数据缺失情况下函数型数据聚类方法及应用

Application of Functional Data Clustering Methods on Missing Data

本文主要讨论了函数型数据的聚类方法,将其应用于中医宗气数据进行实证分析。函数型数据假定认为离散的时间观测由真实存在的连续时间函数决定,这一连续时间函数可以通过无穷多个基函数及其系数表示。函数型聚类的方法有原始数据聚类法、筛选方法和自适应方法。当某些时间点上的样本观测存在缺失时,原始数据聚类法无法计算样本所属类别。筛选方法用于完整时间观测数据的函数型聚类问题,在数据存在缺失时,虽然可以进行函数曲线的拟合,但是效果并不理想,因此聚类效果也不好。自适应方法不仅适用于完整观测而且可以解决存在缺失的函数型数据的聚类。本文将自适应方法应用于存在缺失的中医宗气时间观测,将老年人按照宗气水平分成宗气充足、宗气水平一般、宗气不足三类人群。函数型聚类的自适应方法划分人群特征的效果比较好。

This article mainly introduces the functional clustering methods and demonstrates its performance by the real analysis of Chinese medical Zong Qi data. The functional clustering analysis hypothesizes that the discrete time series observations are dominated by a continuous function of time, which can be expressed by infinite basis functions.Functional clustering methods include raw data method, filtering method and adaptive method. When dealing with the sparse data clustering analysis, raw data method encounters the difficulty of matrix calculation due to the lack of data on some time grids. Filtering method suits for full time data, while when facing missing data, the fitting curve is inaccurate so that the clustering outcome cannot be explainable. Adaptive method can be applied flexibly to both full time and sparsely sampled data. In the real analysis section, the adaptive method is used to cluster the sparsely sampled Chinese medical Zong Qi time series data, where the elderly individuals are divided into three clusters, the ones with high level of Zong Qi, the ones with moderate level and those with low level. The adaptive method performs well on clustering individuals.