profile)数据是一类广泛存在的质量数据类型。为了能够尽快监测出线性轮廓内自相关过程中的异常,针对质量数据仅存在正常样本的情况,提出了基于一类支持向量机(one-class Support Vector Machine,OCSVM)的监控方法。首先,介绍OCSVM方法原理;其次,构建OCSVM监控模型,通过数值仿真实验模拟得到平均运行长度,并给出详细的仿真过程;再次,以平均运行长度为准则,分析高斯核函数与多项式核函数对OCSVM方法监控性能的影响,结果表明:监控AR(1)模型时,多项式核函数具有优势;最后,将多项式核函数的仿真结果与传统的一些控制图进行对比,结果表明:当标准差以及斜率、截距同时发生变化时,OCSVM方法监控效果优于其他控制图;当自相关系数ρ=0.1(弱相关)截距发生较大偏移以及ρ=0.9(强相关)截距发生偏移时,OCSVM方法监控效果优于其他控制图。展开更多
This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression model...This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.展开更多
In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of commo...In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.展开更多
随机森林是机器学习领域中一种常用的分类算法,具有适用范围广且不易过拟合等优点.为了提高随机森林处理多分类问题的能力,提出一种基于空间变换的随机森林算法(space transformation based random forest algorithm,ST-RF).首先,给出...随机森林是机器学习领域中一种常用的分类算法,具有适用范围广且不易过拟合等优点.为了提高随机森林处理多分类问题的能力,提出一种基于空间变换的随机森林算法(space transformation based random forest algorithm,ST-RF).首先,给出一种考虑优先类别的线性判别分析方法(priority class based linear discriminant analysis,PCLDA),利用针对优先类别的投影矩阵对样本进行空间变换,以增强优先类别样本与其他类别样本的区分效果.进而,将PCLDA方法引入随机森林构建过程中,在为每棵决策树随机选择一个优先类别保证随机森林多样性的基础上,利用PCLDA方法创建侧重于不同优先类别的决策树,以提高单棵决策树的分类准确性,从而实现集成模型整体分类性能的有效提升.最后,在10个标准数据集上对ST-RF算法与7种典型随机森林算法进行比较分析,验证所提算法的有效性,并将基于PCLDA的空间变换策略应用到对比算法中,对改进前后的算法性能进行比较分析.实验结果表明:ST-RF算法在处理多分类问题方面具有明显优势,所提出的空间变换策略具有较强的普适性,可以显著提升原算法的分类性能.展开更多
基金Supported by the National Natural Science Foundation of China(11161033)Supported by the Inner Mongolia Normal University Talent Project Foundation(RCPY-2-2012-K-036)+1 种基金Supported by the Inner Mongolia Normal University Graduate Research Innovation Foundation(CXJJS14053)Supported by the Inner Mongolia Autonomous Region Graduate Research Innovation Foundation(S20141013525)
文摘Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).
文摘Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the estimators βn* and gn*forβ and g are obtained by using class K and the least square methods. It is shown that βn* is asymptotically normal and gn* achieves the convergent rate O(n-1/3).
基金Supported by the National Defense Pre-Research Foundation of China (Grant No.9140A05070107BQ0204)
文摘In this paper,a new multiclass classification algorithm is proposed based on the idea of Locally Linear Embedding(LLE),to avoid the defect of traditional manifold learning algorithms,which can not deal with new sample points.The algorithm defines an error as a criterion by computing a sample's reconstruction weight using LLE.Furthermore,the existence and characteristics of low dimensional manifold in range-profile time-frequency information are explored using manifold learning algorithm,aiming at the problem of target recognition about high range resolution MilliMeter-Wave(MMW) radar.The new algorithm is applied to radar target recognition.The experiment results show the algorithm is efficient.Compared with other classification algorithms,our method improves the recognition precision and the result is not sensitive to input parameters.
文摘在复杂产品的制造过程中,轮廓(profile)数据是一类广泛存在的质量数据类型。为了能够尽快监测出线性轮廓内自相关过程中的异常,针对质量数据仅存在正常样本的情况,提出了基于一类支持向量机(one-class Support Vector Machine,OCSVM)的监控方法。首先,介绍OCSVM方法原理;其次,构建OCSVM监控模型,通过数值仿真实验模拟得到平均运行长度,并给出详细的仿真过程;再次,以平均运行长度为准则,分析高斯核函数与多项式核函数对OCSVM方法监控性能的影响,结果表明:监控AR(1)模型时,多项式核函数具有优势;最后,将多项式核函数的仿真结果与传统的一些控制图进行对比,结果表明:当标准差以及斜率、截距同时发生变化时,OCSVM方法监控效果优于其他控制图;当自相关系数ρ=0.1(弱相关)截距发生较大偏移以及ρ=0.9(强相关)截距发生偏移时,OCSVM方法监控效果优于其他控制图。
文摘This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.
文摘In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.
文摘随机森林是机器学习领域中一种常用的分类算法,具有适用范围广且不易过拟合等优点.为了提高随机森林处理多分类问题的能力,提出一种基于空间变换的随机森林算法(space transformation based random forest algorithm,ST-RF).首先,给出一种考虑优先类别的线性判别分析方法(priority class based linear discriminant analysis,PCLDA),利用针对优先类别的投影矩阵对样本进行空间变换,以增强优先类别样本与其他类别样本的区分效果.进而,将PCLDA方法引入随机森林构建过程中,在为每棵决策树随机选择一个优先类别保证随机森林多样性的基础上,利用PCLDA方法创建侧重于不同优先类别的决策树,以提高单棵决策树的分类准确性,从而实现集成模型整体分类性能的有效提升.最后,在10个标准数据集上对ST-RF算法与7种典型随机森林算法进行比较分析,验证所提算法的有效性,并将基于PCLDA的空间变换策略应用到对比算法中,对改进前后的算法性能进行比较分析.实验结果表明:ST-RF算法在处理多分类问题方面具有明显优势,所提出的空间变换策略具有较强的普适性,可以显著提升原算法的分类性能.
