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中文摘要：
分析了函数型数据主成分分析的原理。在此基础上,提出了一种函数型数据的聚类分析方法,以及在低维空间对原始高维数据进行直观表达的方法。给出了函数型数据的距离定义,并分析了这种距离的定义与欧氏距离的关系。提出函数型数据聚类分析的新方法：1）通过变换把离散数据转化为函数数据;2）进行函数型主成分分析;3）利用提取的前几个主成分构成低维空间,在该低维空间中,采用普通的聚类方法进行聚类分析。采用人体肢体多普勒超声血管造影的数据对所提出的方法的合理性进行验证。结果表明该方法可以有效地对函数型数据进行分类,分类结果与专家临床结论相符,因而有助于临床上对样本做客观判断。该方法不依赖专家的经验判断,且计算过程简便,易于计算机实现及临床应用。
英文摘要：
Analyze the mechanism of Principal Component Analysis for functional data. Propose a new method of Functional Data Clustering, with which visualizing the original high dimensional datum intuitively in a low dimensional space is realizable. After giving a definition of distance between functions, investigate the relationship between the argued form of distance and the Euclidean distance. The steps of proposed method of clustering analysis for functional data are： 1） Develop functional datum from discrete datum; 2） Apply Functional Principal Component Analysis; 3） In a low-dimensional space expanded by the first several components, implement ordinary clustering methods. To test the validity of the proposed method, a practical case of Human Limbs Doppler Angiography is applied. The result is effective and in accordance with medical diagnosis, thereby the method could contribute to clinical practice without experts＇ support. The involved calculation is easy to achieve by computer.
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