中文摘要：

函数型数据能够反映数据的内在规律,利用该特点可以挖掘数据更多的潜在信息。在对传统聚类算法研究的基础上,首次提出将导函数距离引入函数型数据的聚类中,设计了函数型数据的分步系统聚类算法,给出了算法的具体步骤。利用随机模拟对算法的有效性进行了检验,并针对40个国家41年的人均GDP数据进行了实例研究,结果表明,该算法能够对函数型数据进行有效聚类。此外,基于此算法提出了一种函数型数据的数据补齐方法,实例研究结果表明,该预测方法能够对函数型数据进行有效地补齐。

英文摘要：

Functional data are capable of revealing the internal characteristics of data,thus can be employed to explore more potential information.Based on traditional clustering methods,we propose a step-by-step hierarchical clustering algorithm for functional data.To the best of our knowledge,this is the first result that has successfully incorporated functional derivative distances,in addition to functional distances,into clustering.Specifically,the algorithm is described in details and its effectiveness is tested using numerical simulation.Some experimental results implemented using the GDP data of 40 countries during the past 41 years show that the method can cluster functional data effectively.As an important application,we further present a prediction method and the experimental results show that the method can effectively predict functional data.