κ-均值聚类算法的改进及其在冰脊表面形态分析中的应用  

Improvement of the k-mean Clustering Algorithm and Its Application in the Analysis of the Surface Morphology of Ice Ridges

作　　者：谭冰[1] 王骁力[1] 李志军[2] 卢鹏[2] 

机构地区：[1]南阳师范学院数学与统计学院,河南南阳473061 [2]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024

出　　处：《数学的实践与认识》2015年第13期140-145,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(41276191;41306207);国家海洋局极地考察办公室对外合作支持项目(IC201209);国家海洋局2012公益性行业科研专项"北极航道适航性评估及航道预报系统研制与示范"(201205007-05);2015年河南省高等学校重点科研项目(15B110007)

摘　　要：针对传统k-均值聚类算法事先必须获知类别数和难以确定初始聚类中心的缺点,建立了关于聚类中心和类别数k的双层规划模型,结合粒子群算法确定出聚类中心,通过在迭代过程中不断更新准则函数的方法搜索并确定出最佳类别数惫,基于所建模型,提出了一种改进的k-均值聚类算法,并将算法应用于冰脊表面形态分析中.结果表明,算法得到的聚类结果不但具有相邻类别边界清晰的优点,而且能够较好地反映出地理位置和生长环境对冰脊形成的影响.To improve the traditional k-means clustering algorithm, we establish a bi-level programming model with relevant to the division of the sample set and the cluster number k, and propose a corresponding algorithm （PSOJ-K） to search for the optimal cluster centers and the optimal cluster number k. In this improved algorithm, the clustering center is determined by combining the sample mean and Particle Swarm Optimization （PSO）, and the criterion function is constantly updated in the iteration process for the search of the optimal k. This improved k-mean clustering algorithm is then used to analyze the morphology of ice ridges. The results show that the boundaries of the clusters are very clear and the influences of the geographical locations and the growing environment on the formation of ice ridges can be reflected perfectly by the clustered results.

关 键 词：粒子群算法 κ-均值聚类 冰脊表面形态 

分 类 号：P731.15[天文地球—海洋科学]