基于范数的多维数据模糊聚类方法

根据多维数据间相似度的定义,阐述了数据相似度与向量范数之间的关系,提出了一种基于范数的多维数据模糊聚类方法·该方法把每一个多维数据看做一个多维向量,利用与向量有关的范数对其中的数据进行排序,得到一个近似聚类族解·同理,对每一个近似聚类使用另一个范数做进一步分解,求解多维数据模糊聚类的近似解·最后,对得到的每一个近似聚类使用传统方法求出准确聚类·使用该方法不需建立模糊相似关系即可进行多维数据的近似聚类,总共所需访问数据库的次数也较小,因此具有较好的性能,特别适合于针对大型数据库的聚类·

Norm-Based Fuzzy Clustering Method for Multi-Dimension Data

The relationship between the similitude of data and the norm of a vector was discussed according to the definition of the similitude between multi-dimension data. A norm-based fuzzy clustering method for multi-dimension data was proposed. Each multi-dimension datum is regarded as a multi-dimension vector, and the data are sorted according to the vector-related norms. The approximate solution of clustering is presented. Each approximate cluster is further decomposed according to another norm by the same way. Then, the approximate solution of fuzzy clustering for multi-dimension data can be obtained. Finally, the exact clusters can be found from the approximate clusters using traditional methods. The fuzzy similarity relation does not need to be built when approximately clustering for multi-dimension data, so the total counts of accessing database is comparatively small. Hence, the method proposed is high efficient and fits to the clustering of large databases.