基于B-样条基底展开的曲线聚类方法

随着大数据时代的来临,近年来函数型数据分析方法成为研究的热点问题,针对曲线的聚类分析方法引起了学界的关注.给出一种曲线聚类的方法:以L2距离作为亲疏程度的度量,在B样条基底函数展开表述下,将曲线本身信息、曲线变化信息引入聚类算法构建,并实现了曲线聚类与传统多元统计聚类方法的对接.作为应用,以城乡收入函数聚类实例验证了该曲线聚类方法,结果表明,在引入曲线变化信息的情况下,比仅考虑曲线本身信息能够取得更好的聚类效果.

Curves Clustering Using B-splines Expansion

With the coming age of big data, functional data analysis as well as curves clustering aroused lots of concern in recent years. Using L2 distance as the closeness measurement, a curve clustering approach was proposed in this paper, the curve and it＇s change was considered in our clustering algorithm, which were approximated by B-splines functions expansion, and the L2 distance was reduced to traditional Euclidean distance, so the curves clustering was becoming multivariate clustering algorithm. As an application, urban and rural income function clustering instance was included in this paper, and the result shows that including of the curve change information could obtain a better clustering effect than only the curve itself was considered.