Traditional clustering algorithms often struggle to produce satisfactory results when dealing with datasets withuneven density. Additionally, they incur substantial computational costs when applied to high-dimensional...Traditional clustering algorithms often struggle to produce satisfactory results when dealing with datasets withuneven density. Additionally, they incur substantial computational costs when applied to high-dimensional datadue to calculating similarity matrices. To alleviate these issues, we employ the KD-Tree to partition the dataset andcompute the K-nearest neighbors (KNN) density for each point, thereby avoiding the computation of similaritymatrices. Moreover, we apply the rules of voting elections, treating each data point as a voter and casting a votefor the point with the highest density among its KNN. By utilizing the vote counts of each point, we develop thestrategy for classifying noise points and potential cluster centers, allowing the algorithm to identify clusters withuneven density and complex shapes. Additionally, we define the concept of “adhesive points” between two clustersto merge adjacent clusters that have similar densities. This process helps us identify the optimal number of clustersautomatically. Experimental results indicate that our algorithm not only improves the efficiency of clustering butalso increases its accuracy.展开更多
The purpose of this paper is to investigate the k-nearest neighbor classification rule for spatially dependent data.Some spatial mixing conditions are considered,and under such spatial structures,the well known k-neare...The purpose of this paper is to investigate the k-nearest neighbor classification rule for spatially dependent data.Some spatial mixing conditions are considered,and under such spatial structures,the well known k-nearest neighbor rule is suggested to classify spatial data.We established consistency and strong consistency of the classifier under mild assumptions.Our main results extend the consistency result in the i.i.d.case to the spatial case.展开更多
针对化工过程数据中存在缺失数据的问题,在保持局部数据结构特征的基础上提出了基于局部加权重构的化工过程数据恢复算法。通过定位缺失的数据点并以符号Na N(Not a Number)标记,将缺失的数据集分为完备数据集和不完备数据集。不完备的...针对化工过程数据中存在缺失数据的问题,在保持局部数据结构特征的基础上提出了基于局部加权重构的化工过程数据恢复算法。通过定位缺失的数据点并以符号Na N(Not a Number)标记,将缺失的数据集分为完备数据集和不完备数据集。不完备的数据集按照完整性的大小依次找到它们在完备数据集中相应的k个近邻,根据误差平方和最小的原则,求出k个近邻相应的权值,用k个近邻及相应的权值重构出缺失的数据点。将该算法应用在不同缺失率下的两种化工过程数据中并与望最大化主成分分析(EM-PCA)法和平均值(MA)两种传统的数据恢复算法相比较,该算法的恢复数据误差最小,并且计算速度相比EM-PCA算法平均提高了2倍。实验结果表明,局部加权重构的化工过程数据恢复算法可以有效地对数据进行恢复,提高了数据的利用率,适用于非线性化工过程缺失数据的恢复。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
Various methods have been used to estimate the amount of above ground forest biomass across landscapes and to create biomass maps for specific stands or pixels across ownership or project areas. Without an accurate es...Various methods have been used to estimate the amount of above ground forest biomass across landscapes and to create biomass maps for specific stands or pixels across ownership or project areas. Without an accurate estimation method, land managers might end up with incorrect biomass estimate maps, which could lead them to make poorer decisions in their future management plans. The goal of this study was to compare various imputation methods to predict forest biomass and basal area, at a project planning scale (a combination of ground inventory plots, light detection and ranging (LiDAR) data, satellite imagery, and climate data was analyzed, and their root mean square error (RMSE) and bias were calculated. Results indicate that for biomass prediction, the k-nn (k = 5) had the lowest RMSE and least amount of bias. The second most accurate method consisted of the k-nn (k = 3), followed by the GWR model, and the random forest imputation. For basal area prediction, the GWR model had the lowest RMSE and least amount of bias. The second most accurate method was k-nn (k = 5), followed by k-nn (k = 3), and the random forest method. For both metrics, the GNN method was the least accurate based on the ranking of RMSE and bias.展开更多
<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under so...<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under some mild conditions, it is shown that the estimators are uniformly strongly consistent for both randomly complete data and censored data.展开更多
To overcome the limitations of the traditional stage-discharge models in describing the dynamic characteristics of a river, a machine learning method of non-parametric regression, the locally weighted regression metho...To overcome the limitations of the traditional stage-discharge models in describing the dynamic characteristics of a river, a machine learning method of non-parametric regression, the locally weighted regression method was used to estimate discharge. With the purpose of improving the precision and efficiency of river discharge estimation, a novel machine learning method is proposed： the clustering-tree weighted regression method. First, the training instances are clustered. Second, the k-nearest neighbor method is used to cluster new stage samples into the best-fit cluster. Finally, the daily discharge is estimated. In the estimation process, the interference of irrelevant information can be avoided, so that the precision and efficiency of daily discharge estimation are improved. Observed data from the Luding Hydrological Station were used for testing. The simulation results demonstrate that the precision of this method is high. This provides a new effective method for discharge estimation.展开更多
基金National Natural Science Foundation of China Nos.61962054 and 62372353.
文摘Traditional clustering algorithms often struggle to produce satisfactory results when dealing with datasets withuneven density. Additionally, they incur substantial computational costs when applied to high-dimensional datadue to calculating similarity matrices. To alleviate these issues, we employ the KD-Tree to partition the dataset andcompute the K-nearest neighbors (KNN) density for each point, thereby avoiding the computation of similaritymatrices. Moreover, we apply the rules of voting elections, treating each data point as a voter and casting a votefor the point with the highest density among its KNN. By utilizing the vote counts of each point, we develop thestrategy for classifying noise points and potential cluster centers, allowing the algorithm to identify clusters withuneven density and complex shapes. Additionally, we define the concept of “adhesive points” between two clustersto merge adjacent clusters that have similar densities. This process helps us identify the optimal number of clustersautomatically. Experimental results indicate that our algorithm not only improves the efficiency of clustering butalso increases its accuracy.
文摘The purpose of this paper is to investigate the k-nearest neighbor classification rule for spatially dependent data.Some spatial mixing conditions are considered,and under such spatial structures,the well known k-nearest neighbor rule is suggested to classify spatial data.We established consistency and strong consistency of the classifier under mild assumptions.Our main results extend the consistency result in the i.i.d.case to the spatial case.
文摘针对化工过程数据中存在缺失数据的问题,在保持局部数据结构特征的基础上提出了基于局部加权重构的化工过程数据恢复算法。通过定位缺失的数据点并以符号Na N(Not a Number)标记,将缺失的数据集分为完备数据集和不完备数据集。不完备的数据集按照完整性的大小依次找到它们在完备数据集中相应的k个近邻,根据误差平方和最小的原则,求出k个近邻相应的权值,用k个近邻及相应的权值重构出缺失的数据点。将该算法应用在不同缺失率下的两种化工过程数据中并与望最大化主成分分析(EM-PCA)法和平均值(MA)两种传统的数据恢复算法相比较,该算法的恢复数据误差最小,并且计算速度相比EM-PCA算法平均提高了2倍。实验结果表明,局部加权重构的化工过程数据恢复算法可以有效地对数据进行恢复,提高了数据的利用率,适用于非线性化工过程缺失数据的恢复。
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).
文摘Various methods have been used to estimate the amount of above ground forest biomass across landscapes and to create biomass maps for specific stands or pixels across ownership or project areas. Without an accurate estimation method, land managers might end up with incorrect biomass estimate maps, which could lead them to make poorer decisions in their future management plans. The goal of this study was to compare various imputation methods to predict forest biomass and basal area, at a project planning scale (a combination of ground inventory plots, light detection and ranging (LiDAR) data, satellite imagery, and climate data was analyzed, and their root mean square error (RMSE) and bias were calculated. Results indicate that for biomass prediction, the k-nn (k = 5) had the lowest RMSE and least amount of bias. The second most accurate method consisted of the k-nn (k = 3), followed by the GWR model, and the random forest imputation. For basal area prediction, the GWR model had the lowest RMSE and least amount of bias. The second most accurate method was k-nn (k = 5), followed by k-nn (k = 3), and the random forest method. For both metrics, the GNN method was the least accurate based on the ranking of RMSE and bias.
基金Project supported by the National Natural Science Foundation of China.
文摘<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under some mild conditions, it is shown that the estimators are uniformly strongly consistent for both randomly complete data and censored data.
基金supported by the Key Fund Project of the Sichuan Provincial Department of Education (Grant No. 11ZA009)the Fund Project of Sichuan Provincial Key Laboratory of Fluid Machinery (Grant No.SBZDPY-11-5)the Key Scientific Research Project of Xihua University (Grant No. Z1120413)
文摘To overcome the limitations of the traditional stage-discharge models in describing the dynamic characteristics of a river, a machine learning method of non-parametric regression, the locally weighted regression method was used to estimate discharge. With the purpose of improving the precision and efficiency of river discharge estimation, a novel machine learning method is proposed： the clustering-tree weighted regression method. First, the training instances are clustered. Second, the k-nearest neighbor method is used to cluster new stage samples into the best-fit cluster. Finally, the daily discharge is estimated. In the estimation process, the interference of irrelevant information can be avoided, so that the precision and efficiency of daily discharge estimation are improved. Observed data from the Luding Hydrological Station were used for testing. The simulation results demonstrate that the precision of this method is high. This provides a new effective method for discharge estimation.
