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
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.
