一种基于统计流形的聚类算法

考虑数据点之间局部统计性质的差异，结合K平均算法提出一种基于统计流形的聚类算法.通过计算数据点邻域的均值和协方差，将原始数据点云映射到正态分布族流形中，成为参数点云.在正态分布族流形上构造不同的度量结构，分别应用K平均方法，对参数点云进行聚类，从而将对应的原始数据分类.此算法可以应用到点云去噪.采用基于不同差异函数的算法，对含高密度噪声的点云去噪，并给出模拟仿真结果.仿真结果表明，采用KL散度作为差异函数的算法有较好的去噪效果，体现出该算法在去噪应用中的潜力. 

A Clustering Algorithm Based on Statistical Manifold

Considering the difference of local statistical properties between data points,and combining with K-means algorithm,a novel clustering algorithm based on statistical manifold was proposed. By calculating the mean and covariance of the neighborhood of the data points,the original data point cloud was mapped to the normal distribution family manifold to form the parameter point cloud. Different measurement structures were constructed on the normal distribution family manifold,and K-means method was applied to cluster the parameter point cloud,so as to classify the corresponding original data. To verify the effect in the point cloud denoising,the algorithms based on different difference function were used to denoise the point cloud with high density noise,and simulation analysis was carried out. The simulation results show that the algorithm using KL divergence as difference function can get a better denoising effect,verifying the potential of the algorithm in denoising application.